Статті в журналах: "Invariant ellipsoid method"

1

O’Dell, Brian D., and Eduardo A. Misawa. "Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (April 17, 2000): 98–103. http://dx.doi.org/10.1115/1.1434269.

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This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.

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2

Furtat, I. B., P. A. Gushchin, and A. A. Peregudin. "Disturbance Attenuation with Minimization of Ellipsoids Restricting Phase Trajectories in Transition and Steady State." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 4 (April 11, 2020): 195–99. http://dx.doi.org/10.17587/mau.21.195-199.

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Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state.

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3

Fedele, Giuseppe. "Invariant Ellipsoids Method for Chaos Synchronization in a Class of Chaotic Systems." International Journal of Robotics and Control Systems 2, no. 1 (January 28, 2022): 57–66. http://dx.doi.org/10.31763/ijrcs.v2i1.533.

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This paper presents an invariant sets approach for chaos synchronization in a class of master-slave chaotic systems affected by bounded perturbations. The method provides the optimal state-feedback gain in terms of the minimal ellipsoid that guarantees minimum synchronization error bound. The problem of finding the optimal invariant ellipsoid is formulated in terms of a semi-definite programming problem that can be easily solved using various simulation and calculus tools. The effectiveness of the proposed criterion is illustrated by numerical simulations on the synchronization of Chua's systems.

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4

Tan, Chun Kiat, Jianliang Wang, Yew Chai Paw, and Fang Liao. "Autonomous ship deck landing of a quadrotor using invariant ellipsoid method." IEEE Transactions on Aerospace and Electronic Systems 52, no. 2 (April 2016): 891–903. http://dx.doi.org/10.1109/taes.2015.140850.

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5

LIU, YANQING, and FEI LIU. "FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS." ANZIAM Journal 56, no. 2 (October 2014): 138–49. http://dx.doi.org/10.1017/s1446181114000315.

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AbstractWe consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.

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6

Vrazhevsky, S. A., J. V. Chugina, I. B. Furtat, and D. E. Konovalov. "Optimization of Invariant Ellipsoid Technique for Sparse Controllers Design." Mekhatronika, Avtomatizatsiya, Upravlenie 23, no. 1 (January 18, 2022): 3–12. http://dx.doi.org/10.17587/mau.23.3-12.

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The paper deals with the method for the design of linear controllers with sparse state feedback matrices for control the plants under conditions of unknown and bounded disturbances. The importance of the sparsity property in feedback can be explained by two factors. First, by minimizing the columnar norm of the feedback matrix in the control it becomes pos- sible to use a minimum number of measuring devices. Secondly, by minimizing the row norm of the feedback matrix, the required number of executive (control) devices is minimized. Both properties, if they are achievable in the synthesis of the controller, reduce the cost of the system and improve the fault tolerance and quality of regulation by reducing the structural complexity. The search algorithm for sparse matrices is based on the method of invariant ellipsoids and is formulated as a solution to a system of linear matrix inequalities with additional constraints. A special set of optimization conditions is proposed which for a disturbed system minimizes overshoot and overshoots in transient processes of the disturbed closed- loop system simultaneously with minimizing errors in the steady state. The proposed method also assumes the possibility of minimizing both the row norm of the feedback matrix and the column one, while preserving the robustness properties, which makes it possible to solve the sparse control problem (a sparse control is understood as a linear controller with a sparse feedback matrix). The efficiency of the proposed control scheme is confirmed by the results of computer modeling and comparison with some existing ones.

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7

Mendelson, Shahar. "Approximating the covariance ellipsoid." Communications in Contemporary Mathematics 22, no. 08 (January 30, 2020): 1950089. http://dx.doi.org/10.1142/s0219199719500895.

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We explore ways in which the covariance ellipsoid [Formula: see text] of a centered random vector [Formula: see text] in [Formula: see text] can be approximated by a simple set. The data one is given for constructing the approximating set is [Formula: see text] that are independent and distributed as [Formula: see text]. We present a general method that can be used to construct such approximations and implement it for two types of approximating sets. We first construct a set [Formula: see text] defined by a union of intersections of slabs [Formula: see text] (and therefore [Formula: see text] is actually the output of a simple neural network). We show that under minimal assumptions on [Formula: see text] (e.g. [Formula: see text] can be heavy-tailed) it suffices that [Formula: see text] to ensure that [Formula: see text]. In some cases (e.g. if [Formula: see text] is rotation invariant and has marginals that are well behaved in some weak sense), a smaller sample size suffices: [Formula: see text]. We then show that if the slabs are replaced by well-chosen ellipsoids, the same degree of approximation is true when [Formula: see text]. The construction is based on the small-ball method.

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8

Juarez, Raymundo, Vadim Azhmyakov, A. Tadeo Espinoza, and Francisco G. Salas. "An implicit class of continuous dynamical system with data-sample outputs: a robust approach." IMA Journal of Mathematical Control and Information 37, no. 2 (May 21, 2019): 589–606. http://dx.doi.org/10.1093/imamci/dnz015.

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Abstract This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.

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9

Polyakov, Andrey, and Alex Poznyak. "Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control." Automatica 47, no. 7 (July 2011): 1450–54. http://dx.doi.org/10.1016/j.automatica.2011.02.013.

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10

Juárez, R., V. Azhmyakov, and A. Poznyak. "Practical Stability of Control Processes Governed by Semiexplicit DAEs." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/675408.

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This paper deals with a new approach to robust control design for a class of nonlinearly affine control systems. The dynamical models under consideration are described by a special class of structured implicit differential equations called semi-explicit differential-algebraic equations (of index one), in the presence of additive bounded uncertainties. The proposed robust feedback design procedure is based on an extended version of the classical invariant ellipsoid technique that we call the Attractive Ellipsoid (AE) method. The theoretic schemes elaborated in our contribution are illustrated by a simple computational example.

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11

Davila, J., and A. Poznyak. "Sliding mode parameter adjustment for perturbed linear systems with actuators via invariant ellipsoid method." International Journal of Robust and Nonlinear Control 21, no. 5 (May 13, 2010): 473–87. http://dx.doi.org/10.1002/rnc.1599.

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12

Matušů, Radek, Bilal Şenol, and Libor Pekař. "Value-Set-Based Approach to Robust Stability Analysis for Ellipsoidal Families of Fractional-Order Polynomials with Complicated Uncertainty Structure." Applied Sciences 9, no. 24 (December 12, 2019): 5451. http://dx.doi.org/10.3390/app9245451.

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This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, multilinear, polynomic, and general uncertainty structure, combined with the uncertainty bounding set in the shape of an ellipsoid. The robust stability of these families is investigated using the zero exclusion condition, supported by the numerical computation and visualization of the value sets. Four illustrative examples are elaborated, including the comparison with the families of fractional-order polynomials having the standard box-shaped uncertainty bounding set, in order to demonstrate the applicability of this method.

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13

Olama, Alireza, Mokhtar Shasadeghi, Amin Ramezani, Mostafa Khorramizadeh, and Paulo R. C. Mendes. "Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee." Transactions of the Institute of Measurement and Control 41, no. 9 (October 11, 2018): 2475–87. http://dx.doi.org/10.1177/0142331218801126.

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This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

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14

Yang, Ning, Dongyan Chen, and Jun Hu. "Resilient set-membership state estimation for nonlinear complex networks with time-delay and incomplete measurements." MATEC Web of Conferences 336 (2021): 08017. http://dx.doi.org/10.1051/matecconf/202133608017.

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Taking the incomplete measurements and the weighted try-once-discard (WTOD) protocol into account, this paper develops a novel resilient set-membership state estimation (RSMSE) method for time-varying nonlinear complex networks with time-invariant delay. A classic interval matrix technique is utilized to describe incomplete measurements. The Taylor series expansion is applied to dispose the nonlinearities, where the high-order terms of the linearization errors are described by norm-bounded uncertainties. To mitigate the communication burden, the WTOD protocol is introduced, where only one node can send updated data through a shared communication network at each certain transmission step. Using the recursive linear matrix inequalities (RLMIs), a series of ellipsoidal sets including the state vector can be determined. The desirable estimator gain and a smallest possible estimation ellipsoid can be calculated via solving the convex optimization problem. Lastly, we use an illustrative example to show the feasibility of the introduced RSMSE technique.

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15

Li, Long, and Zhang He. "Automatic Calibration of the 3D Vector Magnetometer." Advanced Materials Research 591-593 (November 2012): 1256–59. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1256.

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Embedded sensors are an emerging trend in mobile consumer devices. In this work a new algorithm is derived for the onboard calibration of three-axis magnetometers. The proposed calibration method is written in the sensor frame, and compensates for the combined effect of all linear time-invariant distortions, namely soft iron, hard iron, three-dimensional sensor non-orthogonally, scale factors, null-shift, arbitrary bias, among others. The new algorithm can be separated into two steps: In the first step, obtain the ellipsoid fitting parameters from comparing the difference between the measured value and the actual vector. In a second step, a calibration algorithm is adopted to compensate for magnetometers distortions. According to the model parameters the measured data is corrected to improve the precision of magnetometer. Simulation and experimental results with sensors data are presented and discussed, supporting the application of the algorithm to commercial and military platforms.

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16

Wen, Ji Wei. "Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation." Applied Mechanics and Materials 303-306 (February 2013): 1193–99. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1193.

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A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

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17

McCoy, Airlie J., Robert A. Nicholls, and Thomas R. Schneider. "SCEDS: protein fragments for molecular replacement inPhaser." Acta Crystallographica Section D Biological Crystallography 69, no. 11 (October 4, 2013): 2216–25. http://dx.doi.org/10.1107/s0907444913021811.

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A method is described for generating protein fragments suitable for use as molecular-replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of Cαatoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lowerRfactor after ten cycles of all-atom refinement withREFMAC5 than the original template structure. The method has been implemented in the softwarePhaser.

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18

Kim, Sangtae, and P. V. Arunachalam. "The general solution for an ellipsoid in low-Reynolds-number flow." Journal of Fluid Mechanics 178 (May 1987): 535–47. http://dx.doi.org/10.1017/s0022112087001368.

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The general solution for low-Reynolds-number flow about an ellipsoid is derived by the singularity method and by representation in ellipsoidal harmonics. It is shown that, as in potential flow, the focal ellipse is the image system for the ellipsoid. A simple transformation which resembles a step in the derivation of the Dirichlet potential is introduced and its implications are explored. This transformation converts the velocity representation for an nth-order ambient field into that for the (n + 1)th-order field. The method furnishes an explanation for the invariance of the domain of the singularity distribution (the focal ellipse) with respect to the ambient field. Faxén relations for all multipole moments for arbitrary Stokes flow are derived in both integral and symbolic operator forms.

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19

Polyak, B. T., and M. V. Topunov. "Filtering under nonrandom disturbances: the method of invariant ellipsoids." Doklady Mathematics 77, no. 1 (February 2008): 158–62. http://dx.doi.org/10.1134/s1064562408010390.

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20

Rubin, Donald B., and Neal Thomas. "Affinely Invariant Matching Methods with Ellipsoidal Distributions." Annals of Statistics 20, no. 2 (June 1992): 1079–93. http://dx.doi.org/10.1214/aos/1176348671.

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21

Nazin, S. A., B. T. Polyak, and M. V. Topunov. "Rejection of bounded exogenous disturbances by the method of invariant ellipsoids." Automation and Remote Control 68, no. 3 (March 2007): 467–86. http://dx.doi.org/10.1134/s0005117907030083.

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22

Bezrodna, I., V. Svystov, and D. Bezrodny. "ANALYSIS OF ACOUSTIC ANISOTROPY PARAMETERS OF PYROXENE-MAGNETITE ROCKS OF THE PISCHANKA STRUCTURE." Visnyk of Taras Shevchenko National University of Kyiv. Geology, no. 1 (88) (2020): 40–45. http://dx.doi.org/10.17721/1728-2713.88.06.

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The analysis of the results of acoustic properties of rocks study of Pischans`ka iron-ore structure is presented. The aim of the work is to establish the features of the distribution of acoustic properties and parameters of acoustic anisotropy in samples of core rocks selected from the well No. 3 of the Pischans`ka structure to determine the nature of its occurrence. A sample of 35 samples from the depth range 144-273 m is divided into 3 groups of rocks, namely: magnetite-pyroxene, quartz-magnetitepyroxene and biotite-amphibole crystalline shales. Based on an invariant polarization method, a number of acoustic laboratory measurements have been carried out. The values of the measured phase velocities "quasi-longitudinal" and two "quasi-transverse" waves at the stage of measurements showed significant acoustic anisotropy of the rocks. The ranges of the measured speeds of the collection samples are 7661 ÷ 5046 m / s for longitudinal waves and 4232 ÷ 2648 m/s for transverse ones. The difference in values measured for each of the sides of the cubic rhombic dodecahedron is from 100 to 800 m / s and from 0 to 500 m/s for Vp and Vs, respectively. The parameters of an acoustic ellipsoid were calculated, on the basis of which the division of samples into 3 main groups has been performed, according to the acoustic texture: acoustically linear, shale and rhombic. Separately, a group of samples with a more complex texture was discovered. The analysis of coefficients of anisotropy by different methods is carried out: longitudinal, transverse and relative acoustic anisotropy. Most of the samples are characterized by low or average acoustic anisotropy (from 2 to 7 %). A group of highly anisotropic rocks (11–14 %), represented by samples of biotite-amphibole crystalline silicates, is singled out. According to the parameters of the acoustic tensor of most samples, the transverse isotropic type of symmetry inherent to samples from the depth intervals 174–220 m and 222–232 m, while the smaller part is rhombic, is inherent. Differences in the parameters of anisotropy of samples can be explained by the significant heterogeneity of their textures, namely: micro cracks, minerals of various sizes, shapes and orientations. The results of the research show that the acoustic properties of the samples are quite heterogeneously distributed along the investigated depth range. This indicates the difficult conditions for the formation of rocks at different depths and the presence of different types of deformations, which accompanied the formation of the Pischans`ka structure.

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23

Gonzalez-Garcia, S., A. E. Polyakov, and A. S. Poznyak. "Using the method of invariant ellipsoids for linear robust output stabilization of spacecraft." Automation and Remote Control 72, no. 3 (March 2011): 540–55. http://dx.doi.org/10.1134/s0005117911030064.

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24

Decardi-Nelson, Benjamin, and Jinfeng Liu. "Robust Economic MPC of the Absorption Column in Post-Combustion Carbon Capture through Zone Tracking." Energies 15, no. 3 (February 3, 2022): 1140. http://dx.doi.org/10.3390/en15031140.

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Several studies have reported the importance of optimally operating the absorption column in a post-combustion CO2 capture (PCC) plant. It has been demonstrated in our previous work how economic model predictive control (EMPC) has a great potential to improve the operation of the PCC plant. However, the use of a general economic objective such as maximizing the absorption efficiency of the column can cause EMPC to drive the state of the system close to the constraints. This may lead to solvent overcirculation and flooding, which are undesirable. In this work, we present an EMPC with zone tracking algorithm as an effective means to address this problem. The proposed control algorithm incorporates a zone tracking objective and an economic objective to form a multi-objective optimal control problem. To ensure that the zone tracking objective is achieved in the presence of model uncertainties and time-varying flue gas flow rate, we propose a method to modify the original target zone with a control invariant set. The zone modification method combines both ellipsoidal control invariant set techniques and a back-off strategy. The use of ellipsoidal control invariant sets ensure that the method is applicable to large scale systems such as the absorption column. We present several simulation case studies that demonstrate the effectiveness and applicability of the proposed control algorithm to the absorption column in a post-combustion CO2 capture plant.

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Hamdi, Walid, Wissal Bey, and Naceur Benhadj Braiek. "Constrained Uncertain System Stabilization with Enlargement of Invariant Sets." Complexity 2020 (August 10, 2020): 1–11. http://dx.doi.org/10.1155/2020/1468109.

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An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

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26

Romanenko, Victor D., and Yuriy L. Milyavsky. "Control automation of impulse processes in cognitive maps with constrained disturbance suppression based on invariant ellipsoids method." System research and information technologies, no. 2 (June 26, 2017): 29–39. http://dx.doi.org/10.20535/srit.2308-8893.2017.2.03.

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27

Balce, A. E. "Comparison of block adjustment methods and accuracies of photogrammetric point determination." CISM journal 42, no. 3 (January 1988): 217–25. http://dx.doi.org/10.1139/geomat-1988-0021.

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This paper compares accuracy results of photogrammetric block adjustments using independent models, and bundles without added parameters, with block-invariant added parameters and with image-wise added parameters. Three real test blocks at scales of 1:4000,1:8000 and 1:60 000 were adjusted individually using the aforementioned methods. The root-mean-square (RMS) errors of discrepancies at checkpoints were compared and analyzed. It appeared that bundle adjustments with block-invariant added parameters gave the best results which were then used as the basis for comparing the RMS values of standard errors of independent model and bundle adjustments and of confidence ellipsoids of bundle adjustment, and accuracies estimated using RMS errors of residuals of independent model adjustments. The RMS values of standard errors of bundle adjustments appeared to be consistent, except for small-scale photography (smaller than 1:10 000). On the other hand, accuracies estimated using RMS errors of residuals of independent model adjustments appeared to be consistent, except in planimetry for large-scale photography (larger than 1:10 000). Hence, in the absence of checkpoints, standard errors of bundle adjustments may be used to estimate accuracy of photogrammetric point determination, except for small-scale photography which may then be estimated using the RMS errors of residuals of independent model adjustments.

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28

Liu, Yanxia, Zhikai Hu, and JianJun Fang. "Two-step calibration method for three-axis magnetic sensor error based on particle swarm optimization." Sensor Review 40, no. 5 (August 24, 2020): 577–83. http://dx.doi.org/10.1108/sr-01-2020-0013.

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Purpose The three-axis magnetic sensors are mostly calibrated by scalar method such as ellipsoid fitting and so on, but these methods cannot completely determine the 12 parameters of the error model. A two-stage calibration method based on particle swarm optimization (TSC-PSO) is proposed, which makes full use of the amplitude invariance and direction invariance of Earth’s magnetic field vector. Design/methodology/approach The TSC-PSO designs two-stage fitness function. Stage 1: design a fitness function of the particle swarm by the amplitude invariance of the Earth’s magnetic field to obtain a preliminary error matrix G and the bias error B. Stage 2: further design the fitness function of the particle swarm by the invariance of the Earth’s magnetic field to obtain a rotation matrix R, thereby determining the error matrix uniquely. Findings The proposed TSC-PSO can completely determine 12 unknown parameters in error model and further decrease the maximum fluctuation error of the Earth’s magnetic field amplitude and the absolute error of heading. Practical implications The proposed TSC-PSO provides an effective solution for three-axis magnetic sensor error compensation, which can greatly reduce the price of magnetic sensors and be used in the fields of Earth’s magnetic survey, drilling and Earth’s magnetic integrated navigation. Originality/value The proposed TSC-PSO has significantly improved the magnetic field amplitude and heading accuracy and does not require additional heading reference. In addition, the method is insensitive to noise and initialization conditions, has good robustness and can converge to a global optimum.

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29

Soliman, Hisham M., Hassan A. Yousef, Rashid Al-Abri, and Khaled A. El-Metwally. "Decentralized Robust Saturated Control of Power Systems Using Reachable Sets." Complexity 2018 (September 12, 2018): 1–12. http://dx.doi.org/10.1155/2018/2563834.

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Electric power grids are highly nonlinear complex systems. This manuscript presents a novel approach to the stabilization of large power systems. The proposed control satisfied three constraints: decentralization, input saturation imposed in practice, and robustness against load changes. The large power system is decomposed into subsystems, for each a decentralized controller is designed. The effect of the rest of the system on each subsystem is considered as an external disturbance and represented in norm-bounded form. A new approach to solve this problem is proposed in the present paper. The approach is based on the method of invariant ellipsoids, and the tool of linear matrix inequalities (LMI) is utilized to solve the resulting optimization problem. Control of multimachine power system is studied using the proposed control. Comparison with other techniques is also given.

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Zhou, Huajie, Wenbo Chen, Chengliang Xuan, Zhangrong Qin, and Binghai Wen. "Three-dimensional simulation of red blood cell particle sedimentation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, January 17, 2022, 095440622110641. http://dx.doi.org/10.1177/09544062211064103.

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The red blood cell particle is important in the research studies of blood flow and drug delivery. The biconcave shape makes the motions of the red blood cell particle in fluids more complex than sphere or ellipsoid. Sedimentation behaviors of a red blood cell particle in long circular tubes are investigated by using the lattice Boltzmann method with the Galilean-invariant momentum exchange method. Different blockage ratios and the particle to fluid density ratios are considered. One periodic and two steady sedimentation modes are discovered. When the blockage ratio rises, the motion mode of particles changed from horizontal mode to inclined mode. With the increase of the particle to fluid density ratio, the sedimentation mode changed from the inclined mode to the horizontal mode, and the time of the particles reaching the stable state is obviously distinct in different sedimentation modes. Surprisingly, the oscillatory mode is observed in the larger blockage ratio and lower density ratio of particle to fluid. These works may be able to make active promotions to the research studies of blood circulation of humans.

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Dorofieiev, Yu I., and L. M. Lyubchyk. "BULLWHIP EFFECT IN SUPPLY CHAINS REDUCING BY DECENTRALIZED INVENTORY CONTROL BASED ON INVARIANT ELLIPSOIDS METHOD." Radio Electronics, Computer Science, Control, no. 1 (May 13, 2017). http://dx.doi.org/10.15588/1607-3274-2017-1-18.

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Fan, Jinhua, Youmin Zhang, and Zhiqiang Zheng. "Adaptive Observer-Based Integrated Fault Diagnosis and Fault-Tolerant Control Systems Against Actuator Faults and Saturation." Journal of Dynamic Systems, Measurement, and Control 135, no. 4 (May 13, 2013). http://dx.doi.org/10.1115/1.4023763.

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A challenging problem on observer-based, integrated fault diagnosis and fault-tolerant control for linear systems subject to actuator faults and control input constraints is studied in this paper. An adaptive observer approach is used for the joint state-fault magnitude estimation, and a feedback controller is designed to stabilize the closed-loop system without violating the actuator limits in the presence of actuator faults. Matrix inequality conditions are provided for computation of design parameters of the observer and the feedback controller, and the admissible initial conditions and estimation errors are bounded by invariant ellipsoidal sets. The design results are closely related to the fault magnitude and variation rate, and a necessary condition on the admissible fault magnitudes dependent on the control limits is directly obtained from the design process. The proposed design framework allows a direct application of the pole placement method to obtain stabilization results. To improve the system performance, a nonlinear programming-based optimization algorithm is proposed to compute an optimized feedback gain, whereas the one obtained by pole placement can be taken as an initial feasible solution for nonlinear optimization. Numerical studies with two flight control systems demonstrate the effectiveness of proposed design techniques.

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Calvo, C. J., M. Zarzoso, A. Guill, A. Tormos, L. Such, A. Alberola, J. Millet, and F. J. Chorro-Gasco. "Simultaneous atrial and ventricular restitution and fibrillation analyses using a low-cost scalable panoramic whole-heart optical mapping configuration for whole-heart imaging of translational models." European Heart Journal 42, Supplement_1 (October 1, 2021). http://dx.doi.org/10.1093/eurheartj/ehab724.3324.

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Abstract Introduction Optical mapping (OM) is the primary method for imaging electrophysiologically relevant parameters from the outer surface of Langendorff-perfused hearts. However, current panoramic OM systems are financially challenging, require multiple sensors to map wide areas of the surface with overlapping regions and missing areas of interest due to the intrinsic shape of the heart. We proposed different panoramic configurations to dynamically characterize atrial and ventricular function during arrhythmia and, in presence of a coronary occlusion. Methods We devised both a multi-sensor and a single sensor system integrated with the perfusion circuit comprising sensor elements, a control system for led illumination, electrical stimulation and sensing of physiological variables. Two configurations were tested: A multi-sensor panoramic approach including different camera views and, a precision near-ellipsoidal curved mirror (highly concentrated reflectance in the range 380nm-800nm), with exponential profile and diameter to harbor small to large hearts was used. Twelve-rabbits and two pig hearts were included in the study. OM was performed using di-4 ANDBQPQ near-infrared dye and 5–10uM blebbistatine. Initial camera calibration was done using a fishnet-like pattern and nylon landmarks. We characterized signal-tonoise ratios (SNR) of reconstructed action potentials (AP) and obtained parametric maps of the activation process. A custom-built computational pipeline for accurate motion compensation and AP reconstructions was used. Hearts were stimulated until ventricular fibrillation (VF) was induced with and without presence of a coronary occlusion in the LADartery (LADCO). Results High SNRs spatial maps were obtained after AP reconstruction (42.24±4.23dB,stimulated; 23.31±5.24dB,VF) in the most restrictive set-up, the single-sensor near-ellipsoidal configuration. Quantified activation and repolarization dynamic restitution properties were assigned to anatomically labelled scale-invariant areas in the atrium and ventricles during the induction process. Atrial and ventricular restitution dynamics could be reconstructed and analyzed simultaneously. Slower conduction (CT) and higher dispersion in repolarization (DoR) was observed after LADCO in LV (CT: 13.4±5.31ms-vs-22.42±6.82ms,DoR:23.24±4.23ms-vs-38.03±9.17ms,p<0.05). During VF, more heterogeneous activation patterns, enhanced left-to-right VV spectral gradient profiles, and spatially constraint shorter-lived filaments, partially explained the disturbances observed during LADCO. Results obtained with a direct multiple sensor configuration allowed for complete tracking of dominant sources, yet presenting overlapped information. Conclusion Hereby results comparing two low-cost configurations for panoramic imaging are presented and validated for the study of cardiac propagation throughout the whole epicardial surface for the study of arrhythmia, drug interventions and cardiovascular disease. Funding Acknowledgement Type of funding sources: Public grant(s) – National budget only. Main funding source(s): CIBERcv

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