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Relevant bibliographies by topics / Invariant ellipsoid method

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Journal articles

Academic literature on the topic 'Invariant ellipsoid method'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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Journal articles on the topic "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 (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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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 (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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Fedele, Giuseppe. "Invariant Ellipsoids Method for Chaos Synchronization in a Class of Chaotic Systems." International Journal of Robotics and Control Systems 2, no. 1 (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 (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 (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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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 (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 (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 (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 (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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