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Relevant bibliographies by topics / Differential Algebraic Inequality

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Academic literature on the topic 'Differential Algebraic Inequality'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Differential Algebraic Inequality"

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Reis, Timo, and Matthias Voigt. "The Dissipation Inequality for Differential-Algebraic Systems." PAMM 14, no. 1 (December 2014): 11–14. http://dx.doi.org/10.1002/pamm.201410004.

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Reis, Timo, Olaf Rendel, and Matthias Voigt. "The Kalman–Yakubovich–Popov inequality for differential-algebraic systems." Linear Algebra and its Applications 485 (November 2015): 153–93. http://dx.doi.org/10.1016/j.laa.2015.06.021.

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Allouche, Benyamine, Antoine Dequidt, Laurent Vermeiren, and Michel Dambrine. "Modeling and PDC fuzzy control of planar parallel robot." International Journal of Advanced Robotic Systems 14, no. 1 (January 1, 2017): 172988141668711. http://dx.doi.org/10.1177/1729881416687112.

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Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential–algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential–algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

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Uppal, Tarun, Soumyendu Raha, and Suresh Srivastava. "Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation." International Journal of Turbo & Jet-Engines 35, no. 4 (December 19, 2018): 373–83. http://dx.doi.org/10.1515/tjj-2016-0057.

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Abstract Modern day gas turbines are prime movers in land, air and sea. They have stringent performance requirements to meet the complex mission objectives. Optimal control strategies can help them meet their performance objectives more efficiently. A novel inverse simulation method for optimal control and system analysis studies using Differential Algebraic Equality/Inequality (DAE/DAI) technique is brought out in this paper with a case study. The gas turbine model together with safety constraints and performance specifications is represented as a high index DAI/DAE system. The solution for this DAE/DAI system is obtained using a new numerical approach that is capable of handling both equality and inequality constraints on system dynamics. The algorithm involves direct numerical integration of a DAI formulation in a time stepping manner using Sequential Quadratic Programming (SQP) solver that detects and satisfy active constraints at each time step (mesh point). In this unique approach the model and the constraints are always solved together. The method ensures stable solution at each time step, local minimum at each iteration of simulation and provides a regularised basis to the solver. Compared to other existing computationally intensive techniques in usage, this approach is easy, ensures continuous constraint satisfaction and provides a viable option for Model Predictive Control (MPC) of gas turbine engines.

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Pop, Nicolae. "Generalized Newton’s method for solving nonlinear and nondifferentiable algebraic systems." Journal of Numerical Analysis and Approximation Theory 44, no. 1 (December 18, 2015): 93–99. http://dx.doi.org/10.33993/jnaat441-1058.

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In this paper a model based on non-smooth equations is proposed for solving a non-linear and non-differential equation obtained by discretization of a quasi-variational inequality that models the frictional contact problem. The main aim of this paper is to show that the Newton method based on the plenary hull of the Clarke generalized Jacobians (the non-smooth damped Newton method) can be implemented for solving Lipschitz non-smooth equation.

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Reis, Timo, and Matthias Voigt. "The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions." Systems & Control Letters 86 (December 2015): 1–8. http://dx.doi.org/10.1016/j.sysconle.2015.09.003.

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Qingfei, Pan, Zhang Zifang, and Huang Jingchang. "Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays andp-Laplacian." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/405939.

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The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays andp-Laplacian. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.

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Lê, Công-Trình, and Tien-Son Phạm. "On tangent cones at infinity of algebraic varieties." Journal of Algebra and Its Applications 17, no. 08 (July 8, 2018): 1850143. http://dx.doi.org/10.1142/s0219498818501438.

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In this paper, we define the geometric and algebraic tangent cones at infinity of algebraic varieties and establish the following version at infinity of Whitney’s theorem [Local properties of analytic varieties, in Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) (Princeton University Press, Princeton, N. J., 1965), pp. 205–244; Tangents to an analytic variety, Ann. of Math. 81 (1965) 496–549]: The geometric and algebraic tangent cones at infinity of complex algebraic varieties coincide. The proof of this fact is based on a geometric characterization of the geometric tangent cone at infinity using the global Łojasiewicz inequality with explicit exponents for complex algebraic varieties. Moreover, we show that the tangent cone at infinity of a complex algebraic variety is actually the part at infinity of this variety [G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, 2nd extended edn. (Springer, Berlin, 2008)]. We also show that the tangent cone at infinity of a complex algebraic variety can be computed using Gröbner bases.

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Wu, Dongli, Hao Zhang, Yunping Liu, Weihua Fang, and Yan Wang. "Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness." International Journal of Aerospace Engineering 2022 (June 20, 2022): 1–17. http://dx.doi.org/10.1155/2022/8004478.

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The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. However, it can be challenging to meet the requirements of real-time for the high complexity. A differential flat theory based on B-spline trajectory planning can replace the optimal control problem with nonlinear programming and be a good means to achieve the efficient trajectory planning of an UAV under multiple dynamic constraints. This research verifies the feasibility of this theory with actual flight experiments.

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Wu, Qiong, Zhimin Yao, Zhouping Yin, and Hai Zhang. "Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach." Mathematical Biosciences and Engineering 19, no. 9 (2022): 9220–43. http://dx.doi.org/10.3934/mbe.2022428.

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<abstract><p>This paper investigates the finite time synchronization (Fin-TS) and fixed time synchronization (Fix-TS) issues on Caputo quaternion delayed neural networks (QDNNs) with uncertainty. A new Caputo fractional differential inequality is constructed, then Fix-TS settling time of the positive definite function is estimated, which is very convenient to derive Fix-TS condition to Caputo QDNNs. By designing the appropriate self feedback and adaptive controllers, the algebraic discriminant conditions to achieve Fin-TS and Fix-TS on Caputo QDNNs are proposed based on quaternion direct method, Lyapunov stability theory, extended Cauchy Schwartz inequality, Jensen inequality. Finally, the correctness and validity of the presented results under the different orders are verified by two numerical examples.</p></abstract>

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Dissertations / Theses on the topic "Differential Algebraic Inequality"

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Spiteri, Raymond J. "Solution methods for differential systems subject to algebraic inequality constraints." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25165.pdf.

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Dabrowski, Yoann. "Free entropies, free Fisher information, free stochastic differential equations, with applications to Von Neumann algebras." Thesis, Paris Est, 2010. http://www.theses.fr/2010PEST1015.

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Ce travail étend nos connaissances des entropies libres et des équations différentielles stochastiques (EDS) libres dans trois directions. Dans un premier temps, nous montrons que l'algèbre de von Neumann engendrée par au moins deux autoadjoints ayant une information de Fisher finie n'a pas la propriété $Gamma$ de Murray et von Neumann. C'est un analogue d'un résultat de Voiculescu pour l'entropie microcanonique libre. Dans un second temps, nous étudions des EDS libres à coefficients opérateurs non-bornés (autrement dit des sortes d' EDP stochastiques libres ). Nous montrons la stationnarité des solutions dans des cas particuliers. Nous en déduisons un calcul de la dimension entropique libre microcanonique dans le cas d'une information de Fisher lipschitzienne. Dans un troisième et dernier temps, nous introduisons une méthode générale de résolutions d'EDS libres stationnaires, s'appuyant sur un analogue non-commutatif d'un espace de chemins. En définissant des états traciaux sur cet analogue, nous construisons des dilatations markoviennes de nombreux semigroupes complètement markoviens sur une algèbre de von Neumann finie, en particulier de tous les semigroupes symétriques. Pour des semigroupes particuliers, par exemple dès que le générateur s'écrit sous une forme divergence pour une dérivation à valeur dans la correspondance grossière, ces dilatations résolvent des EDS libres. Entre autres applications, nous en déduisons une inégalité de Talagrand pour l'entropie non-microcanonique libre (relative à une sous-algèbre et une application complètement positive). Nous utilisons aussi ces déformations dans le cadre des techniques de déformations/rigidité de Popa
This works extends our knowledge of free entropies, free Fisher information and free stochastic differential equations in three directions. First, we prove that if a $W^{*}$-probability space generated by more than 2 self-adjoints with finite non-microstates free Fisher information doesn't have property $Gamma$ of Murray and von Neumann (especially is not amenable). This is an analogue of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy. Second, we study a general free stochastic differential equation with unbounded coefficients (``stochastic PDE"), and prove stationarity of solutions in well-chosen cases. This leads to a computation of microstates free entropy dimension in case of Lipschitz conjugate variable. Finally, we introduce a non-commutative path space approach to solve general stationary free Stochastic differential equations. By defining tracial states on a non-commutative analogue of a path space, we construct Markov dilations for a class of conservative completely Markov semigroups on finite von Neumann algebras. This class includes all symmetric semigroups. For well chosen semigroups (for instance with generator any divergence form operator associated to a derivation valued in the coarse correspondence) those dilations give rise to stationary solutions of certain free SDEs. Among applications, we prove a non-commutative Talagrand inequality for non-microstate free entropy (relative to a subalgebra $B$ and a completely positive map $eta:Bto B$). We also use those new deformations in conjunction with Popa's deformation/rigidity techniques, to get absence of Cartan subalgebra results

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Books on the topic "Differential Algebraic Inequality"

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Tretkoff, Paula. Algebraic Surfaces and the Miyaoka-Yau Inequality. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0005.

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This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.

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Optimization of Objective Functions: Analytics. Numerical Methods. Design of Experiments. Moscow, Russia: Fizmatlit Publisher, 2009.

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Book chapters on the topic "Differential Algebraic Inequality"

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Ascher, Uri M. "Numerical Methods for Differential Systems with Algebraic Equality and Inequality Constraints." In Hybrid Systems: Computation and Control, 3. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45873-5_2.

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Conference papers on the topic "Differential Algebraic Inequality"

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Fabien, Brian C. "A Simple Continuation Method for the Solution of Optimal Control Problems With State Variable Inequality Constraints." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13617.

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This paper develops a simple continuation method for the approximate solution of optimal control problems with pure state variable inequality constraints. The method is based on transforming the inequality constraints into equality constraints using nonnegative slack variables. The resultant equality constraints are satisfied approximately using a quadratic loss penalty function. The solution of the original problem is obtained by solving the transformed problem with a sequence of penalty weights that tends to zero. The penalty weight is treated as the continuation parameter. The necessary conditions for a minimum are written as a boundary value problem involving index-1 differential-algebraic equations (BVP-DAE). The BVP-DAE include the complementarity conditions associated with the inequality constraints. The paper shows that the necessary conditions for optimality of the original problem and the transformed problems are remarkably similar. In particular, the BVP-DAE for each problem differ by a linear term related to the Lagrange multipliers associated with the state variable inequality constraints. Numerical examples are presented to illustrate the efficacy of the proposed technique. Specifically, the paper presents results for; (1) the optimal control of a simplified model of a gantry crane system, (2) the optimal control of a rigid body moving in the vertical plane, and (3) the trajectory optimization of a planar two-link robot. All problems include pure state variable inequality constraints.

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