Ensemble approximations for constrained dynamical systems using Liouville equation

Article Automation & Control Systems

Cone-Copositive Lyapunov Functions for Complementarity Systems: Converse Result and Polynomial Approximation

Marianne Souaiby et al.

Summary: This article establishes the existence of Lyapunov functions and describes algorithms for their numerical computation. By constructing cone-copositive Lyapunov functions, the stability analysis of state-constrained systems is addressed. The article proves that exponentially stable complementarity systems always admit a continuously differentiable cone-copositive Lyapunov function, and further investigates the approximation methods for this function.

IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2022)

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Article Computer Science, Software Engineering

Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators

Kanat Camlibel et al.

Summary: This article studies the solutions of time-dependent differential inclusions, constructing a sequence of functions parameterized by the sampling time and proving its convergence to the unique solution of the original differential inclusion. The results are applied to develop conditions for well-posedness of differential equations interconnected with nonsmooth time-dependent complementarity relations.

MATHEMATICAL PROGRAMMING (2022)

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Article Mathematics

Optimization and discrete approximation of sweeping processes with controlled moving sets and perturbations

Tan H. Cao et al.

Summary: This paper explores a new class of optimal control problems for perturbed sweeping processes with measurable controls and smooth controls in polyhedral moving sets. By developing a constructive discrete approximation procedure and deriving necessary optimality conditions for discrete optimal solutions, efficient suboptimality conditions for the original sweeping control problem are obtained.

JOURNAL OF DIFFERENTIAL EQUATIONS (2021)

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Article Mathematics

Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework

Benoit Bonnet et al.

Summary: In this paper, a general framework for studying differential inclusions in the Wasserstein space of probability measures is proposed, with solutions defined as absolutely continuous curves driven by measurable selection functions taking values in the space of vector fields. The foundational results of Filippov's theorem, Relaxation theorem, and compactness of solution sets are proved in this setting, based on novel estimates on solutions of continuity equations. These contributions are then applied to derive a new existence result for fully non-linear mean-field optimal control problems with closed-loop controls.

JOURNAL OF DIFFERENTIAL EQUATIONS (2021)

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Article Mathematics, Applied