Necessary conditions for local controllability of a particular class of systems with two scalar controls

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-10-16 DOI:10.1051/cocv/2023073

Laetitia Giraldi, Pierre Lissy, Clément Moreau, Jean-Baptiste Pomet

引用次数: 2

Abstract

We consider affine control systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions of local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in $\mathrm{L}^{\infty}$ or small in $\mathrm{W}^{1,\infty}$. These results are illustrated with several examples.

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一类具有两个标量控制的特定系统的局部可控性的必要条件

考虑具有两个标量控制的仿射控制系统，其中一个控制向量场在平衡状态下消失。我们陈述了围绕该平衡的局部可控性的两个必要条件，涉及系统向量场的迭代Lie括号，控制要么是有界的，在$\mathrm{L}^{\infty}$中小，要么在$\mathrm{W}^{1,\infty}$中小。用几个例子说明了这些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

自引率

7.10%

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.