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Abstract <p>The author develops a way of constructing an approximate reachability set for a controlled system that is nonlinear with respect to state variables with discrete time. Strict geometric constraints are imposed on the control parameters. To solve this problem, he uses a procedure developed earlier and applied to a case with a continuous time and differential equations. The necessary estimate of the reachability set can be obtained as level set of a special piecewise-defined value function constructed on a grid of simplexes in the state space. Formulas are presented for calculating the coefficients of such a function that allow analyses of the difference between a case with a discrete time and another with a continuous time. Piecewise affine value functions and the corresponding internal and external estimates of the reach set are calculated for a model example.</p>

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Approximation of the Reachability Set of a Nonlinear Controlled System with Discrete Time

  • 期刊论文

  • 发表日期：

    2025年3月29日

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  • P. A. Tochilin

摘要

Abstract

The author develops a way of constructing an approximate reachability set for a controlled system that is nonlinear with respect to state variables with discrete time. Strict geometric constraints are imposed on the control parameters. To solve this problem, he uses a procedure developed earlier and applied to a case with a continuous time and differential equations. The necessary estimate of the reachability set can be obtained as level set of a special piecewise-defined value function constructed on a grid of simplexes in the state space. Formulas are presented for calculating the coefficients of such a function that allow analyses of the difference between a case with a discrete time and another with a continuous time. Piecewise affine value functions and the corresponding internal and external estimates of the reach set are calculated for a model example.