Abstract
A conflict control system with state constraints is under consideration. A method for finding viability kernels (the largest subsets of state constraints where the system can be confined) is proposed. The method is related to differential games theory essentially developed by N. N. Krasovskii and A. I. Subbotin. The viability kernel is constructed as the limit of sets generated by a Pontryagin-like backward procedure. This method is implemented in the framework of a level set technique based on the computation of limiting viscosity solutions of an appropriate Hamilton–Jacobi equation. To fulfill this, the authors adapt their numerical methods formerly developed for solving time-dependent Hamilton–Jacobi equations arising from problems with state constraints. Examples of computing viability sets are given.
Highlights
In many technical control problems, it is necessary to keep a controlled system within prescribed state constraints in the presence of disturbances
Viability theory [2] can be considered as an alternative approach
The book [5] considers a wide range of questions related to the analysis and construction of viability sets
Summary
In many technical control problems, it is necessary to keep a controlled system within prescribed state constraints in the presence of disturbances Such a control process is usually considered on a large (infinite) time interval, and no performance index is used. The viability kernel is constructed as the limit of sets generated by a Pontryagin-like backward procedure (see [9]) The idea of such a passage to the limit was proposed in [10] for linear systems with discrete time. An approximation scheme for finding the solvability kernel for a general class of nonlinear autonomous controlled system is proposed. This algorithm is numerically implemented in terms of level sets.
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