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A constructive method for solving stabilization problems

Vadim Azhmyakov — 2000

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.

Optimal control processes associated with a class of discontinuous control systems: Applications to sliding mode dynamics

Arturo Enrique Gil García;  Vadim Azhmyakov;  Michael V. Basin — 2014

Kybernetika

This paper presents a theoretical approach to optimal control problems (OCPs) governed by a class of control systems with discontinuous right-hand sides. A possible application of the framework developed in this paper is constituted by the conventional sliding mode dynamic processes. The general theory of constrained OCPs is used as an analytic background for designing numerically tractable schemes and computational methods for their solutions. The proposed analytic method guarantees consistency...

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