Higher‐order techniques for some problems of nonlinear control | Zendy

Andrey Sarychev | Zendy

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Higher‐order techniques for some problems of nonlinear control

Author(s) -

Andrey Sarychev

Publication year - 2002

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1080/10241230306725

Subject(s) - controllability , nonlinear system , observability , feedback linearization , control theory (sociology) , mathematics , maximum principle , linearization , optimal control , nonlinear control , stability (learning theory) , lagrange multiplier , mathematical optimization , control (management) , computer science , quantum mechanics , artificial intelligence , machine learning , physics

A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems

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