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Higher-order techniques for some problems of nonlinear control

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  • Andrey V. Sarychev

Abstract

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.

Suggested Citation

  • Andrey V. Sarychev, 2002. "Higher-order techniques for some problems of nonlinear control," Mathematical Problems in Engineering, Hindawi, vol. 8, pages 1-26, January.
    • Handle: RePEc:hin:jnlmpe:301856
    DOI: 10.1080/10241230306725
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