Higher-order techniques for some problems of nonlinear control

Mathematical Problems in Engineering

Andrey V. Sarychev¹ 

[1] Dipartimento di Matematica per le Decisioni, Universita di Firenze, V. C. Lombroso 6/17, Firenze 50134, Italy;

关键词: Nonlinear control;    Optimal control;    Generalized inputs;    Stability and stabilization;    Averaging;    Geometric control.;   

DOI  :  10.1080/10241230306725

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown