Synthesis of optimal control for nonlinear third order systems

Wiesław Szwiec

GDML_Books, (1986), p.

Résumé

The paper is devoted to a certain problem in the theory of synthesis of optimal control. The fundamental results of research in the synthesis of optimal control for second order systems are given in [1], [2], [5], [10]. In particular, in [2] and [5] some specific nonlinear systems are investigated, namely the systems related with the differential equations of the forms̈ + F(s,ṡ) = u or s̈ + F(s,ṡ,u) = 0where u is a control parameter in the interval [—1,1]. Some results concerning third order linear systems are presented in [7], [8], [9] and [12]. The main purpose of this paper is the formulation of the synthesis of optimal control for a class of nonlinear dynamic systems of the third order corresponding to a differential equation of the form(1) ͘s̈ = F(s,ṡ,s̈,u) where u ∈ [-1,1].

CONTENTS1. Formulation of the problem.......................................................................................................................52. Necessary conditions for the optimality of control.....................................................................................73. Some properties of extremal trajectories.................................................................................................124. Inequalities describing the mutual position of the trajectories $K^+(0)$,K¯(p),K¯(0),$K^+(q)$................315. Remark on the existence of common points of the trajectories K¯(0), K¯(p) and $K^+(r)$ and of the trajectories $K^+(0)$, $K^+(q)$ and K¯(s)...........................................................................................................................................................376. Mutual position of the trajectories $K^+(r)$ and $K¯(s)$.........................................................................477. The uniqueness of an extremal control. Synthesis of optimal control......................................................56References.................................................................................................................................................60

Détail

EUDML-ID : urn:eudml:doc:268453