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Synthesis of optimal control for nonlinear third order systems

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Szwiec W.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Formulation of the problem.......................................................................................................................5 2. Necessary conditions for the optimality of control.....................................................................................7 3. Some properties of extremal trajectories.................................................................................................12 4. Inequalities describing the mutual position of the trajectories $K^+(0)$,K¯(p),K¯(0),$K^+(q)$................31 5. 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)...........................................................................................................................................................37 6. Mutual position of the trajectories $K^+(r)$ and $K¯(s)$.........................................................................47 7. The uniqueness of an extremal control. Synthesis of optimal control......................................................56 References.................................................................................................................................................60

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1 Szwiec W.

1 1986

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Synthesis of optimal control for nonlinear third order systems