Approximate relaxed descent method for optimal control problems

• Autorzy: Chryssoverghi I. , Coletsos J. , Kokkinis B.
• Języki publikacji: EN

Abstrakty

EN

We consider an optimal control problem for systems governed by ordinary differential equations with control constraints. Since no convexity assumptions are made on the data, the problem is reformulated in relaxed form. The relaxed state equation is discretized by the implicit trapezoidal scheme and the relaxed controls are approximated by piecewise constant relaxed controls. We then propose a combined descent and discretization method that generates sequences of discrete relaxed controls and progressively refines the discretization. Since here the adjoint of the discrete state equation is not defined, we use, at each iteration, an approximate derivative of the cost functional defined by discretizing the continuous adjoint equation and the integral involved by appropriate trapezoidal schemes. It is proved that accumulation points of sequences constructed by this method satisfy the strong relaxed necessary conditions for optimality for the continuous problem. Finally, the computed relaxed controls can be easily approximated by piecewise constant classical controls.

Słowa kluczowe

EN

descent method; discretization; optimal control; relaxed controls

PL

dyskretyzacja; kontrola relaksacyjna; sterowanie optymalne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2001
• Tom: Vol. 30, no 4
• Strony: 385--404
• Opis fizyczny: Bibliogr. 13 poz.,

Twórcy

autor

Chryssoverghi I.

autor

Coletsos J.

autor

Kokkinis B.