Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems

• Autorzy: Chryssoverghi I.
• Języki publikacji: EN

Abstrakty

EN

This paper addresses the numerical solution of optimal control problems for systems described by ordinary differential equations with control constraints. The state equation is discretized by a general explicit Runge-Kutta scheme and the controls are approximated by functions that are piecewise polynomial, but not necessarily continuous. We then propose an approximate gradient projection method that constructs sequences of discrete controls and progressively refines the discretization. Instead of using the exact discrete cost derivative, which usually requires tedious calculations, we use here an approximate derivative of the cost functional denned by discretizing the continuous adjoint equation by the same Runge-Kutta scheme backward and the integral involved by a Newton-Cotes integration rule, both involving maximal order intermediate approximations. The main result is that strong accumulation points in L2, if they exist, of sequences generated by this method satisfy the weak necessary conditions for optimality for the continuous problem. In the unconstrained case and under additional assumptions, we prove strong convergence in L2 and derive an a posteriori error estimate. Finally, numerical examples are given.

Słowa kluczowe

EN

optimal control; gradient projection method; discretization; non-matching Runge-Kutta schemes; piecewise polynomial controls

PL

dyskretyzacja; sterowanie optymalne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 2
• Strony: 425--451
• Opis fizyczny: Bibliogr. 14 poz., wykr.

Twórcy

autor

Chryssoverghi I.

• Department of Mathematics, School of Applied Mathematics and Physics National Technical University Zografou Campus 157 80 Athens, Greece

Bibliografia

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