Real-time computation of feedback controls for constrained optimal control problems. I: Neighbouring extremals. (English) Zbl 0675.49023

Pesch, Hans Josef

Optim. Control Appl. Methods 10, No. 2, 129-145 (1989).

Summary: A numerical method is developed for the real-time computation of neighbouring optimal feedback controls for constrained optimal control problems. The first part of this paper presents the theory of neighbouring extremals. Besides a survey of the theory of neighbouring extremals, special emphasis is laid on the inclusion of complex constraints, e.g. state and control variable inequality constraints and discontinuities of the system equations at interior points. The numerical treatment of these constraints is particularly emphasized. The linearization of all necessary conditions of optimal control theory leads to a linear, multipoint, boundary value problem with linear jump conditions that is especially well suited for numerical treatment.
[For part II see the author, ibid. 10, No.2, 147-171 (1989; Zbl 0675.49024).]

MSC:

49M05	Numerical methods based on necessary conditions
65K10	Numerical optimization and variational techniques
93B40	Computational methods in systems theory (MSC2010)
49K15	Optimality conditions for problems involving ordinary differential equations
93C15	Control/observation systems governed by ordinary differential equations
49J30	Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)

Keywords:

real-time computation; neighbouring optimal feedback controls; inequality constraints; linearization; necessary conditions; jump conditions

Citations:

Zbl 0675.49024

References:

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