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On an algorithm for optimal control using Pontryagin’s maximum principle. (English) Zbl 0592.49018

The author studies the well-posedness and the convergence of an iterative algorithm proposed by Y. Sakawa and Y. Shindo [IEEE Trans. Autom. Control AC-25, 1149-1153 (1980; Zbl 0489.49017)] for the resolution of an optimal control problem associated with an ordinary differential equation. It is shown that in the case where the control enters in a linear way in the state equation and in a quadratic way in the criterion, the algorithm is equivalent to a gradient plus projection method in some new metric.
Reviewer: O.Cârjă

MSC:

49M05 Numerical methods based on necessary conditions
49K15 Optimality conditions for problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
90C52 Methods of reduced gradient type
93B40 Computational methods in systems theory (MSC2010)
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations

Citations:

Zbl 0489.49017
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