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A new computational strategy for optimal control problem with a cost on changing control. (English) Zbl 1350.49043

Summary: In this paper, we consider a class of optimal control problems where the cost function is the sum of the terminal cost, the integral cost and the full variation of control. Here, the full variation of a control is defined as the sum of the total variations of its components. By using the control parameterization technique in conjunction with the time scaling transformation, we develop a new computational algorithm for solving this type of optimal control problem. Rigorous convergence analysis is provided for the new method. For illustration, we solve two numerical examples to show the effectiveness of the proposed method.

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
49J15 Existence theories for optimal control problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
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