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A modified pseudospectral scheme for accurate solution of Bang-Bang optimal control problems. (English) Zbl 1272.49065
Summary: In the present contribution, a modified Legendre pseudospectral scheme for accurate and efficient solution of bang-bang optimal control problems is investigated. In this scheme control and state functions are considered as piecewise constant and piecewise continuous polynomials, respectively, and the switching points are also taken as decision variables. Furthermore, for simplicity in discretization, the integral formulation of the dynamical equations is considered. Thereby, the problem is converted into a mathematical programming problem which can be solved by the well-developed parameter optimization algorithms. The main advantages of the present method are that: (i) it obtains good results even by using a small number of collocation points and the rate of convergence is high; (ii) the switching times can be captured accurately; and (iii) the wrongly chosen number of switching points can be detected by the results of the method. These are illustrated through a numerical implementation of the method on three examples and the efficiency of the method is reported.

MSC:
49M30 Other numerical methods in calculus of variations (MSC2010)
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
Software:
OPQ
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