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A Chebyshev polynomial method for optimal control with state constraints. (English) Zbl 0647.49023

Summary: This paper presents a numerical technique for solving nonlinear constrained optimal control problems. The method extends previous contributions to nonlinear unconstrained optimal control problems and is based upon a Chebyshev series expansion of state and control. The differential and integral expressions from the system dynamics and the performance index, the boundary conditions and other general conditions are converted into some algebraic equations. State inequality constraints are transformed into equality constraints through the use of slack variables. The technique may start from a feasible or non-feasible trajectory and avoids problems of singular arcs. The applicability is illustrated on two well-known state variable inequality constrained optimal control problems. Extensions of the approach to problems with other equality and inequality constraints on state and control are described but have not yet been tested on practical examples.

MSC:

49M37 Numerical methods based on nonlinear programming
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
49K15 Optimality conditions for problems involving ordinary differential equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
65K10 Numerical optimization and variational techniques
93B40 Computational methods in systems theory (MSC2010)
93C15 Control/observation systems governed by ordinary differential equations
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