Abstract
A computationally efficient method, which uses finite orthogonal expansions to approximate state and control variables, is developed to obtain suboptimal control for time-varying systems with multiple state and control delays and with quadratic cost. Shifted Legendre polynomials form the basis of expansions as a consequence of their useful properties. The Galerkin method is used to reduce the problem to one of minimizing a quadratic form with linear algebraic constraints. The solution of a coupled two-point boundary-value problem with both delayed and advanced terms, which is always required in applying the Pontryagin's maximum principle to the optimization of delay systems, is thus avoided.
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