Abstract
An efficient direct method of using the finite set orthogonal series expansion is presented for the finite-time optimal; control of linear discrete-time systems with a quadratic performance index. Discrete Legendre orthogonal polynomials are used as the expansion basis, owing to their unity weight and useful properties. The main advantage of this method is that the optimal control problem is simplified to finding the sequence of control that minimizes a performance index of quadratic form with linear algebraic constraints. A general formulation of the method is given and numerical examples are shown to demonstrate the effectivness of the method.
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