Legendre polynomials method in time-optimal control of linear single - input systems
J. Pełczewski · Control and Cybernetics · 1998
The paper deals with application of shifted Legen dre polynomials in the time-optimal control problem for a linear, time invariant, undisturbed , single-input system. It was assumed that the normality condition of t he t ime-optimal cont rol is satis fied , the state matrix is nonsingular, and all its eigenvalues are real nonposit ive. T he method of evaluating the approximate switching instants of the bang-bang control is presented. The proposed com putational procedure is based on the solution of algebraic matrix equation, which corresponds to the differential state equation , and was obtained according to the properties of Legendre polynomials.