LEGENDRE POLYNOMIALS METHOD IN TIME-OPTIMAL CONTROL OF LINEAR SINGLE - INPUT SYSTEMS

The paper deals with application of shifted Legendre polynomials in th e time-optimal control problem for a linear, time invariant, undisturb ed, single-input system. It was assumed that the normality condition o f the time-optimal control is satisfied, the state matrix is nonsingul ar, and all its eigenvalues are real nonpositive. The method of evalua ting the approximate switching instants of the bang-bang control is pr esented. The proposed computational procedure is based on the solution of algebraic matrix equation, which corresponds to the differential s tate equation, and was obtained according to the properties of Legendr e polynomials.