Application of General Orthogonal Polynomials on Tracking Problem of Time-varying Systems Optimal Control

A new method is presented for solving the tracking problem of time-varying systems optimal control. The approach starts by applying general orthogonal polynomials operational matrices and using finite GOPs expansion to approximate state, control variable and performance index, then differential equation and integration equation convert into algebraic forms, the control problem becomes one of finding the GOPs coefficients of the control variable alone with minimizes the cost function, so the method avoids solving the nonlinear Riccati equation and the calculation procedure become effective and straightforward. An illustrative numerical example is interpreted to support this technique.