广义正交多项式在时变系统跟踪问题中的应用

采用广义正交多项式的展开技术,利用其积分、乘积运算阵,对于时变线性系统最优控制中的跟踪问题,直接从最优控制的性能泛函入手,将最优控制问题转化为代数极值问题,从而避免了求解非线性Riccati方程,得到了一个较为简便的算法,并结合实例说明了方法的可行性.

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.