Optimal tracking of time varying linear systems via general orthogonal polynomials

The authors extend the application of general orthogonal polynomials (GOP) for solving the optimal tracking problem of time-varying linear systems. By applying the Pontryagin maximum principle, it can be deduced that two time-varying vector matrix differential equations must be solved to obtain the optimal control law. By using the concepts of the GOP product matrix and the GOP coefficient matrix and by using the operational properties of forward and backward integration, these two linear differential equations can be converted to two simple linear equation systems. An example with good results is used to demonstrate the usefulness of the proposed method