Optimal state-feedback design for non-linear feedback-linearisable systems

This paper addresses the problem of optimal state-feedback design for a class of non-linear systems. The method is applicable to all non-linear systems which can be linearised using the method of state-feedback linearisation. The alternative is to use linear optimisation techniques for the linearised equations, but then there is no guarantee that the original non-linear system behaves optimally. The authors use feedback linearisation technique to linearise the system and then design a state feedback for the feedback-linearised system in such a way that it ensures optimal performance of the original non-linear system. The method cannot ensure global optimality of the solution but the global stability of the non-linear system is ensured. The proposed method can optimise any arbitrary smooth function of states and input, including the conventional quadratic form. The proposed method can also optimise the feedback linearising transformation. The method is successfully applied to control the design of a flexible joint dynamic and the results are discussed. Compared with the conventional linear quadratic regulator (LQR) technique, the minimum value of cost function is significantly reduced by the proposed method.