A method for construction of suboptimal non-linear regulators by minimax algorithm†

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Abstract
A method is proposed for an approximate construction of the optimal state regulator for an autonomous non-linear system with quadratic performance index. The method is bused upon the instantaneous linearization technique developed by Pearson. In the method of instantaneous linearization, the non-linear system is approximated by a state-dependent linear model. However, the solution is not optimal in general because of the arbitrariness of the linearized model. The purpose of the present paper is to correct the shortcomings of this method. First, an optimality condition for the control law obtained by the method of instantaneous linearization is derived. Secondly, by making use of this condition, a systematic procedure is presented to determine a suboptimal feedback control for a second-order system. A minimax algorithm is used to design the linearized model closely approximating the original system within a prescribed region in the state space. The validity of the present method is shown by examining typical examples.

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