Nonlinear Adaptive Control Design for Affine Systems

A nonlinear adaptive approach based on differential geometry and state space identification is presented for the control of affine systems. An affine system is transformed to an input/output linear process by internal state feedback. First the optimal controller that minimizes the given quadratic cost function is designed for the linearized system. Finally we design a nonlinear adaptive controller that identifies the process model online using state space identification. The system switches to the adaptive control strategy when the process dynamics change. The implementation of the proposed control strategy is simple and efficient with mature algebraic algorithms. The effectiveness and robustness of the proposed control design is demonstrated by a simulation example.