Adaptive high-gain stabilization of 'minimum-phase' nonlinear systems

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Abstract
The authors present an adaptive high-gain controller which can stabilize minimum-phase nonlinear systems with strong relative degree. The basic structure of the control method is similar to adaptive control methods in the sense that there are two feedback loops. The inner loop is a high-gain feedback loop with a plant and a controller. The controller is completely specified except for a scalar parameter, the high-gain parameter. The controller is designed such that the stabilization of the closed loop will be achieved if the high-gain parameter is chosen large enough. This feature facilitates a simple procedure of tuning the high-gain parameter by increasing it monotonically until it is large enough. The tuning of the parameter is set up by the outer loop. The high-gain parameter is increased in a stepwise fashion so as to follow a continuous-time parameter which is determined by an adaptation rule. The stepwise incrementation plays a crucial role in simplifying the analysis, since between any two switching points the controller is a simple linear time-invariant one.