Adaptive Control of Systems with Nonlinearities

This chapter presents a general adaptive inverse approach for control of plants with uncertain nonsmooth actuator nonlinearities such as dead-zone, backlash, hysteresis, and other piecewise-linear characteristics which are common in control systems and often limit system performance. This chapter gives an overview of various state feedback and output feedback control designs for linear, nonlinear, single-input and single-output, and multi-input and multi-output plants as well as open problems in this area of major theoretical and practical relevance. A key problem is to develop linearly parametrized error models suitable for developing adaptive laws to update the inverse and feedback controller parameters, which is solved for various considered cases. The chapter shows that control systems with commonly used linear or nonlinear feedback controllers such as a model reference, PID, pole placement, feedback linearization, or backstepping can be combined with an adaptive inverse to handle actuator nonlinearities.