Adapting the Direction of the Search Vector for Direct Adaptive Continuous-Time Nonlinear Systems

In adaptive control algorithms, the adaptation routine (e.g., least squares or gradient) is usually used to adjust the controller parameters to approximate the ideal controller that is assumed to exist. Searching for the ideal parameter vector, a gradient-based hybrid adaptive routine is used here for continuous-time nonlinear systems. The adjustment of the parameter vector is usually based on minimizing the squared error. For direct adaptive control, in this paper an algorithm is presented to adapt the direction of the search vector so that the instantaneous control energy is minimized. Hence, the overall adaptive routine minimizes not only the squares error but also the instantaneous control energy. Stability results of the presented algorithm show that boundedness of the error is dependent on the length of the search vector.