Stable auto-tuning of the direction of descent for gradient-based nonlinear adaptive control systems

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, approximators such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. We present an algorithm to tune the direction of descent for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithm, the direction of descent is obtained by minimizing the instantaneous control energy. We show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. Finally, we illustrate the performance of the proposed algorithm via a simple surge tank example