Stable auto-tuning of adaptive fuzzy/neural controllers for nonlinear discrete-time 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. In this paper, we present algorithms to tune some of the parameters (e.g., the adaptation gain and 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 algorithms, the adaptation gain and the direction of descent are obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. We will also compare the direct and indirect adaptive control schemes and illustrate their performance via a simple surge tank example.