Stable adaptive control and recursive identification using radial Gaussian networks

Previous work has provided the theoretical foundations of a constructive design procedure for uniform approximation of smooth functions to a chosen degree of accuracy using networks of Gaussian radial basis functions. This construction and the guaranteed uniform bounds were shown to provide the basis for stable adaptive neurocontrol algorithms for a class of nonlinear plants. The authors detail and extend these ideas in three directions. First, some practical details of the construction are provided, explicitly illustrating the relation between the free parameters in the network design and the degree of approximation error on a particular set. Next, the original adaptive control algorithm is modified to permit incorporation of additional prior knowledge of the system dynamics, allowing the neurocontroller to operate in parallel with conventional fixed or adaptive controllers. Finally, it is shown how the Gaussian network construction may also be utilized in recursive identification algorithms with similar guarantees of stability and convergence