On stability theory for nonlinear control schemes with intelligent networks

Learning methods are currently of great interest to (sections) of the control systems community. There is an ever increasing volume literature on neural networks. At best, this work has shown that, appropriately chosen intelligent control type schemes, or architectures are capable of synthesising control laws for partially known systems. A large class of these approaches employ iterative techniques to adjust the variable parameters of the architecture and hence develop discrete time models of the inverse dynamics of the process to be controlled. The resulting trained network is then used as the basis of a nonlinear control law. It is important to note, however, that this general approach has several major drawbacks. These drawbacks are some of the fundamental reasons why the adaptive control community moved away from gradient based methods in favour of a formal stability theory. Currently, a number of research groups, including The Advanced Systems Research Group at Southampton, are investigating the feasibility of analogue network designs for the control of continuous time nonlinear dynamic systems. One idea which has already received considerable attention is to combine an adaptation law with a sliding mode, or variable structure controller to give a globally stable closed-loop system with good tracking properties. The presentation reviews progress to-date with particular emphasis on stability theory. Some ongoing work and areas for short to medium term further development are also briefly outlined