Convex fuzzy controller: neuro-fuzzy and convex optimisation

This paper reports a design of a convex fuzzy control system using a confluence of fuzzy logic, neural networks and convex optimisation. It can be shown that a fuzzy set X can be represented as a convex fuzzy restriction R(X;θ) which restricts θ to range in a convex subspace of a Cartesian product space. This fuzzy theory indicates that the fuzzy relations and the compositional rule of inference can be similarly characterised in terms of convex sets. In this way, principles and methods of convexity, optimisation and, most recently, linear matrix inequality (LMI) can be brought to bear on the task of characterising solutions to such problems. The result is hybrid relationships among fuzzy logic, neural network and convex optimisation. Neuro-fuzzy control alone has almost no stability criteria for uncertain dynamical system. But convex fuzzy control, introduced here, has stability results derived from parameter dependent Lyapunov function