Integrated design of a linear/neuro-adaptive controller in the presence of norm-bounded uncertainties

Adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network (NN) design parameters to performance requirements. This study proposes a methodology for the design of an integrated linear-adaptive model reference controller that guarantees component-wise boundedness of the tracking error within an a priori specified compact domain. The approach is based on the design of a robust invariant ellipsoidal set where both the NN reconstruction error and the neuro-adaptive control are considered as bounded persistent uncertainties. We show that all the performance and control requirements for the closed-loop system can be expressed as linear matrix inequality constraints. This brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem. An advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design parameters and their impact on the requirements. This produces an integrated linear/neuro-adaptive performance-oriented design methodology. A numerical example is used to illustrate the approach.