Design of an amplitude-bounded output feedback adaptive neural control with guaranteed componentwise performance

This paper proposes a methodology for the design of a mixed output feedback linear and adaptive neural controller that guarantees componentwise boundedness of the tracking error within an a priori specified compact polyhedron for an uncertain nonlinear system. The approach is based on the design of a robust invariant ellipsoidal set where the adaptive neural network (NN) control is modeled as an amplitude-bounded signal. A linear error observer is employed to recover the unmeasured states, and a linear gain controller is used to enforce the containment of the ellipsoidal set within the performance polyhedron. The analysis and design of the observer and linear controller is set up as an LMI problem. The linear observer/controller scheme is then augmented with a general adaptive NN element having the purpose of approximating and compensating for the unknown nonlinearities thus providing performance improvement. The only requirement for the adaptive control signals is that their amplitudes must be confined within pre-specified limits. For this purpose, a novel mechanism called adaptive control redistribution is introduced to manage the adaptive NN control confinement during the online operation. A numerical example is used to illustrate the design methodology.