Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function

TLDR

The authors develop an adaptive neural controller for output‑feedback nonlinear systems that uses a barrier Lyapunov function to pre‑define and maintain a compact domain for unknown dynamics. The controller employs online neural‑network approximation based solely on output measurements, with the barrier Lyapunov function enforcing boundedness and keeping the arguments of the unknown functions within the valid compact superset. The resulting closed‑loop system achieves semiglobal boundedness of all signals and drives the tracking error into a small neighborhood of zero, as confirmed by simulation results.

Abstract

In this brief, adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions. The unknown functions are handled via on-line neural network (NN) control using only output measurements. A barrier Lyapunov function (BLF) is introduced to address two open and challenging problems in the neuro-control area: 1) for any initial compact set, how to determine a priori the compact superset, on which NN approximation is valid; and 2) how to ensure that the arguments of the unknown functions remain within the specified compact superset. By ensuring boundedness of the BLF, we actively constrain the argument of the unknown functions to remain within a compact superset such that the NN approximation conditions hold. The semiglobal boundedness of all closed-loop signals is ensured, and the tracking error converges to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach.