Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints

TLDR

Barrier Lyapunov functions have been successfully applied to strict‑feedback and pure‑feedback nonlinear systems to enforce state constraints. The paper proposes an adaptive neural‑network output‑feedback optimized controller for strict‑feedback nonlinear systems with unknown internal dynamics and immeasurable states constrained to compact sets. The design employs neural networks to approximate unknown dynamics, an adaptive observer to estimate unmeasured states, barrier‑type optimal cost functions, an actor‑critic architecture, and backstepping to construct virtual and actual optimal controllers. The resulting controller guarantees bounded closed‑loop signals, keeps all states within the prescribed compact sets, requires fewer dynamic assumptions than existing methods, and is validated through numerical and practical examples.

Abstract

This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.