Composite Adaptive Multi-Layer NN Control of Strict-Feedback Systems

Abstract

Despite versatile control adaptive multi-layer neural network (MNN) schemes have been proposed in the literature, however, most of these works are based on three-layer NNs and rely on the linearization technique, therefore ensure local stability only. In this regard, this paper aims to synthesize a composite adaptive controller (CAC) based directly on a general MNN for uncertain strict-feedback systems without such restrictions. The challenge is threefold, i.e., attaining an unfiltered and nonlocal PER, an estimation of the state derivative, and formulating a stable composite update algorithm. First, an observer for estimating both the state derivatives and the prediction errors (PERs) is constructed. Next, the so-called approximate identity tool is invoked for quantifying the corresponding error bounds and rendering the corresponding gain selection easy. On the other hand, by taking advantages of the positive definiteness of the gradient of PERs with respect to the neural weights and incorporating the robust compensation technique, a stable composite update algorithm is formulated. Without resorting to the popular linearization approach, the proposed design ensures the semi-globally uniformly ultimate bounded (SGUUB) stability of the closed-loop system and convergence of the tracking error and PER to the vicinity of zero simultaneously.

Keywords

• Composite adaptive
• strict-feedback
• multi-layer neural networks
• prediction errors
• state observer
• approximate identity