Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design

ABSTRACT

Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN₁) is synthesised offline. However, another linear-in-weight neural network (called as NN₂) is trained online and augmented to NN₁ in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN₃) online. Training of NN₃ is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN₂ successfully to capture the required optimal relationship. The overall architecture is named as ‘Dynamically Re-optimised single network adaptive critic (DR-SNAC)’. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.

KEYWORDS:

• Optimal control
• neural networks
• adaptive systems
• single network adaptive critic
• neuro-adaptive control
• adaptive optimal control

Disclosure statement

No potential conflict of interest was reported by the authors.