Symmetry (May 2023)
Approximate Optimal Tracking Control for Partially Unknown Nonlinear Systems via an Adaptive Fixed-Time Observer
Abstract
This paper investigates a novel adaptive fixed-time disturbance observer (AFXDO)-based approximate optimal tracking control architecture for nonlinear systems with partially unknown dynamic drift and perturbation under an adaptive dynamic programming (ADP) scheme. To attenuate the impact of disturbance, a novel AFXDO was designed based on the principle of a fixed-time stable system without prior information of disturbance, making disturbance observer errors converge to zero in a fixed time independent of initial estimation error. Additionally, approximate optimal control is conducted by incorporating the real-time estimation of AFXDO into a critic-only ADP framework to stabilize the dynamics of tracking errors and strike a balance between consumption and performance. In particular, to address the heavy calculation burden and oscillation phenomenon in the traditional actor–critic structure, an improved adaptive update law with a variable learning rate was developed to update the weight for adjusting the optimal cost function and optimal control policy simultaneously, avoiding the initial chattering phenomenon and achieving a prescribed convergence without resorting to dual networks. With the efforts of AFXDO and a weight law with a variable learning rate, the track errors were achieved with fast transient performance and low control consumptions in a fixed time. By revisiting Lyapunov stability, the tracking error and weight estimation error were proven to be uniformly ultimately bounded, and the designed control tended to optimal control. The simulations were carried out on quadrotor tracking to demonstrate the effectiveness of the developed control scheme, which achieves rapid convergence by lower control consumption in 4 s, where the cost function is reduced by 19.13%.
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