Prescribed Performance Control of Uncertain Euler-Lagrange Systems Subject to Full-State Constraints

• Published in: IEEE transaction on neural networks and learning systems Vol. 29; no. 8; pp. 3478 - 3489
• Main Authors: Zhao, Kai, Song, Yongduan, Ma, Tiedong, He, Liu
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Artificial neural networks; Barrier Lyapunov function (BLF); Computer simulation; Convergence; Error analysis; error transformation; Hazards; Liapunov functions; Lyapunov methods; Neural networks; Nussbaum gain technique; prescribed tracking performance; robust adaptive neural control; Robustness; Stability; System effectiveness; Tracking control; Uncertainty
• DOI: 10.1109/TNNLS.2017.2727223
• ISSN: 2162-237X; 2162-2388

This paper studies the zero-error tracking control problem of Euler-Lagrange systems subject to full-state constraints and nonparametric uncertainties. By blending an error transformation with barrier Lyapunov function, a neural adaptive tracking control scheme is developed, resulting in a solution with several salient features: 1) the control action is continuous and <inline-formula> <tex-math notation="LaTeX">\mathscr C^{1} </tex-math></inline-formula> smooth; 2) the full-state tracking error converges to a prescribed compact set around origin within a given finite time at a controllable rate of convergence that can be uniformly prespecified; 3) with Nussbaum gain in the loop, the tracking error further shrinks to zero as <inline-formula> <tex-math notation="LaTeX">t\to \infty </tex-math></inline-formula>; and 4) the neural network (NN) unit can be safely included in the loop during the entire system operational envelope without the danger of violating the compact set precondition imposed on the NN training inputs. Furthermore, by using the Lyapunov analysis, it is proven that all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness and benefits of the proposed control method are validated via computer simulation.