Adaptive Fixed-Time Control for MIMO Nonlinear Systems With Asymmetric Output Constraints Using Universal Barrier Functions

• Published in: IEEE transactions on automatic control Vol. 64; no. 7; pp. 3046 - 3053
• Main Author: Jin, Xu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; Adaptive fixed-time control; Adaptive systems; asymmetric constraints; Asymmetry; Backstepping; Control systems; Convergence; MIMO (control systems); MIMO communication; MIMO nonlinear systems; Nonlinear control; Nonlinear systems; Robot arms; Tracking control; Tracking errors; Uncertainty; universal barrier functions; unmatched system uncertainties
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2874877

In this note, we propose a novel adaptive fixed-time control scheme for output tracking problems of a class of multi-input multi-output (MIMO) nonlinear systems with asymmetric output constraint requirements, using a new universal barrier function . It is universal in the sense that the proposed scheme is a general one that also works for systems with symmetric constraints or without constraint requirements, without changing the control structure. Novel adaptive estimations and analysis are introduced to address system uncertainties in the fixed-time convergence settings. We show that under the proposed novel control scheme, each element in the system output tracking error vector of the MIMO nonlinear system can converge into small sets near zero with fixed-time convergence rate, while the asymmetric output constraint requirements on each element of the output tracking error are satisfied at all time. The proposed scheme can effectively deal with unmatched system uncertainties and uncertain gain functions. In the end, a simulation example on a two-degree-of-freedom robot manipulator is presented to demonstrate the efficacy of the proposed scheme.