Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

• Published in: Automatica (Oxford) Vol. 47; no. 3; pp. 452 - 465
• Main Authors: Chen, Mou, Ge, Shuzhi Sam, Ren, Beibei
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-03-2011; Elsevier
• Subjects: Adaptative systems; Adaptive control systems; Adaptive tracking control; Applied sciences; Automation; Backstepping control; Coefficients; Command filter; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Derivatives; Design engineering; Dynamical systems; Exact sciences and technology; Input constraint; Law; Nonlinear dynamics; Nonlinear systems; Tracking control; Backstepping control; Input constraint; Nonlinear systems; Command filter; Adaptive tracking control; Spectral radius; Perron value; Control program; Non linear control; Control synthesis; Adaptive control; Control constraint; Uncertain system; Bounded perturbation; Actuator; State constraint; MIMO system; Tracking task; Non linear system; Recursive algorithm; Constrained optimization; Control loop; Filter; Symmetric matrix; Output feedback; Derivative control; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2011.01.025

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.