Control of nonlinear systems with time-varying output constraints

• Published in: Automatica (Oxford) Vol. 47; no. 11; pp. 2511 - 2516
• Main Authors: Tee, Keng Peng, Ren, Beibei, Ge, Shuzhi Sam
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2011; Elsevier
• Subjects: Adaptative systems; Adaptive control; Applied sciences; Asymptotic properties; Automation; Barrier function; Barriers; Computer science; control theory; systems; Constraints; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Dynamical systems; Exact sciences and technology; Lyapunov methods; Mathematical models; Modelling and identification; Nonlinear dynamics; Time-varying systems; Tracking errors; Constraints; Barrier function; Adaptive control; Time-varying systems; Lyapunov methods; Performance evaluation; Transient response; Non linear control; Constraint satisfaction; Control synthesis; Output signal; Non linear system; Modeling; Control constraint; Time varying system; Uncertain system; Optimal trajectory; Model reference adaptive control systems; Tracking error; Asymptotic approximation; System identification; Output feedback; Lyapunov function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2011.08.044

This paper presents control design for strict feedback nonlinear systems with time-varying output constraints. An asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to ensure constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. Through a change of tracking error coordinates, we eliminate the explicit dependence of the BLF on time, thereby simplifying the analysis of constraint satisfaction. We show that asymptotic output tracking is achieved without violation of the output constraint, and also quantify the transient performance bound as a function of time that converges to zero. To handle parametric model uncertainty, we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation. The performance of the proposed control is illustrated through a simulation example.