Control of nonlinear systems with time-varying output constraints

Keng Peng Tee, Beibei Ren, Shuzhi Sam Ge

Research output: Contribution to journalArticlepeer-review

686 Scopus citations


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.

Original languageEnglish
Pages (from-to)2511-2516
Number of pages6
Issue number11
StatePublished - Nov 2011


  • Adaptive control
  • Barrier function
  • Constraints
  • Lyapunov methods
  • Time-varying systems


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