Brief paper: Control of nonlinear systems with time-varying output constraints

  • Authors:

  • Keng Peng Tee;Beibei Ren;Shuzhi Sam Ge

  • Affiliations:

  • Institute for Infocomm Research, A*STAR, Singapore 138632, Singapore;Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore and Department of Mechanical & Aerospace Engineering, University of California, San ...;Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore and The Robotics Institute, and School of Computer Science and Engineering, Univers ...

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

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.