This chapter addresses the tracking control problem for a class of nonlinear systems with simultaneously considering input saturation and prescribed performance constraints. We formally propose a novel Tunnel Prescribed Performance with brief expressions, which not only simplifies the design process, but also achieves smaller overshoot performance owing to the tight feasible region established by the parallel performance. Based on the proposed Tunnel Prescribed Performance, we further develop a unified yet concise Finite-time Tunnel Prescribed Performance, which can adaptive adjusted its orientation based on different initial conditions. Compared with the classical funnel-shape prescribed performance functions, our tunnel-shape Finite-time Tunnel Prescribed Performance can not only provide tight allowable set leading to better transient performance, but also user-specified settling time in advance instead of relying on the initial conditions as depicted in finite-time control. Therefore, two control strategies, namely, Tunnel Prescribed Control and Finite-time Tunnel Prescribed Control, are proposed for nonlinear systems such that the tracking errors can evolve within the tunnel prescribed performance even in the presence of uncertainties, such as actuator faults, time delay, and input saturation. Both control strategies can achieve robust tracking performance against uncertainties and less conservatism control design. The effectiveness of the proposed control strategies is verified by numerical simulations.

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Constrained Control of Nonlinear System with Input Saturation and Tunnel Prescribed Performance Constraints

  • Ruihang Ji,
  • Shuzhi Sam Ge,
  • Dongyu Li

摘要

This chapter addresses the tracking control problem for a class of nonlinear systems with simultaneously considering input saturation and prescribed performance constraints. We formally propose a novel Tunnel Prescribed Performance with brief expressions, which not only simplifies the design process, but also achieves smaller overshoot performance owing to the tight feasible region established by the parallel performance. Based on the proposed Tunnel Prescribed Performance, we further develop a unified yet concise Finite-time Tunnel Prescribed Performance, which can adaptive adjusted its orientation based on different initial conditions. Compared with the classical funnel-shape prescribed performance functions, our tunnel-shape Finite-time Tunnel Prescribed Performance can not only provide tight allowable set leading to better transient performance, but also user-specified settling time in advance instead of relying on the initial conditions as depicted in finite-time control. Therefore, two control strategies, namely, Tunnel Prescribed Control and Finite-time Tunnel Prescribed Control, are proposed for nonlinear systems such that the tracking errors can evolve within the tunnel prescribed performance even in the presence of uncertainties, such as actuator faults, time delay, and input saturation. Both control strategies can achieve robust tracking performance against uncertainties and less conservatism control design. The effectiveness of the proposed control strategies is verified by numerical simulations.