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Self-Adjusting Prescribed Performance Control for Nonlinear Systems with Input Saturation

Zhuwu Shao, Yujuan Wang, Huanyu Yang, Yongduan Song

TL;DR

This work tackles the limitation of fixed PF decay rates in prescribed performance control for nonlinear systems with input saturation. It introduces a performance index function (PIF) to serve as a reference for online adjustment of the PF decay rate $\delta(t)$, enabling both contraction of the PF envelope and faster convergence when control authority allows. The approach combines backstepping and adaptive control with two saturation-aware update rules, proving boundedness of all signals and PF-feasibility under disturbances and saturation. The proposed method removes the need to predefine initial PF values, reduces required input peaks, and offers practical benefits for accelerated yet safe performance in saturated actuators. A set of numerical examples on MSD-type systems corroborates the advantages over fixed-decay PPC methods.

Abstract

Among the existing works on enhancing system performance via prescribed performance functions (PPFs), the decay rates of PPFs need to be predetermined by the designer, directly affecting the convergence time of the closed-loop system. However, if only considering accelerating the system convergence by selecting a big decay rate of the performance function, it may lead to the severe consequence of closed-loop system failure when considering the prevalent actuator saturation in practical scenarios. To address this issue, this work proposes a control scheme that can flexibly self-adjust the convergence rates of the performance functions (PFs), aiming to achieve faster steady-state convergence while avoiding the risk of error violation beyond the PFs' envelopes, which may arise from input saturation and improper decay rate selection in traditional prescribed performance control (PPC) methods. Specifically, a performance index function (PIF) is introduced as a reference criterion, based on which the self-adjusting rates of the PFs are designed for different cases, exhibiting the following appealing features: 1) It can eliminate the need to prespecify the initial values of the PFs. In addition, it can also accommodate arbitrary magnitudes of initial errors while avoiding excessive initial control efforts. 2) Considering actuator saturation, this method can not only reduce the decay rates of the PFs when necessary to avoid violation of the PFs, but also increase the decay rates to accelerate system convergence when there is remaining control capacity. Finally, several numerical simulations are conducted to confirm the effectiveness and superiority of the proposed method.

Self-Adjusting Prescribed Performance Control for Nonlinear Systems with Input Saturation

TL;DR

This work tackles the limitation of fixed PF decay rates in prescribed performance control for nonlinear systems with input saturation. It introduces a performance index function (PIF) to serve as a reference for online adjustment of the PF decay rate , enabling both contraction of the PF envelope and faster convergence when control authority allows. The approach combines backstepping and adaptive control with two saturation-aware update rules, proving boundedness of all signals and PF-feasibility under disturbances and saturation. The proposed method removes the need to predefine initial PF values, reduces required input peaks, and offers practical benefits for accelerated yet safe performance in saturated actuators. A set of numerical examples on MSD-type systems corroborates the advantages over fixed-decay PPC methods.

Abstract

Among the existing works on enhancing system performance via prescribed performance functions (PPFs), the decay rates of PPFs need to be predetermined by the designer, directly affecting the convergence time of the closed-loop system. However, if only considering accelerating the system convergence by selecting a big decay rate of the performance function, it may lead to the severe consequence of closed-loop system failure when considering the prevalent actuator saturation in practical scenarios. To address this issue, this work proposes a control scheme that can flexibly self-adjust the convergence rates of the performance functions (PFs), aiming to achieve faster steady-state convergence while avoiding the risk of error violation beyond the PFs' envelopes, which may arise from input saturation and improper decay rate selection in traditional prescribed performance control (PPC) methods. Specifically, a performance index function (PIF) is introduced as a reference criterion, based on which the self-adjusting rates of the PFs are designed for different cases, exhibiting the following appealing features: 1) It can eliminate the need to prespecify the initial values of the PFs. In addition, it can also accommodate arbitrary magnitudes of initial errors while avoiding excessive initial control efforts. 2) Considering actuator saturation, this method can not only reduce the decay rates of the PFs when necessary to avoid violation of the PFs, but also increase the decay rates to accelerate system convergence when there is remaining control capacity. Finally, several numerical simulations are conducted to confirm the effectiveness and superiority of the proposed method.
Paper Structure (10 sections, 25 equations, 4 figures, 2 tables)

This paper contains 10 sections, 25 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Control Design without Considering Input Constraints
  4. Performance Index Function
  5. Self-Tuning Decay Rate Design without Input Saturation Consideration
  6. Self-Tuning Decay Rate and Controller Design under Input Saturation
  7. Self-Tuning of Decay Rate
  8. Adaptive Control Design with Input Saturation
  9. Numerical Simulations on MSD system
  10. Conclusions

Figures (4)

  • Figure 1: The control performance corresponding to (a) this work, and (b) work zhao2021adaptive.
  • Figure 2: The tracking error in (a) this work, and (b) work zhao2021adaptive.
  • Figure 3: The control performance corresponding to $x_1(0) = 0.6$ m; (a) this work, (b) work zhao2021adaptive.
  • Figure 4: The control performance corresponding to $x_1(0) = -0.6$ m; (a) this work, (b) work zhao2021adaptive.