Non-monotonic prescribed performance specifications in tracking control of input-limited nonlinear systems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-11 DOI:10.1016/j.cnsns.2025.109016

Yaming Zheng , Yu Xia

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引用次数: 0

Abstract

Most existing prescribed performance boundaries are designed to be strictly monotonically decreasing, which may not always be advantageous. When control input fail to meet the prescribed performance requirements, strict monotonicity can lead to constraint failure and singularity problem. This paper proposes novel non-monotonic prescribed performance specifications for tracking control of input-limited nonlinear systems, allowing for customized relaxation of constraint boundaries in cases where input is limited. By incorporating quadratic characteristics into the prescribed performance design, transient input oscillation is effectively suppressed. Coupled with a local asymmetric design, the prescribed performance boundaries impose asymmetric constraints during transients and symmetric constraints during steady-state, enabling effective regulation of output overshoot and preventing any bias in the steady-state tracking error. The proposed scheme, grounded in Lyapunov stability theory, guarantees that all signals within the closed-loop system are ultimately uniformly bounded, with the tracking error compelled to evolve within the prescribed boundaries within the prescribed time. Simulation results validate the effectiveness and superiority of the scheme.

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输入受限非线性系统跟踪控制中的非单调规定性能规范

大多数现有规定的性能边界都被设计成严格的单调递减，这可能并不总是有利的。当控制输入不能满足规定的性能要求时，严格的单调性会导致约束失效和奇异性问题。本文提出了一种新的非单调的规定性能规范，用于输入受限非线性系统的跟踪控制，允许在输入受限的情况下自定义松弛约束边界。通过在规定的性能设计中加入二次特性，有效地抑制了瞬态输入振荡。加上局部非对称设计，规定的性能边界在瞬态时施加非对称约束，在稳态时施加对称约束，从而有效地调节输出超调并防止稳态跟踪误差中的任何偏差。该方案以Lyapunov稳定性理论为基础，保证闭环系统内所有信号最终均匀有界，跟踪误差在规定时间内被迫在规定边界内演化。仿真结果验证了该方案的有效性和优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.