基于自然边界的严格反馈非线性系统约束控制策略
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中国石油大学(北京)

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TP13

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Constrained control strategy for strict-feedback nonlinear systems based on natural boundary
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    摘要:

    本文针对一类严格反馈非线性系统的状态约束控制问题展开研究. 现有预设性能等约束控制方法通常需要预先设定约束边界, 这可能造成因边界设置远宽于系统实际动态范围而导致控制冗余. 为克服此问题, 本文提出一种先评估、后约束的切换控制新思路. 首先, 在假设系统非线性项及其偏导有界的条件下, 通过结合反步法与李雅普诺夫稳定性理论, 解析推导了系统在无约束控制器作用下的状态轨迹上界. 该上界表征了无约束控制时状态的潜在最大幅值. 然后设计了一种切换控制策略: 仅当预设边界小于自然边界时, 才启用约束控制器以保证状态不越界; 反之, 则采用无约束控制器, 在保证相同闭环性能的同时, 避免因引入额外项而产生的控制冗余与复杂度. 在满足状态约束的前提下, 相较于约束控制方法, 本文提出的控制策略能够在较小的控制力度下实现期望的跟踪控制.仿真结果验证了该方法的有效性与可行性.

    Abstract:

    This paper investigates the state-constrained control problem for a class of strict-feedback nonlinear systems. Existing constrained control methods, such as those with prescribed performance, typically require pre-setting constraint boundaries. This may lead to control redundancy if the set boundaries are far wider than the actual dynamic range of the system. To overcome this issue, this paper proposes a novel switching control idea of assess first, then constrain . Firstly, with the assumption that the nonlinear terms of the system and their partial derivatives are bounded, the state trajectory upper bound of the system with an unconstrained controller is analytically derived by integrating backstepping and Lyapunov stability theory. This upper bound characterizes the potential maximum amplitude of the state under unconstrained control. Based on this, a switching control strategy is then designed. a constrained controller is activated only when the artificially preset constraint boundary is smaller than this upper bound to prevent state violation. Otherwise, an unconstrained controller is employed to maintain the same closed-loop performance while avoiding the control redundancy and complexity introduced by additional terms. The proposed control strategy not only satisfies the state constraints but also achieves the desired tracking control with less control effort than the constrained control method. Simulation results confirm its effectiveness and feasibility.

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  • 收稿日期:2025-12-29
  • 最后修改日期:2026-06-10
  • 录用日期:2026-06-11
  • 在线发布日期: 2026-06-24
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