Funnel Control for Uncertain Nonlinear Systems Under Soft and Hard Output Constraints: A Direct Modification Approach
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摘要: 本文研究了一类同时存在软、硬输出约束的不确定非线性系统跟踪控制问题. 其中, 安全相关的输出约束被建模为不可违背的硬约束, 而期望的跟踪性能则通过可调节的软约束加以刻画. 针对软、硬约束可能发生冲突的情形, 引入一种光滑过渡函数, 并基于此构造凸组合算子对软约束边界进行直接修正, 从而保证其与硬约束的兼容性. 在此基础上, 将硬约束与修正后的软约束进行统一整合, 构造具有光滑边界的约束结构. 基于该约束结构并结合漏斗控制技术, 提出一种低复杂度鲁棒控制算法, 确保系统同时满足硬约束与修正后的软约束. 与现有基于辅助动态系统的软约束间接调整方法不同, 所提策略无需引入额外动态系统, 从而得到结构简洁、易于实现的静态控制器. 此外, 在软、硬约束冲突发生时, 该方法能够将软约束的违背量严格限制在硬约束所必需的最小违背量之上的预设容差范围内, 且在有限时间内实现约束解耦, 优先确保硬约束的严格满足. 仿真结果验证了该方法的有效性.Abstract: This paper investigates the tracking control problem for a class of uncertain nonlinear systems subject to simultaneous soft and hard output constraints. The safety-related output constraints are modeled as inviolable hard constraints, while the desired tracking performance is characterized by adjustable soft constraints. To address potential conflicts between soft and hard constraints, a smooth transition function is introduced, based on which convex combination operators are constructed to directly modify the soft constraint boundaries, thereby ensuring their compatibility with the hard constraints. On this basis, the hard constraints and the modified soft constraints are consolidated to construct a constraint structure with smooth boundaries. Based on this consolidated constraint structure and combined with funnel control techniques, a low-complexity robust control algorithm is proposed to ensure the simultaneous satisfaction of the hard constraints and the modified soft constraints. Unlike existing methods that rely on auxiliary dynamic systems to indirectly adjust soft constraints, the proposed strategy eliminates the need for extra dynamic systems, resulting in a structurally simple and easy-to-implement static controller. Furthermore, when conflicts occur, the proposed method strictly confines the violation of soft constraints within a prescribed tolerance above the minimum violation necessitated by the hard constraints, and achieves constraint decoupling within a finite time, thereby prioritizing the strict satisfaction of hard constraints. Simulation results verify the effectiveness of the proposed method.
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Key words:
- nonlinear systems /
- uncertain systems /
- hard constraints /
- soft constraints /
- funnel control
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图 2 修正后的软约束边界$\overline{p}$和$\underline{p}$
Fig. 2 Modified soft constraint boundaries $\overline{p}$ and $\underline{p}$
图 3 整合的光滑约束边界$\overline{\rho}$和$\underline{\rho}$
Fig. 3 Consolidated smooth constraint boundaries $\overline{\rho}$ and $\underline{\rho}$
图 6 不同容差参数$\delta$下软约束违背量对比
Fig. 6 Comparison of soft-constraint violation under different tolerance parameters $\delta$
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