多输入系统联合容量约束下的可容许性保持控制

中文摘要 AI 辅助

本文研究受联合容量约束的多输入严格反馈非线性系统的控制问题，其中可容许输入集是各执行器限制的耦合子集。与现有逐通道强制执行执行器边界、可能不必要地抑制可容许控制方向的约束处理方法不同，我们开发了一种各向异性联合可容许性保持输入实现（AJ-APIR）框架，该框架显式利用联合约束的几何结构。所提出的实现构造了一个状态相关的增益矩阵，其谱分解将指令输入相对于约束边界分解为法向和切向方向。法向分量在接近边界时被衰减，而切向分量得以保留，这使得可容许控制能量能够在不损失跟踪权限的情况下重新分配。与反步控制器集成后，AJ-APIR框架保证了联合可容许集在所有时间内的前向不变性。我们建立了跟踪误差指数收敛到零以及所有闭环信号一致有界性，并刻画了联合约束下的指令需求行为。针对受功率预算约束的典型二阶双输入非线性系统的仿真结果证明了所提方法在强制执行联合输入约束方面的有效性。

英文摘要

This paper addresses the control of multi-input strict-feedback nonlinear systems subject to a joint capacity constraint, in which the admissible input set is a coupled subset of the individual actuator limits. Unlike existing constraint-handling methods that enforce actuator bounds channel by channel and may unnecessarily suppress admissible control directions, we develop an Anisotropic Joint-Admissibility-Preserving Input Realization (AJ-APIR) framework that explicitly exploits the geometry of the joint constraint. The proposed realization constructs a state-dependent gain matrix whose spectral decomposition separates the commanded input into normal and tangential directions relative to the constraint boundary. The normal component is attenuated as the boundary is approached, while the tangential component is preserved, which allows the admissible control effort to be redistributed without loss of tracking authority. Integrated with a backstepping controller, the AJ-APIR framework guarantees forward invariance of the joint admissible set for all time. We establish exponential convergence of the tracking error to zero together with uniform boundedness of all closed-loop signals, and characterize the resulting command-demand behavior under the joint constraint. Simulation results for a representative second-order, two-input nonlinear system subject to a power-budget constraint demonstrate the efficacy of the proposed method to enforce the joint input constraint.

发表机构

• Indian Institute of Technology Bombay（印度理工学院孟买分校）
• University of Cincinnati（辛辛那提大学）

机构由 AI 辅助整理，请以论文原文为准。