具有排除约束的鲁棒模型预测轨迹跟踪控制

doi:10.12305/j.issn.1001-506X.2025.03.27

摘要/Abstract

摘要：

针对具有不确定性和排除约束的轨迹跟踪控制问题, 提出计算高效的鲁棒模型预测不可达轨迹跟踪控制算法。首先, 引入一条满足所有约束的可行周期参考轨迹, 并计算不确定性系统状态集和所有排除约束集之间的分离超平面, 生成排除约束安全集, 将固有非凸的排除约束凸化为闭多胞体约束。然后, 引入辅助变量, 将具有排除约束的轨迹规划问题和跟踪控制问题集成到同一个优化问题中, 并利用二次规划进行求解, 实际系统状态轨迹收敛于最优可达参考轨迹。此外, 该算法可以保证迭代可行性和鲁棒稳定性。最后, 通过仿真验证了算法的有效性和高效性。

关键词: 不确定性系统, 排除约束, 不可达轨迹, 鲁棒模型预测控制

Abstract:

For trajectory tracking control problems with uncertainties and exclusion constraints, a computationally efficient robust model predictive unreachable trajectory tracking control algorithm is proposed. Firstly, a feasible periodic reference trajectory satisfying all constraints is introduced and the separating hyperplanes between the uncertain system state set and all exclusion constraint sets are calculated. The exclusion constraint safe sets are generated and the inherently nonconvex exclusion constraints are converted into closed polyhedral constraints. Then, by introducing auxiliary variables, the trajectory planning problem with exclusion constraints and the tracking control problem are integrated into an optimization problem, which is solved using quadratic programming and the actual system state trajectory converges to the optimal reachable reference trajectory. In addition, the algorithm can ensure the recursive feasibility and the robust stability. Finally, the effectiveness and efficiency of the proposed algorithm are verified by the simulation.

Key words: uncertain system, exclusion constraint, unreachable trajectory, robust model predictive control

中图分类号:

TP13

孙海迪, 戴荔, 王沛展, 夏元清. 具有排除约束的鲁棒模型预测轨迹跟踪控制[J]. 系统工程与电子技术, 2025, 47(3): 951-960.

Haidi SUN, Li DAI, Peizhan WANG, Yuanqing XIA. Robust model predictive control for trajectory tracking with exclusion constraint[J]. Systems Engineering and Electronics, 2025, 47(3): 951-960.

图/表 4

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