切换线性系统的连续时间约束线性二次调节器
Continuous-Time Constrained Linear Quadratic Regulator for Switched Linear Systems
- Universita’ di Pisa（比萨大学）
- Centro di Ricerca “Enrico Piaggio”（恩里科·皮亚杰研究中心）
- Dipartimento di Ingegneria dell’Informazione（信息工程系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对切换线性系统的连续时间约束线性二次调节器问题，提出通过固定切换序列并优化区间持续时间来间接优化切换序列，推导代价函数及其梯度的解析表达式，实现高效优化并提升计算效率。
AI中文摘要：
切换系统由一族受切换规则支配的子系统表征，广泛应用于复杂的现实场景。然而，其固有的切换动态在相分析和控制设计方面带来了重大挑战。为解决这些挑战，我们提出了一个求解切换线性系统的连续时间约束线性二次调节器（CT-CLQR）问题的框架。我们的方法将时间范围划分为有限数量的区间，每个区间与一个特定的系统模式相关联。这些区间的持续时间由切换时刻参数化，从而实现了问题的重构。我们通过固定切换序列并优化区间持续时间来间接优化切换序列。我们推导了代价函数及其梯度的解析表达式，这对高效优化至关重要。与现有技术中对状态演化施加等式约束的方法不同，我们的方法在代价函数中固有地考虑了状态演化。这不仅简化了问题表述，还通过离线预计算共享项减少了计算开销，从而提高了在线操作的效率。所提出的方法显著推进了现有技术，提供了改进的计算效率和灵活性。我们通过全面的数值示例展示了该方法的有效性，展示了其在实际应用中的潜力。
英文摘要：
Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications.
