发表机构
Ben-Gurion University of the Negev（内盖夫本-古里安大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于微分博弈的分而治之控制方法，通过建立纳什均衡合成组合控制器，在倒立摆、四旋翼案例中验证其性能优于LQR，可解决多目标动力系统的竞争控制问题。
AI 中文摘要
我们提出了一种新颖的分而治之控制设计方法，该方法利用微分博弈来处理单智能体多目标动力系统问题。所提框架将每个控制目标与一个虚拟输入关联，并在代表参与者之间建立非合作的有限或无限时域微分博弈。每个参与者会针对其特定目标、整个系统状态以及其他虚拟输入优化专属的虚拟代价函数，同时考虑其余参与者的最优策略。通过为该博弈建立纳什均衡，我们合成了一个组合控制器，该控制器可在竞争目标间实现稳定平衡，为控制工程师提供了一个直观且模块化的框架，便于在设计周期中重新调整参数。我们针对连续时间和离散时间动力系统均提供了形式化数学推导，目标是处理大规模单智能体应用，此类应用中复杂且动态冲突的控制目标使得全局加权方法难以实施。为验证该方法，我们开发了一个开源Python软件包，用于实现求解无限时域微分博弈中出现的耦合代数黎卡提方程的新型数值算法。我们在两个基准案例研究中评估了该方法： cart上的倒立摆和非线性分层控制四旋翼。将所得的闭环性能与经典线性二次调节器（LQR）在各种瞬态和稳态控制指标上进行对比，结果显示该方法在轨迹跟踪和鲁棒多目标调节方面表现更优。
英文摘要
We introduce a novel Divide and Conquer control design methodology leveraging differential games in single-agent, multi-objective dynamical systems. The proposed framework associates each control objective with a virtual input and establishes a non-cooperative, finite or infinite horizon differential game among representative players. Each player optimizes a distinct virtual cost function tailored to its specific goal, the full system state, and the other virtual inputs, while accounting for the remaining players' optimal policies. By establishing a Nash Equilibrium for this game, we synthesize a composite controller that achieves a stable balance across competing objectives, providing control engineers with an intuitive and modular framework for parameter re-tuning throughout the design cycle. We provide formal mathematical derivations for both continuous-time and discrete-time dynamical systems, targeting large-scale single-agent applications where complex, dynamically conflicting control objectives make global weighting intractable. To demonstrate the methodology, we developed an open-source Python package implementing a novel numerical algorithm for solving Coupled Algebraic Riccati Equations arising in infinite-horizon differential games. We evaluate the approach on two benchmark case studies: an inverted pendulum on a cart and a non-linear hierarchically controlled quadrotor. The resulting closed-loop performance is compared against the classical Linear Quadratic Regulator (LQR) across various transient and steady-state control metrics, demonstrating superior trajectory tracking and robust multi-objective regulation.
CommentsThesis submitted in partial fulfillment of the requirements for the Master of Sciences degree, The Department of Computer Science, The Faculty of Natural Sciences, Ben-Gurion University of the Negev, Israel
