Distributed Continuous-time Optimization for Multi-agent Dynamical Systems under Realistic Challenges

分布式运动协调，其中多个代理实现集体运动模式只有本地信息和交互，有许多应用。尽管协作优化具有重要作用，但现有的分布式运动协调研究成果很少对团队目标函数进行优化，而分布式优化研究（主要是离散时间算法）没有明确考虑连续时间的物理动力学。分布式连续时间优化对于使多个物理智能体仅在局部信息和交互下协同实现运动协调和团队优化具有重要意义。尽管最近在分布式连续时间优化方面取得了一些成果，但它们相当有限，对凸目标函数提出了限制性假设，没有解决现实挑战，即i)完全分布式设计，ii)有限时间收敛，iii)时变目标函数，以及iv)物理代理动力学。特殊的假设限制了应用领域，而现实的挑战分别与以下方面相关：i)分布式算法的实际实现，ii)时间关键型任务，iii)要求对实时变化做出响应的应用，以及iv)真实的物理系统。尽管它们具有相关性和重要性，但上述每个问题在很大程度上都未被探索，更不用说它们的组合了。提出的研究旨在解决这些现实挑战。涉及多智能体系统以及与优化和网络系统相关领域的众多民用、国土安全和军事应用将从拟议的研究中受益。该项目的目标是在现实挑战下，结合一般凸函数和有向图，解决具有局部信息和交互的物理代理的分布式连续时间优化问题。该方案包括5个重点，即1)全分布连续时间优化，2)有限时间分布连续时间优化，3)目标函数时变分布连续时间优化，4)物理agent动力学分布连续时间优化，5)实验验证。在推力1中，PI将设计和分析新的自适应全分布式优化算法，该算法对拓扑变化和团队中代理的添加/移除具有鲁棒性，并且具有状态依赖性递减收益。在推力2中，PI将通过将分布式跟踪和估计与开关机制驱动的自适应增益相结合，设计和分析新的无约束/有约束的有限时间全分布式优化算法。在推力3中，PI将解决时变目标函数变化率的宽松条件，不存在Hessians，以及局部目标函数的不完全知识等问题。在推力4中，PI将设计和分析新的分布式优化算法，考虑拉格朗日和更一般的未知非线性动力学。在推力5中，来自推力1-4的分布式控制法则将在自主机器人团队中进行实验验证。该项目将解决分布式控制和优化中的许多开放性问题，对多智能体系统的理论和应用具有重要的推动作用。

Distributed motion coordination, where multiple agents achieve collective motion patterns with only local information and interaction, has numerous applications. Despite the important role of cooperative optimization, existing results on distributed motion coordination seldom optimize a team objective function while those on distributed optimization (primarily discrete-time algorithms) do not explicitly account for continuous-time physical dynamics. Distributed continuous-time optimization is of great significance in enabling multiple physical agents to cooperatively achieve motion coordination and team optimization with only local information and interaction. Despite a few recent results on distributed continuous-time optimization, they are rather limited, with restrictive assumptions posed on convex objective functions and not addressing realistic challenges, namely, i) fully distributed design, ii) finite-time convergence, iii) time-varying objective functions, and iv) physical agent dynamics. The special assumptions limit the application domains while the realistic challenges are relevant in, respectively, i) real-world implementation of distributed algorithms, ii) time-critical missions, iii) applications demanding response to real-time changes, and iv) real physical systems. Despite their relevance and importance, each of the above issues is largely unexplored, not to mention a combination. The proposed research aims at addressing these realistic challenges. Numerous civilian, homeland security, and military applications involving multi-agent systems and fields related to optimization and networked systems will benefit from the proposed research.The goal of this project is to address distributed continuous-time optimization for physical agents with local information and interaction under realistic challenges, coupled with general convex functions and directed graphs. The proposal consists five thrusts, namely, 1) fully distributed continuous-time optimization, 2) finite-time distributed continuous-time optimization, 3) distributed continuous-time optimization with time-varying objective functions, 4) distributed continuous-time optimization with physical agent dynamics, and 5) experimental validation. In Thrust 1, the PI will design and analyze novel self-adaptive fully distributed optimization algorithms, robust to topology changes and addition/removal of agents in the team, with state-dependent diminishing gains. In Thrust 2, the PI will design and analyze novel finite-time fully distributed optimization algorithms without/with constraints by combining distributed tracking and estimation with adaptive gains driven by a switching mechanism. In Thrust 3, the PI will tackle issues such as relaxed conditions on changing rates of time-varying objective functions, non-existence of Hessians, and incomplete knowledge of local objective functions. In Thrust 4, the PI will design and analyze novel distributed optimization algorithms accounting for Lagrange and more general unknown nonlinear dynamics. In Thrust 5, distributed control laws from Thrusts 1-4 will be experimentally validated on teams of autonomous robots. The project will solve many open problems in distributed control and optimization and significantly advance theory and applications in multi-agent systems.