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的运动模式，只有本地信息和交互，有许多应用。尽管合作优化的重要作用，分布式运动协调的现有成果很少优化团队的目标函数，而那些分布式优化（主要是离散时间算法）不明确占连续时间的物理动力学。分布式连续时间优化对于多个物理智能体仅利用局部信息和交互就能协同实现运动协调和团队优化具有重要意义。尽管最近有一些关于分布式连续时间优化的结果，但它们相当有限，对凸目标函数提出了限制性假设，并且没有解决现实挑战，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）物理代理动态。特殊的假设限制了应用领域，而现实的挑战是相关的，分别在，i）分布式算法的真实世界的实现，ii）时间关键的任务，iii）应用程序要求响应实时变化，和iv）真实的物理系统。尽管它们的相关性和重要性，上述每一个问题基本上都没有得到探讨，更不用说组合了。拟议的研究旨在解决这些现实的挑战。许多民用，国土安全，军事应用涉及多智能体系统和优化和网络系统相关领域将受益于拟议的研究。本项目的目标是解决分布式连续时间优化的物理代理与本地信息和现实的挑战下的互动，再加上一般凸函数和有向图。该建议包括五个方面，即1）完全分布式连续时间优化，2）有限时间分布式连续时间优化，3）时变目标函数的分布式连续时间优化，4）物理代理动力学的分布式连续时间优化，以及5）实验验证。在Thrust 1中，PI将设计和分析新的自适应全分布式优化算法，对拓扑结构的变化和团队中代理的添加/删除具有鲁棒性，并具有依赖于状态的递减增益。在Thrust 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，设计和分析新的有限时间全分布式优化算法，无/有约束。在Thrust 3中，PI将解决诸如时变目标函数变化率的宽松条件、Hessian不存在以及局部目标函数的不完整知识等问题。在第4阶段，PI将设计和分析新的分布式优化算法，以解决拉格朗日和更一般的未知非线性动态问题。在Thrust 5中，Thrust 1-4的分布式控制律将在自主机器人团队上进行实验验证。该项目将解决分布式控制和优化中的许多开放问题，并显着推进多智能体系统的理论和应用。

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.