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

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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.