Distributed Algorithms for Linearly-Solvable Optimal Control in Networked Multi-Agent Systems
This work addresses control challenges in networked multi-agent systems, offering a distributed approach that is incremental by building on existing linearly-solvable optimal control methods.
The paper tackles distributed optimal control for networked multi-agent systems by partitioning the problem into local subsystems, preserving correlations while reducing communication and computational costs. It achieves this through linear equation solutions for discrete-time systems and approximations for continuous-time systems, with examples in cooperative UAV teams demonstrating effectiveness.
Distributed algorithms for both discrete-time and continuous-time linearly solvable optimal control (LSOC) problems of networked multi-agent systems (MASs) are investigated in this paper. A distributed framework is proposed to partition the optimal control problem of a networked MAS into several local optimal control problems in factorial subsystems, such that each (central) agent behaves optimally to minimize the joint cost function of a subsystem that comprises a central agent and its neighboring agents, and the local control actions (policies) only rely on the knowledge of local observations. Under this framework, we not only preserve the correlations between neighboring agents, but moderate the communication and computational complexities by decentralizing the sampling and computational processes over the network. For discrete-time systems modeled by Markov decision processes, the joint Bellman equation of each subsystem is transformed into a system of linear equations and solved using parallel programming. For continuous-time systems modeled by Itô diffusion processes, the joint optimality equation of each subsystem is converted into a linear partial differential equation, whose solution is approximated by a path integral formulation and a sample-efficient relative entropy policy search algorithm, respectively. The learned control policies are generalized to solve the unlearned tasks by resorting to the compositionality principle, and illustrative examples of cooperative UAV teams are provided to verify the effectiveness and advantages of these algorithms.