Distributed Time-Varying Quadratic Optimal Resource Allocation Subject to Nonidentical Time-Varying Hessians With Application to Multiquadrotor Hose Transportation

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 52; no. 10; pp. 6109 - 6119
• Main Authors: Wang, Bo, Sun, Shan, Ren, Wei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Continuous-time algorithm; Cost function; distributed control; Equality; Heuristic algorithms; Multiagent systems; optimal resource allocation; Optimization; Quadratic forms; Resource allocation; Resource management; Rotary wing aircraft; time-varying system; Time-varying systems; Trajectory; Trajectory optimization; Transportation; Transportation problem
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2021.3137814

This article considers the distributed time-varying optimal resource allocation problem with time-varying quadratic cost functions and a time-varying coupled equality constraint for multiagent systems. The objective is to design a distributed algorithm for agents with single-integrator dynamics to cooperatively satisfy the coupled equality constraint and minimize the sum of all local cost functions. Here, both the coupled equality constraint and cost functions depend explicitly on time. The cost functions are in quadratic form and may have nonidentical time-varying Hessians. To solve the problem in a distributed manner, an estimator based on the distributed average tracking method is first developed for each agent to estimate certain global information. By leveraging the estimated global information and an adaptive gain scheme, a distributed continuous-time algorithm is proposed, which ensures the agents to find and track the time-varying optimal trajectories with vanishing errors. We illustrate the applicability of the proposed method in the optimal hose transportation problem using multiple quadrotors.