Distributed continuous-time algorithm for time-varying optimization with affine formation constraints and application

In this paper, we study a distributed continuous-time optimization problem with affine formation constraints and time-varying cost functions. The solution objective of the problem is to minimize the joint cost function with affine formation constraints and time-varying safety constraints, and the joint cost function consists of local cost functions known only to each intelligence itself. By designing a distributed gradient tracking algorithm, a general form of the problem is solved, and to address the existing problem of discontinuous local cost functions due to obstacles in the unknown environment and the obstacles to the realization of the system for cooperative tracking, an approximate continuous time function and a time-varying positional convergence function are introduced into the design of the local cost function to solve the above problem. By introducing the convergence coefficient of the algorithm, the convergence speed of the estimated solution to the optimal solution is improved. By analyzing the convergence of the designed algorithm, it is proved that the tracking error of the estimated solution to the optimal solution will disappear exponentially and will eventually converge to the domain of the local moving target. The effectiveness of the proposed algorithm is simulated and physically verified by designing and applying a distributed multi-intelligence system framework. © 2024 Chinese Academy of Sciences. All rights reserved.