具有仿射形成约束的分布式连续时间优化算法与应用

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

本文研究了一种具有仿射形成约束与时变代价函数的分布式连续时间优化问题.该问题的求解目标是最小化带有仿射形成约束与时变安全约束的联合代价函数,且该联合代价函数由仅被各智能体自身所知晓的局部代价函数构成.通过设计分布式梯度跟踪算法,求解了该问题的一般形式,并针对现存的由未知环境中障碍物所致的局部代价函数不连续与阻碍系统实现协同跟踪的问题,在局部代价函数设计中引入了近似连续时间函数与时变位置收敛函数以解决上述问题.通过引入算法收敛系数,提升了估计解对最优解的收敛速度.通过对所设计算法的收敛性分析,证明了估计解对最优解的跟踪误差将以指数级消失,且将最终收敛至局部移动目标的领域内.通过设计并应用了分布式多智能体系统框架,对所提出的算法的有效性进行了仿真与实物验证.

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 timevarying 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.