Proximal Gradient Algorithm for Optimal formation Control of Continuous-Time Multi-Agent Systems

A distributed proximal gradient algorithm is proposed in this paper to solve the linear quadratic formation control problem of continuous-time multi-agent systems. Similar to [1], an auxiliary variable is introduced to describe the reference point of formation, which is one of the optimization objectives, and a nonseparable multi-objective optimization problem is formulated. Applying the alternating proximal gradient method of multipliers, the solution to optimal formation control problem is turned into dealing with one simple optimal tracking control problem and two matrix algebraic operation steps alternatively, which saves a lot of computation resources. Numerical examples of homogenous systems, heterogeneous systems and wheeled vehicles are provided to demonstrate the efficiency of the proposed algorithm.