Time-Varying Optimization-Based Approach for Distributed Formation of Uncertain Euler–Lagrange Systems

We investigate a distributed time-varying formation control problem for an uncertain Euler–Lagrange system. A time-varying optimization-based approach is proposed. Based on this approach, the robots can achieve the expected formation configuration and meanwhile optimize a global objective function using only neighboring and local information. We consider the time-varying optimization where the objective functions can change in real time. In this case, the consensus-based formation tracking control issues and formation containment tracking control issues in the literature can be solved by the proposed approach. By a penalty-based method, the robots’ states asymptotically converge to the estimated optimal solution to an equivalent time-varying optimization problem, whose optimal solution can achieve simultaneous formation and optimization. Furthermore, we consider two more general scenarios: 1) the local objective functions can have non-neighbor’s information and 2) the optimization problems can have inequality constraints.