Distributed Parametric Consensus Optimization With an Application to Model Predictive Consensus Problem

In this paper, we study a special class of distributed convex optimization problems-distributed parametric consensus optimization problem (DPCOP), for which a two-stage optimization method including primal decomposition and distributed consensus is provided. Different from traditional distributed optimization problems driving all the local states to a common value, DPCOP aims to solve a system-wide problem with partial common parameters shared amongst local agents in a distributed way. To relax the restriction on the topology, a distributed projected subgradient method is applied in distributed consensus stage to achieve the consensus of local estimated parameters, while the subgradients can be obtained by solving a multiparametric problem locally. For a special class of DPCOPs, a discrete-time distributed algorithm with exponential rate of convergence is provided. Furthermore, the proposed two-stage optimization method is applied to a distributed model predictive consensus problem in order to reach an optimal output consensus at equilibrium points for all agents. The stability analysis for the proposed algorithm is further given. Two case studies on a heterogeneous multiagent system with high-order integrator dynamics are provided to verify the effectiveness of proposed methods.