Distributed Optimization with Preserved Network Connectivity

Abstract

This chapter is concerned with the distributed optimization of a multi-agent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for high-quality information exchange among agents. However, sensing or communication capability is range limited, so it is impractical to simply make an assumption that network connectivity is preserved by default. To address this concern, a class of generalized potentials including discontinuities caused by unexpected obstacles or noises are designed. For a class of quadratic cost functions, based on the potentials, a distributed protocol is proposed to formally guarantee the network connectivity over time and to realize the state agreement in a finite time while the sum of local functions known to individual agents is optimized. Since the right-hand side of the proposed protocol is discontinuous, some non-smooth analysis tools are applied to analyze the system performance. In some practical scenarios, where initial states are unavailable, a distributed protocol is further developed to realize the consensus in a fixed time while solving the distributed optimization problem and maintaining the network connectivity.