Event-Triggered Communication and Data Rate Constraint for Distributed Optimization of Multiagent Systems

This paper is concerned with solving a large category of convex optimization problems using a group of agents, each only being accessible to its individual convex cost function. The optimization problems are modeled as minimizing the sum of all the agents' cost functions. The communication process between agents is described by a sequence of time-varying yet balanced directed graphs which are assumed to be uniformly strongly connected. Taking into account the fact that the communication channel bandwidth is limited, for each agent we introduce a vector-valued quantizer with finite quantization levels to preprocess the information to be exchanged. We exploit an event-triggered broadcasting technique to guide information exchange, further reducing the communication cost of the network. By jointly designing the dynamic event-triggered encoding-decoding schemes and the event-triggered sampling rules (to analytically determine the sampling time instant sequence for each agent), a distributed subgradient descent algorithm with constrained information exchange is proposed. By selecting the appropriate quantization levels, all the agents' states asymptotically converge to a consensus value which is also the optimal solution to the optimization problem, without committing saturation of all the quantizers. We find that one bit of information exchange across each connected channel can guarantee that the optimiztion problem can be exactly solved. Theoretical analysis shows that the event-triggered subgradient descent algorithm with constrained data rate of networks converges at the rate of {O}( {\ln t/{\sqrt {t}}}) . We supply a numerical simulation experiment to demonstrate the effectiveness of the proposed algorithm and to validate the correctness of theoretical results.