Distributed Optimal Control for Consensus in Multi Agent Networked Systems Under Uncertainty

Abstract

Communication represents one of the main practical limitations in distributed multi-agent systems. While a consensus can potentially be rapidly reached through a constant information exchange, such a method may be unrealistic for wireless embedded robotic and sensor networks, where bandwidth and power are significantly limited. In this regard, event-triggered and self-triggered techniques have gained attention as noteworthy alternatives to the conventional periodic solution. Consider a probabilistic approach in the form of a state dependent Poisson process that triggers communication events. In lieu of displacing the theory of event-triggered control, a clever adaptive intensity is proposed that escalates as disagreement grows and tapers off as the nodes reach consensus. The adaptive communication mechanism is integrated with a linear consensus controller and modelled as a stochastic hybrid system with continuous plant dynamics and random sample-and-hold resets. To facilitate the connection between probabilistic communication and mean-square consensus, a quadratic stability method is used, whereas the expected number of communications acts as a measure of communication cost. Numerical research with five, 10, and 20 single-integrator agents are presented for a connected network with uncertain multiplicative parameters.A trade-off between performance and communication rate is demonstrated. For five agents, an increase of the minimum Poisson intensity from 0.2 to 3.0 reduces the integrated disagreement from 4.94 to 2.17 while raising the number of communication events from about 37 to 313. At a practical operating point with minimum intensity of one, the adaptive mechanism exhibits a final disagreement of about 2 × 10−4 with 120 communication events compared to about 245 events for a fixed intensity approach. The results indicate that adaptive Poisson communication effectively and significantly reduces the number of transmissions without a significant expense in performance, although the degree of reduction depends heavily on the minimum rate and number of agents. Thus, the proposed probabilistic communication mechanism is interpreted as an additional degree of freedom that can be tuned rather than a purely stochastic phenomenon.