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This paper investigates the interaction between control and communications in networked systems by studying a class of stochastic approximation algorithms that accommodate random network topology switching processes, time-varying functions, nonlinear dynamics, additive and nonadditive noises, and other uncertainties. Interaction among control strategy and the multiple stochastic processes introduces critical challenges in such problems. By modeling the random switching as a discrete-time Markov chain and studying multiple stochastic uncertainties in a unified framework, it is shown that under broad conditions, the algorithms are convergent. The performance of the algorithms is further analyzed by establishing their rate of convergence and asymptotic characterizations. Simulation case studies are conducted to evaluate the performance of the procedures in various aspects. [ABSTRACT FROM AUTHOR]

Consensus conditions and convergence speeds are crucial for distributed consensus algorithms of networked systems. Based on a basic first-order average-consensus protocol with time-varying topologies and additive noises, this paper first investigates its critical consensus condition on network topology by stochastic approximation frameworks. A new joint-connectivity condition called extensible joint-connectivity that contains a parameter $\delta$ (termed the extensible exponent) is proposed. With this and a balanced topology condition, we show that a critical value of \delta$ for consensus is 1/2$ . Optimization on convergence rate of this protocol is further investigated. It is proved that the fastest convergence rate, which is the theoretic optimal rate among all controls, is of the order 1/t for the worst topologies, which are balanced and satisfy the extensible joint-connectivity condition. For practical implementation, certain open-loop control strategies are introduced to achieve consensus with a convergence rate of the same order as the fastest convergence rate. Furthermore, a consensus condition is derived for nonstationary and strongly correlated random topologies. The algorithms and consensus conditions are applied to distributed consensus computation of mobile ad-hoc networks; and their related critical exponents are derived from relative velocities of mobile agents for guaranteeing consensus. [ABSTRACT FROM PUBLISHER]