Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays

This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the signal, and delays may occur during transmission. These uncertainties are commonly described by means of independent Bernoulli random variables. In the present paper, the model is generalised in two directions: (i) at each sensor, the degradation in the measurements is modelled by sequences of random variables with arbitrary distribution over the interval [0, 1]; (ii) transmission delays are described using three-state homogeneous Markov chains (Markovian delays), thus modelling dependence at different sampling times. Assuming that the measurement noises are correlated and cross-correlated at both simultaneous and consecutive sampling times, and that the evolution of the signal process is unknown, we address the problem of signal estimation in terms of covariances, using the following distributed fusion method. First, the local filtering and fixed-point smoothing algorithms are obtained by an innovation approach. Then, the corresponding distributed fusion estimators are obtained as a matrix-weighted linear combination of the local ones, using the mean squared error as the criterion of optimality. Finally, the efficiency of the algorithms obtained, measured by estimation error covariance matrices, is shown by a numerical simulation example.Ministerio de Economía, Industria y CompetitividadEuropean Union (EU) MTM2017-84199-PAgencia Estatal de Investigació

Distributed Stochastic Subgradient Optimization Algorithms Over Random and Noisy Networks

We study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a communication link. We consider the distributed subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes. By stochastic Lyapunov method, convex analysis, algebraic graph theory and martingale convergence theory, it is proved that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely