An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

On controllability of neuronal networks with constraints on the average of control gains

Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently

Stochastic Leader-Following for Heterogeneous Linear Agents with Communication Delays

We study the leader-following problem for linear stochastic multi-agent systems with uniform and constant communication delays on directed or undirected graphs. We consider both the state feedback and output feedback solutions. In the latter case, the agents can be a set of heterogeneous linear systems. By resorting to a new approach based on the scalar Lambert equation we obtain a constructive design with less conservative closed-form delay bounds. In particular, it is possible to compensate arbitrarily large delays if the agents are not unstable

Control of Multiagent Systems: A Stochastic Pinning Viewpoint

A stochastic pinning approach for multiagent systems is developed, which guarantees such systems being almost surely stable. It is seen that the pinning is closely related to being a Bernoulli variable. It has been proved for the first time that a series of systems can be stabilized by a Brownian noise perturbation in terms of a pinning scheme. A new terminology named “stochastic pinning control” is introduced to describe the given pinning algorithm. Additionally, two general cases that the expectation of the Bernoulli variable with bounded uncertainty or being unknown are studied. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed methods

Formation Control with Unknown Directions and General Coupling Coefficients

Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling coefficients. However, the direction may be unknown in the sensing processes, and the coupling coefficients may also involve negative ones due to some circumstances. This paper introduces these phenomena into a class of displacement-based formation control problem. Then, a geometric approach have been employed to overcome the difficulty of analysis on the introduced phenomena. The purpose of this approach is to construct some convex polytopes for containing the effects caused by the unknown direction, and to analyze the non-convexity by admitting the negative coupling coefficients in a certain range. Under the actions of these phenomena, the constructed polytopes are shown to be invariant in view of the contractive set method. It means that the convergence of formation shape can be guaranteed. Subsequently, an example is given to examine the applicability of derived result