Time-delayed impulsive control for discrete-time nonlinear systems with actuator saturation

This paper focuses on the problem of time-delayed impulsive control with actuator saturation for discrete-time dynamical systems. By establishing a delayed impulsive difference inequality, combining with convex analysis and inequality techniques, some sufficient conditions are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed impulsive controller with actuator saturation. The designed controller admits the existence of some transmission delays in impulsive feedback law, and the control input variables are required to stay within an availability zone. Several numerical simulations are also given to demonstrate the effectiveness of the proposed results.&nbsp

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

Asynchronous Networks and Event Driven Dynamics

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks

Adaptive Control of Dynamically Complex Networks with Saturation Couplings

This paper considers the control problem of dynamically complex networks with saturation couplings. Two novel control schemes in terms of adaptive control are presented to deal with such saturation couplings. Based on the robust idea, the underlying complex network is firstly transformed into a strongly connected network having time-varying uncertainty. However, the upper bound of uncertainty is unknown. Because of such an unavailable bound, a kind of adaptive controller added to each node is proposed such that the closed-loop auxiliary network is uniformly bounded. In particular, the original system states are asymptotically stable. Moreover, in order to avoid adding the desired controller to every node, another different kind of adaptive controller based on the pinning control idea is proposed. Compared with the former method, it is only applied to a part of nodes and has a good operability. Finally, a numerical example is provided to show the effectiveness of our results