Tianguang Chu

Stabilization of networked control systems with data packet dropout and network delays via switching system approach

An iterative approach is proposed to model networked control systems (NCSs) with arbitrary but finite data packet dropout. as switched linear systems. This enables us to apply the rich theory of switched systems to analyzing such NCSs. Sufficient conditions are presented on the stability and stabilization of NCSs with packet dropout and network delays. Stabilizing state/output feedback controllers can be constructed by using the feasible solutions of some linear matrix inequalities. The merit of the iterative approach is that the controllers can make full use of the previous information to stabilize NCSs when the current state measurements can not be transmitted by the network channel instantly. A simulation example is worked out to illustrate the effectiveness of the proposed approach.

Controllability of a Leader–Follower Dynamic Network With Switching Topology

This note studies the controllability of a leader-follower network of dynamic agents linked via neighbor rules. The leader is a particular agent acting as an external input to steer the other member agents. Based on switched control system theory, we derive a simple controllability condition for the network with switching topology, which indicates that the controllability of the whole network does not need to rely on that of the network for every specific topology. This merit provides convenience and flexibility in design and application of multiagent networks. For the fixed topology case, we show that the network is uncontrollable whenever the leader has an unbiased action on every member, regardless of the connectivity of the members themselves. This gives new insight into the relation between the controllability and the connectivity of the leader-follower network. We also give a formula for formation control of the network.

An LMI approach to networked control systems with data packet dropout and transmission delays

The problem of data packet dropout and transmission delays induced by communication channel in networked control systems (NCSs) in both continuous-time case and discrete-time case is studied in this paper. We model the NCSs with data packet dropout and delays as ordinary linear systems with input delays and this enables us to apply the rich theory of delay systems to analysis and design of such NCSs. For the continuous-time case, our technique is based on Lyapunov-Razumikhin function method. For the discrete-time case, we use the Lyapunov-Krasovskii based method. Attention is focused on the design of memoryless state feedback controllers that guarantee stability of the closed-loop systems. We present the admissible bounds of data packet loss and of delays in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed approach.

Stabilization of Networked Control Systems with Data Packet Dropout and Transmission Delays: Continuous-Time Case

The problem of data packet dropout and transmission delays induced by communication channel in networked control systems (NCSs) is studied in this paper. We model the continuous-time NCSs with data packet dropout and transmission delays as ordinary linear systems with time-varying input delays. By using the Lyapunov–Razumikhin function techniques, delaydependent condition on the stabilization of NCSs is obtained in terms of linear matrix inequalities (LMIs). Stabilizing state feedback controllers can then be constructed by using the feasible solutions of some LMIs. The admissible upper bounds of data packet loss and delays can be computed by using the quasi-convex optimization algorithm. Numerical examples illustrate the effectiveness of the proposed approach.

State Feedback Stabilization for Boolean Control Networks

State feedback stabilization for Boolean control networks is investigated in this technical note. Based on the algebraic representation of logical dynamics in terms of the semi-tensor product of matrices, a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller, and a general control design approach is proposed when global stabilization is feasible via state feedback. Instead of designing the logical form of a stabilizing feedback law directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. An example is worked out to illustrate the proposed design procedure.

Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoners dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoners dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.

Controller design for disturbance decoupling of Boolean control networks

We investigate a type of disturbance decoupling problem (DDP) of Boolean control networks. Using the semi-tensor product of matrices, the dynamics of a Boolean control network is expressed in its algebraic form. Under the framework of output-friendly subspace, we give a necessary and sufficient condition for the solvability of DDP by analyzing the redundant variables, and we present a computationally feasible method to construct all the valid feedback control matrices. The logical functions of each controller can be recovered from the obtained feedback control matrix. Finally, an example is provided to show the effectiveness of the proposed method.

Stabilization of networked control systems with data packet dropout via switched system approach

The problem of stabilization of networked control systems (NCSs) with data packet dropout is studied. Sufficient conditions are presented on the stability and stabilization of the NCSs with packet dropout. The novelty of this work lies in that NCSs with arbitrary but finite data packet dropout are modelled as switched linear systems, and this enables us to apply the result of switched systems to the analysis and synthesis of such NCSs. The admissible upper bound of the dropped packets can be determined by a set of linear matrix inequalities (LMIs) which guarantee the stability of the NCSs. Stabilizing controllers (via state feedback and static output feedback) can be constructed by solving a set of LMIs. Also, for an NCS with a convergence rate constraint, similar results are obtained. Examples are worked out to illustrate the effectiveness of the proposed method

Flocking of multi-agent systems with a dynamic virtual leader

This paper considers the flocking problem of a group of autonomous agents moving in Euclidean space with a virtual leader. We investigate the dynamic properties of the group for the case where the state of the virtual leader may be time-varying and the topology of the neighbouring relations between agents is dynamic. To track such a leader, we introduce a set of switching control laws that enable the entire group to generate the desired stable flocking motion. The control law acting on each agent relies on the state information of its neighbouring agents and the external reference signal (or ‘virtual leader’). Then we prove that, if the acceleration of the virtual leader is known, then each agent can follow the virtual leader, and the convergence rate of the centre of mass (CoM) can be estimated; if the acceleration is unknown, then the velocities of all agents asymptotically approach the velocity of the CoM, thus the flocking motion can be obtained. However, in this case, the final velocity of the group may not be equal to the desired velocity. Numerical simulations are worked out to illustrate our theoretical results.

An exponential convergence estimate for analog neural networks with delay

Abstract A componentwise estimate of exponential convergence is obtained for a class of delayed Hopfield type neural networks by using a method based on a comparison principle of delay differential systems. The method is simple and straightforward in analysis, without resorting to any Lyapunov functionals. The result shows explicitly the effect of time delay on exponential decay rate of the networks and is of practical significance for designing fast and stable neural networks. Some existing results via Lyapunov functional method and linear analysis are found to be special cases of the present result.