Modeling, Control And Optimization For Network Control Systems

In the closed-loop feedback systems, control nodes (sensor, controller and actuator nodes) are distributed and connected over a network medium, which are called networked control systems (NCSs). In contrast to the traditional control systems, networked control systems have many advantages such as resource sharing, long-distance operation, less time and easy maintenance, etc. Communication networks have been increasingly employed to exchange information and control signals in modern industry and business fields, and networked control systems have acted on important role and increasingly become a hot research topic. However, insertion of the network, it is inevitable that network-induced delay, packet dropout, packet disordering and other unideal facts exist in NCSs, which will inevitably degrade performance of the control systems or even case the control systems unstable, such that the analysis and design of the control systems become complex and the new challenges to networked control systems have been arisen.Recently, a wide range of research has been reported dealing with problems related to the network-induced delay and packet dropout. However, it should be noted that many issues, such as input constraints, packet dropout compensation, packet disordering-based analysis and control and controllability and observability for NCSs, have not been fully investigated to date. To the best of the author’s knowledge, as for the stability analysis and controller design based on graph theory approach, no results have been available in the literature so far. In this paper, aiming at the aforementioned issues, modeling, control and optimization of NCSs are investigated in terms of the existing results in Lyapunov stability theory, stochastic theory and graph theory under fully considering the unideal facts in NCSs.(1) Controllability and observability of NCSs are investigated. The linear time-invariant system through network is modeled as a discrete time-varying delay system. Based on it, a sufficient and necessary condition for complete controllability of NCSs is presented. Based on Markov characteristic of network-induced delay, a sufficient and necessary condition for completely mean value controllability of NCSs is obtained. Furthermore, the relation between controllability and observability of NCSs and those of the initial time-invariant systems and controllability (observability) realization index are discussed, respectively.(2) Stability analysis and control of NCSs graph theory-based approach are presented. Aiming at the nonlinear networked control systems, a new criterion on stability is presented. Considering the existence of time-varying delay in the network, based on Lyapunov method and graph theory, the sufficient conditions for asymptotic stability of nonlinear discrete-time and nonlinear continuous-time networked control systems are given, respectively. The maximum allowable delay bounds that can preserve stability of the two classes of systems are obtained, respectively. Further, the controller design methods are presented; Aiming at the NCSs with bounded delay and data packet dropout, interval stability of the NCSs is investigated. Based on weighted diagraph theory in graph theory and spectral characterizations of interval matrices, the graphic conditions for interval stability of NCSs are presented. By using the algorithm designed in this dissertation, the feedback controller gains are obtained. Moreover, under the same delay and data packet dropout, several controller gains can be obtained, simultaneously, which will make that NCSs are controlled better.(3) Modeling, control and optimization of NCSs with packet disordering are investigated. A new mathematical model of NCSs is proposed, which can fully describe the phenomenon of packet disordering in NCSs and effectively eliminate the impact of packet disordering on the performance of NCSs. To obtain controller easily, this model is converted into a parameter-uncertain discrete-time system with multi-step delay based on matrix theory. A sufficient condition for robust stability of NCSs is presented. Linear matrix inequality approach has been employed to solve controller design problems; To obtain less conservative results, an improved Lyapunov-Krasovskii functional, which makes use of not only information of both the lower and upper bounds of the time-varying network-induced delay but also many different combinations of state and delayed states in the quadratic form just by introducing matrix Ri and Si (i=1,2,…,h), is proposed, the sufficient conditions for stabilization and H∞control are driven. By solving a minimization problem based on linear matrix inequalities, H∞controller is obtained.(4) Modeling of NCSs with network-induced delay and packet dropout and control and optimization of NCSs with input constraints are studied. Aiming at the long delay (network-induced delay longer than one sampling period), packet dropout and white noise, based on fixed data packet dropout rates and bounded delay, the NCS is modeled as an asynchronous dynamical-switched system constrained by configuration event rates; Based on Lyapunov method, a sufficient condition for robust stability of NCSs with saturated non-linear constraints is presented. Based on it, the sufficient conditions forγsuboptimal and optimal robust H∞control are obtained, respectively. Moreover, the optimal H∞output feedback control law is driven.(5) H∞control of NCSs with packet dropout compensation is investigated. A model of NCSs without packet dropout compensation is established, the condition for asymptotical stability of NCSs is analyzed. To reduce packet dropout effect on the systems, a model of NCS with long delays and dropout compensator is constructed. Based on this model, the sufficient condition for asymptotical stability of the system is presented. Moreover, a convex optimization problem with LMIs constraint is formulated to design the H∞optimal controllers. To the same example, the simulation shows the result of the NCSs with packet dropout compensation is better than that of the systems without packet dropout compensation. Further, the state observer is designed, NCSs with long delays and dropout compensator is modeled as the Markov jumping system, the sufficient condition for stochastic stability with H∞norm bound y is presented, the feedback control law LMI-based method is obtained.