Investigation On Dynamical Systems With Stochastic Time Delays: Analysis And Design Of Networked Control Systems

Feedback control system wherein the control loop is closed through a real-time net-work is known as a networked control system (NCS). In the NCS, the insertion of thecommunication networks definitely always lead to some unavoidable phenomena duringthe data transmission, such as network-induced time delays, data packet dropouts and dis-order, quantization and communication constraints, etc. The network-induced delays anddata packet dropouts play a key role in deterioration of the system performance and some-times can even destabilize the NCS. Limited network bandwidth resource and unreliabil-ity of the data transmission make the time delays and packet dropouts unpredictable andrandom. Furthermore, the stochastic character and complexity of the network-inducedtime delays and data packet dropouts have transformed the real NCS to a complicatedstochastic control system and conventional control theories are not applicable to the NCS.Although the NCS has many advantages such as easy installation, less wiring, easyto extend and maintain, resource sharing and remote control, together with wide appli-cations in practice, the network-induced problems can’t be ignored, which can make theNCS collapse and even cause huge economic losses. Therefore, to investigate intensive-ly the randomness of the communication time delays and packet dropouts, to establisha more real and accurate model for the NCS with time delays and packet dropouts, andto find the reasonable control strategies for the proposed NCS are the primary researchwork. Furthermore, it is meaningful and practical to derive the novel ideas and approach-es for the system analysis and control design aiming at the features of the NCS, and toinvestigate the advanced control strategies suitable for the network environment, whichare also our present research work. The work of this thesis is summarized as follows:Chapter2and Chapter3investigate the stability analysis of the stochastic time delaysystems. To be specific, Chapter2is concerned with the stability analysis of neural net-works with distributed and probabilistic delays. The probabilistic delay satisfies certainprobability distribution. By introducing a stochastic variable with Bernoulli distribution,the neural network with random time delays is transformed into one with deterministicdelays and stochastic parameters. New conditions for the exponential stability of suchneural networks are obtained by employing new Lyapunov-Krasovskii functionals andnovel techniques for achieving delay dependence. The proposed conditions reduce the conservatism by considering not only the range of the time delays, but also the probabilitydistribution of their variation. On the other hand, Chapter3addresses the stability analysisproblem for stochastic neural networks with discrete interval and distributed time-varyingdelays. The interval time-varying delay is assumed to satisfy0<d1≤d(t)≤d2and isdescribed as d(t)=d1+h(t) with0≤h(t)≤d2d1. Based on the idea of partitioningthe lower bound d1, new delay-dependent stability criteria are presented by constructing anovel Lyapunov-Krasovskii functional, which can guarantee the new stability conditionsto be less conservative than those in the literature.Chapter4deals with the problem of feedback control for networked systems withdiscrete and distributed delays subject to quantization and packet dropout. Both a statefeedback controller and observer-based output feedback controller are designed. The infi-nite distributed delay is introduced in the discrete networked domain. Also, it is assumedthat system state or output signal is quantized before being communicated. Moreover,a compensation scheme is proposed to deal with the efect of random packet dropoutthrough communication network. Sufcient conditions for the existence of an admissiblecontroller are established to ensure the asymptotical stability of the resulting closed-loopsystem.Chapter5and6study the problem of predictive output feedback control for net-worked control systems with random communication delays and packet dropouts. Chapter5only considers the case that the networked-induced delays exist in the feedback channelwhile the Chapter6investigates the case that the networked-induced delays exist in boththe feedback channel and the forward channel. A networked predictive control schemeis employed to compensate for random communication delays, which mainly consists ofthe control prediction generator and network delay compensator. Furthermore, a new s-trategy of designing the time-varying predictive controller with mixed random delays fornetworked systems is proposed. Then the system can be formulated as a Markovian jumpsystem. New techniques are presented to deal with the distributed delay in the discrete-time domain. Based on analysis of closed-loop networked predictive control systems, thedesigned predictive time-varying output feedback controller can achieve the desired con-trol performance and also guarantee system stability.In Chapter7, a new class of discrete-time networked nonlinear systems with mixedrandom delays and packet dropouts are introduced, and the H_∞filtering problem for suchsystems is investigated. The mixed stochastic time delays consist of both discrete and infinite distributed delays and the packet dropout phenomenon occurs in a random way,which are all modeled by mutually independent Bernoulli distributed random variables.Furthermore, new techniques are presented to deal with the infinite distributed delay inthe discrete-time domain. Sufcient conditions for the existence of an admissible filterare established, which ensure the asymptotical stability as well as a prescribed H_∞perfor-mance.