Stabilization And Control Of Some Classes Of Networked Control Systems With Limited Information

Recently, the problem of control with limited information has attracted significant attentions. Unlike classical control problem, control with limited information concerns the impact of the capacity of a channel on the performance of systems. A natural question to ask is how much capacity is needed to achieve a specified control performance or estimation accuracy. Meanwhile, how to design a suitable quantizer (i.e. coder-decoder pair) and the controller is also a key issue. All most all research works in this regard concentrates on the works of regular plants for networked control systems (NCSs, for short) with limited information.In this dissertation, we have done in this regard for four different classes of problems as follows:1. stabilization and detection of a class of nonlinear discrete-time systems with limited information;2. synchronization of two identically chaotic systems coupled through a limited capacity communication channel (LCCC) for both continuous-time and discrete-time cases;3. feedback stabilization for linear singularly perturbed systems via a LCCC;4. model-based control of singularly perturbed networked control systems.Firstly, the stability of a class of discrete-time systems with Lipschitz nonlinearities via a LCCC is studied. A sufficient condition for the stabilization of the problem is presented in terms of linear matrix inequalities. A stabilizing coder-decoder-controller is constructed and the condition about the channel capacity is derived. In addition, a corollary is deduced with no input from the obtained result on detection for the discrete-time systems. Finally, one example is worked out to illustrate the efficiency and feasibility of the proposed approach. It is worthy to point out that an auxiliary system is introduced to overcome the difficulty when we extend the result of [64] from the continuous time to the discrete one.Secondly, the problem of synchronization of two identically chaotic systems coupled through a LCCC is addressed. Both the continuous-time and the discrete-time chaos systems are concerned.For the continuous chaos model, using the sampled and encoded information, an impulsive control designed is applied to the response system by resetting its initial state at the beginning of every sampling interval. A coder-decoder-controller is constructed and the condition about, the channel capacity is derived. Finally, the numerical simulation for the Chua's chaotic system is shown to illustrate the obtained result.On the other hand, a new control strategy is given for discrete-time chaos synchronization where the drive system and the response system are coupled via a LCCC. One condition about channel capacity is presented to ensure synchronization between the two chaotic systems coupled by a LCCC. Based on this condition, an explicit coder-decoder pair for the coding algorithm is designed. Finally, the proposed control strategy is applied to the well-known Hénon system and the hyperchaotic maps, respectively, and their numerical simulations illustrate the validity of the obtained result.Thirdly, the state feedback stabilization problems for singularly perturbed linear time-invariant systems (SPLSs for short) via a finite data rate channel using sampled and encoded states is discussed. Taking advantages of the decoupled form of SPLSs and the analysis of matrix perturbation we derive a requirement that defines a bound on the required data rate for the limited data rate network to achieve feedback stabilization. This bound is independent of the small parameter of SPLSs. Based on this requirement, a series of encoding functions and a stabilizing control strategy can be defined in an explicit way. Then, there exists a bound of the small parameter such that SPLSs can be exponentially stabilized under communication constraints by the proposed control strategy for all the small parameter within the desired bound.Finally, the state feedback control of the linear singularly perturbed plant is studied, where the sensor and the controller/actuator are connected via a network and the transmission frequency is constant. In terms of the model-based control, the model plant in the singularly perturbed system is added at the controller/actuator to stabilize the original singularly perturbed system with periodically updating its state by the actual state of the plant provided by the sensor. Moreover, under some certain conditions, independent of the small parameterε, the existence of the bound of the small parameterεis shown to guarantee the globally exponential stability of the whole closed-loop singularly perturbed system. In addition, a numerical simulation is shown to illustrate the results of the paper. Next, we extend our results to include the case where the transmission delay is present. A new error model is proposed and the response of the system is shown as well as the stability of the system is analyzed.In summary, inspired by the work of ([17]) based on observer, the synchronization of two identically chaotic systems with limited information has been successfully investigated. There have been a few works so far in this direction. For NCSs with the plant having singular perturbation structure, this is a first time to be addressed. We solve feedback stabilization of this problem. Moreover, we also extend the model-based approach, which is shown effective to reduce bandwidth restriction for NCSs with regular plant, to the case with plant that is SPLSs.