Research On The Quantized Feedback Control Strategies

Based on Lyapunov theory and logarithmic quantizer, we study the quantized feedback stabilization problem of systems under uniform sampling. In the thesis, we first summarize the background, meanings and developments of the quantized control problem of networked control systems. Then, we study how the quantizer and quantization density affect the stability of the system. At the same time, we give a classification and comparison of the existing quantization methods and feedback control strategies, and summarize the ideas and implementation steps of two effective quantization methods and feedback control strategies. Finally, we consider a new stability analysis method of networked control systems under several quantization situations. The main contents of this thesis are composed of the following three parts:(I) The stability analysis of the feedback control system under state quantizationIn this part, the stabilization problem of quantized feedback control is stud-ied under limited information about state. The relationship among quantization density, sampling period and system transformation matrix is given, which should be satisfied when the corresponding closed-loop system is globally asymptotically stable. Innovations of this part are as follows:(1) Different from the existing literatures, using the logarithmic quantizer and the stabilizing control law taking the form of a certainty equivalence feedback, we achieve the global asymptotic stability of the system. (2) The condition making the closed-loop system globally asymptotically stable reflects the effect of the quantizer and quantization density on stability of the system.(II) The stability analysis of the feedback control system under output quantizationIn this part, the stabilization problem of quantized feedback control is studied under limited information about output. By finding a suitable quantized feedback control strategy, making appropriate disposal for the values of output at sampling times and skillfully using some inequations about the matrix, the relationship among quantization density, sampling period and system transformation matrix is given, which guarantees that the corresponding closed-loop system is globally asymptotically stable. Based on Lyapunov theory, we prove the system is globally asymptotically stable under the relationship.(Ⅲ) The stability analysis of the feedback control system under state and input quantizationIn this part, for practical networked control systems, we study the stabiliza-tion problem of quantized feedback control under limited information about state and control input. In the case, a more general networked control system is studied. By using Lyapunov theory, finding a suitable quantized feedback control strategy, we provide the stability analysis and prove that the corresponding closed-loop system is globally asymptotically stable under condition that the sampling period and each quantization density satisfy some relationship.