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- Type of Document: Ph.D. Dissertation
- Language: Farsi
- Document No: 52148 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Hossein Khalaj, Babak; Farhadi, Alireza; Motahari, Abolfazl
- Abstract:
- In this thesis, we study the observability and stability problems of networked control systems (the control systems which communicate through communication channels) to answer two important questions about different system models. The first is that what is the constraints implied by the stability or observability of systems? (necessary condition on the observability and stability). The second is that under which constraints can we present a design for system to guarantee the observability or stability of systems? (sufficient condition on the observability and stability). Clearly, an efficient design is the one that presents a tight sufficient condition.One of system models addressed in this thesis is a linear dynamic system over one or several parallel AWGN channels. Some new assumptions are considered in this model such as mismatch factor between sampling rate and channel transmission rate, fading phenomena, and the existence of noise over ideal paths. A necessary condition on the stability of this system in the mean square sense is presented according to the channel capacity, eigenvalues of the dynamic matrix, and the mismatch factor. Subsequently, by presenting a new design of encoder, decoder and controller, it is shown that this necessary condition is also sufficient for this system.Furthermore, in this thesis, we present two new nonlinear coding schemes in order to achieve an efficient design for the linear dynamic systems over the parallel Gaussian channels as well as bandlimited AWGN channel for the first time.Nonlinear dynamic systems are also considered in this thesis for two different system models in order to obtain new necessary and sufficient conditions on the observability and stability.In the first model, it is assumed that the output signal of an uncontrolled dynamic system is transmitted through a communication channel. For this system, a necessary condition on the observability (tracking) is obtained according to system Lyapunov exponents and the channel capacity. Subsequently, by designing a new coding scheme, a sufficient condition is presented in order to track the uncontrolled nonlinear system over the digital noiseless,packet erasure, and AWGN channels, respectively, in sure, almost sure, and mean square senses.The second nonlinear model considered in this thesis is a controlled nonlinear dynamic system over digital noiseless and packet erasure channels. For this system, the observability and stability problems are addressed in sure and almost sure senses. As the results,the necessary and sufficient conditions are obtained according to the eigenvalues of the system Jacobin matrix and the channel capacity. Finally, it is shown that these obtained conditions are reduced to the well-known results for the special case of linear dynamic systems
- Keywords:
- Lyapunov Exponent ; Networked Control ; Stability ; Tracking ; Observability ; Dynamical Systems ; Capacity ; Communication Channel
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