Dissertation/Thesis Abstract

Data-based Analysis and Control for Nonlinear Dynamical Systems
by Wang, Zhuo, Ph.D., University of Illinois at Chicago, 2013, 144; 3573413
Abstract (Summary)

In recent years, human society has entered the age of big data. With the rapid development of information sciences and technology, many businesses and industries have undergone great changes. While the scale of the enterprises is increasing, production technology, production equipments and industrial processes are becoming more and more complex. As a consequence, traditional methods for analyzing and controlling the system, which need to establish mathematical models based on physical and chemical mechanisms, have become infeasible. Due to modern digital sensor, digital storage, digital communication and processing technologies and their universal applications, these enterprises generate a vast amount of data on a daily basis, which reflect various information about the system dynamics. How to effectively use these online and offline data to combine data mining, pattern recognition and computer technologies with control theory and systems engineering, has become a very important issue that needs to be addressed.

The aim of our work is to develop some data-based methods not only for system analysis, but also for nonlinear systems control under the condition of no explicit mathematical models. The study on system properties is an important topic in control theory and systems engineering. We first develop a series of data-based methods for analyzing the state/output controllability and state observability, the stability of the equilibrium point, the input-to-state stability as well as the input-to-output stability of linear discrete-time systems, which have unknown parameter matrices. These data-based methods only use measured data to compute the state/output controllability matrices and the state observability matrix, in order to verify the corresponding properties. Compared with the traditional model-based approaches, which have to identify the system parameter matrices, they have the advantages of higher calculation precision and lower computational complexity. We then develop some data-based methods to analyze the stability of a class of nonlinear discrete-time systems, which have unknown mathematical models. These methods also study the domain of attraction for the asymptotically stable equilibrium point, by using the measured state data.

After system analysis, we give a direct data-based output feedback control (DDBOFC) method for a class of nonlinear systems, which have unknown mathematical models. This method is characterized by the low requirement for the priori knowledge about the system dynamics, and it studies the control problem in two stages. In the first stage, we assumed that there are not measurement noises or process noises in the measured data. We apply a fast sampling technique to measure the output signal, which contains information about the nonlinear system. The zero-order hold (ZOH) as well as the control switch are also applied to collect system information. Then, the corresponding Jacobian matrices are calculated according to these sampled output data, and the feedback gain matrix is calculated and adjusted based on these Jacobian matrices. Theoretical analysis on the convergence and simulation results demonstrate the feasibility of this DDBOFC method. In the second stage, we study the case where there are measurement noises in the sampled output data. We still apply the fast sampling, the ZOH and the control switch for information collection. This method applies a data-based least squares estimation (DBLSE) algorithm to obtain the best unbiased estimators of corresponding Jacobian matrices, based on which the feedback gain matrix is calculated and adjusted. Also, we present theoretical analysis and computer simulation to demonstrate the feasibility.

The last part of this thesis is an indirect data-based output feedback control (IDBOFC) method for a class of nonlinear discrete-time systems, which have unknown mathematical models. This IDBOFC method is also based on some prior knowledge about the system. We first use the neural network and historical I/O data to establish an equivalent model, which approximates the original system. Then, with this approximate model and the measured output data, we use a nonlinear programming method to estimate the corresponding Jacobian matrices. The feedback controller is designed in real-time according to these Jacobian matrices, which can drive the output signal to its desired value.

Indexing (document details)
Advisor: Liu, Derong
School: University of Illinois at Chicago
School Location: United States -- Illinois
Source: DAI-B 74/12(E), Dissertation Abstracts International
Subjects: Computer Engineering, Electrical engineering, Systems science
Keywords: Control engineering, Controllability, Jacobian matrices, Output feedback control, Zero-order hold
Publication Number: 3573413
ISBN: 978-1-303-43588-1
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