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博士 （情報科学） >
A Study on Noise-Based Global Asymptotic Stabilization and Optimization Method
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| Title: | A Study on Noise-Based Global Asymptotic Stabilization and Optimization Method |
| Other Titles: | ノイズを用いた大域的漸近安定化・最適化に関する研究 |
| Authors: | 星野, 健太1 Browse this author |
| Authors(alt): | Hoshino, Kenta1 |
| Keywords: | Stochastic systems | | Global asymptotic stabilization, optimization | | Noise-based stabilization |
| Issue Date: | 25-Mar-2014 |
| Publisher: | Hokkaido University |
| Abstract: | Noise degrades the performance of systems in most cases. However, noise can be used to improve the performance compared to the case of the absence of noise. This thesis studies the noise-based methods for the global asymptotic stabilization and theoptimization problem in control theory. For the asymptotic stabilization problem, this study establishes the method for designing feedback controllers using Wiener processes.For the optimization problem, this study proposes an extremum seeking method that guarantees the convergence of estimation variables to optimum values.Although the global asymptotic stabilization problem is the one of the fundamental problems in the literature of control theory, there exist systems that cannot be stabilized by any smooth time-invariant feedback controllers. This study employs a method usingstochastic feedback controllers to stabilize such systems. When the stochastic feedback controllers are used to stabilize deterministic nonlinear systems, the closed-loop systems are often modeled as Stratonovich stochastic differential equations. In the stabilizationmethod using a stochastic feedback controller, the constructive method for designing controllers for general nonlinear affine systems has not been established when closed-loop systems are given by Stratonovich stochastic differential equations. This thesis proposes a constructive design method based on stochastic control Lyapunov functions.For the optimization problem, this study considers a stochastic extremum seeking method. In extremum seeking methods, dither signals are added to given systems toapproximate the gradient of objective functions, and the optimum is estimated by updating the estimation variable based on the approximated gradient. In previous extremum seeking methods, although the estimation variables approach the optimum sufficiently,the estimation variables do not converge to the optimum. This thesis shows a stochastic extremum seeking method that can guarantee the convergence of the estimation variables to the optimum by introducing the updating mechanism of the estimation variablesbased on the stochastic Lyapunov stability theory.Chapter 1 states the backgrounds and the objectives of this thesis, and Chapter 2 introduces the mathematical preliminaries, which includes the fundamentals of stochastic process, manifolds. Chapter 3 shows the noise-based stabilization method and the method for designing stochastic feedback controllers. This chapter rst shows the problem setting of the global asymptotic stabilization and the design of the controller. Then, we de ne a stochastic control Lyapunov function for the design of stochastic controllers. The design methodis shown based on the stochastic control Lyapunov function. Further, this chapter gives the proof that the designed controllers by the proposed method globally asymptotically stabilize given systems. Moreover, the numerical examples show the global asymptotic stabilization of a nonholonomic system and non-Euclidean systems. In addition, since the designed controller can be seen as an extension of the Sontag-type controller, the designed controllers satisfy inverse optimality. By the inverse optimality, the controllers have a stability margin.Chapter 4 considers homogeneous stochastic systems and discusses their stability, which can be applied to improve the convergence of the stabilization by the noise-based stabilization. This chapter rst explains the homogeneity, and then gives the de nition ofhomogeneous stochastic systems as an extension of homogeneous deterministic systems.Then, the author shows the relation between the homogeneity and the convergence speed of stable homogeneous stochastic systems. Further, a homogeneous feedback controller is shown to preserve the homogeneity of systems and to guarantee the convergence speed of the closed-loop systems. Finally, this chapter also shows the redesign method of the controllers designed by the method described in Chapter 3 to improve the convergence speed in the stabilization of driftless systems.Chapter 5 shows a stochastic extremum seeking method that can guarantee the convergence of estimation variables to an optimum value. After showing the objective of the stochastic extremum seeking method and the problem setting of the optimization problem, the proposed method is shown, which uses the Wiener process to approximate the gradients of objective functions. The proposed method uses a high-pass lter with a state-dependent parameter obtained from the stochastic Lyapunov stability analysis.Also, this chapter gives the proof of the convergence of the estimation variables by the stochastic Lyapunov theory.Chapter 6 states the conclusion of this thesis. |
| Conffering University: | 北海道大学 |
| Degree Report Number: | 甲第11317号 |
| Degree Level: | 博士 |
| Degree Discipline: | 情報科学 |
| Examination Committee Members: | (主査) 教授 山下 裕, 教授 五十嵐 一, 教授 金井 理 |
| Degree Affiliation: | 情報科学研究科（システム情報科学専攻） |
| Type: | theses (doctoral) |
| URI: | http://hdl.handle.net/2115/58181 |
| Appears in Collections: | 学位論文 (Theses) > 博士 （情報科学）
課程博士 (Doctorate by way of Advanced Course) > 情報科学院(Graduate School of Information Science and Technology)
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