published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains xiii, 110 p.; also includes graphics (some col.) Includes bibliographical references (p. 104-110). Available online via OhioLINK's ETD Center

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xiii, 96 p.; also includes graphics Includes bibliographical references (p. 92-96). Available online via OhioLINK's ETD Center

Thesis (Ph.D.)--University of Central Florida, 2009. / Adviser: Chengying Xu. Includes bibliographical references (p. 118-126).

Thesis (Ph. D.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 131-138).

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2005. / On t.p. "2" is lower case and "[infinity]" appears as the infinity symbol. Includes bibliographical references (leaves 110-116). Also available in electronic version.

This thesis investigates Bicoprime Factorisations (BCFs) and their possible uses in robust control theory. BCFs are a generalisation of coprime factorisations, which have been well known and widely used by the control community over the last few decades. Though they were introduced at roughly the same time as coprime factorisations, they have been largely ignored, with only a very small number of results derived in the literature. BCFs are first introduced and the fundamental theory behind them is developed. This includes results such as internal stability in terms of BCFs, parametrisation of the BCFs of a plant and state space constructions of BCFs. Subsequently, a BCF uncertainty structure is proposed, that encompasses both left and right coprime factor uncertainty. A robust control synthesis procedure is then developed with respect to this BCF uncertainty structure. The proposed synthesis method is shown to be advantageous in the following two aspects: (1) the standard assumptions associated with H-infinity control synthesis are directly fulfilled without the need of loop shifting or normalisation of the generalised plant and (2) any or all of the plant's unstable dynamics can be ignored, thus leading to a reduction in the dimensions of the Algebraic Riccati Equations (AREs) that need to be solved to achieve robust stabilisation. Normalised BCFs are then defined, which are shown to provide many advantages, especially in the context of robust control synthesis. When using a normalised BCF of the plant, lower bounds on the achievable BCF robust stability margin can be easily and directly computed a priori, as is the case for normalised coprime factors. Although the need for an iterative procedure is not completely avoided when designing an optimal controller, it is greatly simplified with the iteration variable being scalar. Unlike coprime factorisations where a single ARE needs to be solved to achieve normalisation, two coupled AREs must be satisfied for a BCF to be normalised. Two recursive methods are proposed to solve this problem. Lastly, an example is presented where the theory developed is used in a practical scenario. A quadrotor Unmanned Aerial Vehicle (UAV) is considered and a normalised BCF controller is designed which in combination with feedback linearisation is used to control both the attitude and position of the vehicle.

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京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18402号 / 情博第517号 / 新制||情||91(附属図書館) / 31260 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 山本 裕, 教授 西村 直志, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

The problem of finding a reduced order model, optimal in the H² sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H^∞ constraint to the H² optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of homotopy methods, both the H² optimal and the combined H²/H^∞ model reduction problems are very difficult. For both problems homotopy algorithms based on several formulations—input normal form; Ly, Bryson, and Cannon's 2 X 2 block parametrization; a new nonminimal parametrization—are developed and compared here. For the H² optimal model order reduction problem, these numerical algorithms are also compared with that based on Hyland and Bernstein's optimal projection equations. Both the input normal form and Ly form are very efficient compared to the over parametrization formulation and the optimal projection equations approach, since they utilize the minimal number of possible degrees of freedom. However, they can fail to exist or be very ill conditioned. The conditions under which the input normal form and the Ly form become ill conditioned are examined. The over-parametrization formulation solves the ill conditioning issue, and usually is more efficient than the approach based on solving the optimal projection equations for the H² optimal model reduction problem. However, the over-parametrization formulation introduces a very high order singularity at the solution, and it is doubtful whether this singularity can be overcome by using interpolation or other existing methods. Although there are numerous algorithms for solving Riccati equations, there still remains a need for algorithms which can operate efficiently on large problems and on parallel machines and which can be generalized easily to solve variants of Riccati equations. This thesis gives a new homotopy-based algorithm for solving Riccati equations on a shared memory parallel computer. The central part of the algorithm is the computation of the kernel of the Jacobian matrix, which is essential for the corrector iterations along the homotopy zero curve. Using a Schur decomposition the tensor product structure of various matrices can be efficiently exploited. The algorithm allows for efficient parallelization on shared memory machines. The linear-quadratic-Gaussian (LQG) theory has engendered a systematic approach to synthesize high performance controllers for nominal models of complex, multi-input multioutput systems and hence it is a breakthrough in modern control theory. Homotopy algorithms for both full and reduced-order LQG controller design problems with an H^∞ constraint on disturbance attenuation are developed. The H^∞ constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H² performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H² performance. The algorithms are based on two minimal parameter formulations: Ly, Bryson, and Cannon's 2 X 2 block parametrization and the input normal Riccati form parametrization. An over-parametrization formulation is also proposed. Numerical experiments suggest that the combination of a globally convergent homotopy method with a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm synthesis. / Ph. D.