Research considered investigates the optimal control problem which is constrained by a hyperbolic conservation law (HCL). We carried out a comparative study of the solutions of the optimal control problem subject to each one of the two di erent types of hyperbolic relaxation systems [64, 92]. The objective was to employ the adjoint-based optimization to minimize the cost functional of a matching type between the optimal solution and the target solution. Numerical tests were then carried out and promising results obtained. Finally, an extension was made to the adjoint-based optimization approach to apply second-order schemes for the optimal control problem in which also good numerical results were observed.

Chen Zhiyong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 54-57). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Nonlinear Control --- p.1 / Chapter 1.2 --- Global Stabilization --- p.2 / Chapter 1.3 --- Output Regulation --- p.3 / Chapter 1.4 --- Contributions of the Thesis --- p.4 / Chapter 2 --- Global Robust Stabilization of Cascaded Polynomial Systems --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Preliminaries --- p.6 / Chapter 2.3 --- Basic Results --- p.8 / Chapter 2.4 --- The Algorithm --- p.11 / Chapter 2.5 --- An Example --- p.14 / Chapter 2.6 --- Concluding Remarks --- p.16 / Chapter 3 --- Output Regulation of Singular Nonlinear Systems by Normal Output Feedback --- p.18 / Chapter 3.1 --- Introduction --- p.18 / Chapter 3.2 --- Preliminaries --- p.20 / Chapter 3.3 --- Main Result --- p.24 / Chapter 3.4 --- An Example --- p.34 / Chapter 3.5 --- Concluding Remarks --- p.35 / Chapter 4 --- Robust Output Regulation of Singular Nonlinear Systems --- p.37 / Chapter 4.1 --- Introduction --- p.37 / Chapter 4.2 --- Problem Description and Standard Assumptions --- p.38 / Chapter 4.3 --- A Preliminary Result --- p.40 / Chapter 4.4 --- Solvability of the Problem --- p.48 / Chapter 4.5 --- Concluding Remarks --- p.51 / Chapter 5 --- Conclusions --- p.52 / Bibliography --- p.54 / Biography --- p.58

Wang Jin. / "September 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 93-105). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.

Long bridges tend to develop large deformations under the action of intense dynamical loads such as wind or earthquakes. Unless these deformations are controlled in some fashion, the structure might suffer damage or even collapse. One possible solution to this problem is to apply external forces to the bridge through suspension cables. This work presents an active robust control scheme to suppress the vibrations caused by the vertical ground motion due to an earthquake of a cable-stayed bridge. It is proven both mathematically and through computer simulation that the active nonlinear controller is capable of reducing the amplitude of the vibrations to an arbitrarily small size. This may save the bridge structure during a strong earthquake. It is shown that the control scheme performs satisfactorily even if parts of the system fail during an earthquake. An alternative method to derive the control law using finite elements is also presented. / Graduation date: 1993

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.

No description available.

A new system identification algorithm, multiple autoregressive exogenous (ARX) inputs-based Takagi-Sugeno (TS) fuzzy model, is developed to identify nonlinear behavior of structure-magnetorheological (MR) damper systems. It integrates a set of ARX models, clustering algorithms, and weighted least squares algorithm with a TS fuzzy model. Based on a set of input-output data that is generated from building structures equipped with MR dampers, premise parameters of the ARX-TS fuzzy model are determined by clustering algorithms. Once the premise part is constructed, consequent parameters of the ARX-TS fuzzy model are optimized by the weighted least squares algorithm. To demonstrate the effectiveness of the proposed ARX-TS fuzzy model, it is applied to a three-, an eight-, a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed ARX-TS fuzzy algorithm is effective to identify nonlinear behavior of seismically excited building structures equipped with MR dampers. A new semiactive nonlinear fuzzy control (SNFC) algorithm is developed through integration of multiple Lyapunov-based state feedback gains, a Kalman filter, and a converting algorithm with TS fuzzy interpolation method. First, the nonlinear ARX-TS fuzzy model is decomposed into a set of linear dynamic models that are operated in only a local linear operating region. Based on the decomposed models, multiple Lyapunov-based state feedback controllers are formulated in terms of linear matrix inequalities (LMIs) such that the structure-MR damper system is globally asymptotically stable and the performance on transient responses is guaranteed. Then, the state feedback controllers are integrated with a Kalman filter and a converting algorithm using a TS fuzzy interpolation method to construct semiactive output feedback controllers. To demonstrate the effectiveness of the proposed SNFC algorithm, it is applied to a three-, an eight-, and a twenty-story building structures. It is demonstrated from the numerical simulation that the proposed SNFC algorithm is effective to control responses of seismically excited building structures equipped with MR dampers. In addition, it is shown that the proposed SNFC system is better than a traditional optimal algorithm, H2/linear quadratic Gaussian-based semiactive control strategy.

No description available.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Manufacturing Engineering and Engineering Management in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 167-187)