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Abstract: We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether's theorem are given, in the sense which enlarges the scope of its application. The dissertation looks at extending the second Noether's theorem to optimal control problems which are invariant under symmetry depending upon k arbitrary functions of the independent variable and their derivatives up to some order m. Furthermore, we look at the Conservation Laws, i.e. conserved quantities along Euler-Lagrange extremals, which are obtained on the basis of Noether's theorem. And finally we obtain a generalization of Noether's theorem for optimal control problems. The generalization involves a one-parameter family of smooth maps which may depend also on the control and a Lagrangian which is invariant up to an addition of an exact differential. / (M.Sc.) North-West University, Mafikeng Campus, 2005

In this thesis, a class of control and identification methods on a typical laboratory process - a ball and beam system - are discussed. The ball and beam is a common laboratory process which contains nonlinearity, a double integrator and time-delay. In our project, the hardware made by Wincon (Quanser SRV02 +BB01) is used. The main contribution of this work is the development of a variety of controller design methods, which together with suitable parameter identification techniques provide tools for rapid prototyping for real time control of processes within the laboratory, in preparation for industrial implementation of more complex schemes. The novelty of this work lies in the use of model predictive control (MPC) methods based on a non-minimal state space formulation, which permits the inclusion of process measurements and actuations in the state vector, leading to controller designs which are immediately ready for on-line implementation. A linear MPC controller based on a non-minimal state space model is based on an approximate linear model. The results from simulation and online experiment show that the linear MPC controller realizes a satisfying reference tracking in the face of nonlinearity and time-delay. In the following chapter, a nonlinear Hammerstein model is identified, which is a type of reliable structure for describing nonlinear plants. A nonlinear MPC scheme is developed based on the Hammerstein model. An inversion block is created to cancel the effect of the nonlinearity. The performance IS also tested in both simulation and experiment. Finally, MPC is combined with sliding mode control. The non-minimal state space model is also used here. In the first part of this chapter, the idea underlying sliding mode control contributes a method of modifying the definition of the cost function in MPC. In the second half, MPC is used to design the switching surface in sliding mode control. The performance of tests on the example (ball and beam system) illustrates that these are both valid methods for dealing with complex processes.

Thesis (Ph.D.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (ℓ. 64-65)

Thesis (M.Sci.)--Massachusetts Institute of Technology, 1959. / Includes bibliographical references (leaf 98).

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 97-100). Also available via the Internet.

Thesis (M.S.)--Ohio University, March, 1993. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, November, 1993. / Title from PDF t.p.