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An on-line, suboptimal feedback control algorithm is proposed and demonstrated. The procedure is developed using a variational formulation of the optimal control problem. A convex index of performance is presumed. The Finite Element Method is used in conjunction with a variable mesh gridation scheme to produce accurate local approximations of the weak functional forms that result from the variational formulation. These local results provide a basis for the continual updating of the suboptimal control strategy. The extension of the algorithm to the control of nonlinear dynamical systems is also investigated. The Euler Necessary Conditions that describe the analytical solution of the Optimal Control Problem for the nonlinear plant are linearized using two different approaches, Quasilinearization, and Linearization at a Point. The simulated response of both a linear and a nonlinear dynamical system to the input of the suboptimal control generated using the proposed algorithm is offered in plot form. The closure of the disseration includes a suggested list of recommendations for further research. / Ph. D.

The theory of organization that this thesis proposes possesses a characteristic plasticity that should enable it to span the gap that has traditionally existed between the two broad types of current organizational theories. Generally, one type of theory proposes to describe how organizations should function and the other type proposes to describe how organizations actually do function. The first type of theory often seems to result in proposals derived from formal, mechanistic concepts that are necessary, but largely superficial and not profoundly significant in an operational sense. The second type of theory essentially seems to suggest that an “informal organization'' actually functions to achieve the organizational objectives and such an organization is a function of existing personalities and, as a result, no universally applicable principles appear to exist upon which design considerations can be based. Such conclusions are usually drawn from some form of case studies that inherently produce knowledge that proves incomplete and ephemeral as events move on and organizations evolve. Therefore, this theory seeks to reconcile and integrate the basic principles of these two types of theories by conceptualizing the basic principles of engineering design and statistical stability as they apply to organizational processes. / Master of Science

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves [256]-267). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves [256]-267). Also available on the Internet.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Approved for public release; distribution in unlimited. / This thesis considers the problem of time-optimal spacecraft slew maneuvers. Since the work of Bilimoria and Wie it has been known that the time-optimal reorientation of a symmetric rigid body was not the eigenaxis maneuver once thought to be correct. Here, this concept is extended to axisymmetric and asymmetric rigid body reorientations with idealized independent torque generating devices. The premise that the time-optimal maneuver is not, in general, an eigenaxis maneuver, is shown to hold for all spacecraft configurations. The methodology is then extended to include spacecraft control systems employing magnetic torque rods, a combination of pitch bias wheel with magnetic torque rods, and finally to control systems employing single gimbal control moment gyros. The resulting control solutions, designed within the limitations of the actuators, eliminate the requirement to avoid actuator singularities. Finally, by employing sampled-state feedback the viability of real-time optimal closed loop control is demonstrated.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / by Jorge F. Baca. / M.S.

Repetitive Control (RC) seeks to converge to zero tracking error of a feedback control system performing periodic command as time progresses, or to cancel the influence of a periodic disturbance as time progresses, by observing the error in the previous period. Iterative Learning Control (ILC) is similar, it aims to converge to zero tracking error of system repeatedly performing the same task, and also adjusting the command to the feedback controller each repetition based on the error in the previous repetition. Compared to the conventional feedback control design methods, RC and ILC improve the performance over repetitions, and both aiming at zero tracking error in the real world instead of in a mathematical model. Linear Model Predictive Control (LMPC) normally does not aim for zero tracking error following a desired trajectory, but aims to minimize a quadratic cost function to the prediction horizon, and then apply the first control action. Then repeat the process each time step. The usual quadratic cost is a trade-off function between tracking accuracy and control effort and hence is not asking for zero error. It is also not specialized to periodic command or periodic disturbance as RC is, but does require that one knows the future desired command up to the prediction horizon. The objective of this dissertation is to present various design schemes of improving the tracking performance in a control system based on ILC, RC and LMPC. The dissertation contains four major chapters. The first chapter studies the optimization of the design parameters, in particular as related to measurement noise, and the need of a cutoff filter when dealing with actuator limitations, robustness to model error. The results aim to guide the user in tuning the design parameters available when creating a repetitive control system. In the second chapter, we investigate how ILC laws can be converted for use in RC to improve performance. And robustification by adding control penalty in cost function is compared to use a frequency cutoff filter. The third chapter develops a method to create desired trajectories with a zero tracking interval without involving an unstable inverse solution. An easily implementable feedback version is created to optimize the same cost every time step from the current measured position. An ILC algorithm is also created to iteratively learn to give local zero error in the real world while using an imperfect model. This approach also gives a method to apply ILC to endpoint problem without specifying an arbitrary trajectory to follow to reach the endpoint. This creates a method for ILC to apply to such problems without asking for accurate tracking of a somewhat arbitrary trajectory to accomplish learning to reach the desired endpoint. The last chapter outlines a set of uses for a stable inverse in control applications, including Linear Model Predictive Control (LMPC), and LMPC applied to Repetitive Control (RC-LMPC), and a generalized form of a one-step ahead control. An important characteristic is that this approach has the property of converging to zero tracking error in a small number of time steps, which is finite time convergence instead of asymptotic convergence as time tends to infinity.

Liu Lu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 65-70). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Output Regulation Problem --- p.1 / Chapter 1.2 --- Control Design with Unknown High-frequency Gain Sign --- p.3 / Chapter 1.3 --- Contribution of the Thesis --- p.4 / Chapter 1.4 --- Thesis Outline --- p.5 / Chapter 2 --- Global Robust Stabilization of a Class of Nonlinear Systems --- p.6 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Problem Formulation and Preliminaries --- p.8 / Chapter 2.3 --- Main Result --- p.11 / Chapter 2.4 --- An Example --- p.20 / Chapter 2.5 --- Application of Theorem 2.1 --- p.26 / Chapter 2.5.1 --- Chua's Circuit and Control Problem --- p.26 / Chapter 2.5.2 --- Solvability of the Control Problem --- p.28 / Chapter 2.5.3 --- Simulation Results --- p.32 / Chapter 2.5.4 --- Conclusion --- p.33 / Chapter 2.6 --- Conclusion --- p.36 / Chapter 3 --- Global Robust Output Regulation of Nonlinear Systems in Output Feedback Form --- p.39 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Output Regulation Converted to Stabilization --- p.42 / Chapter 3.3 --- Main Result --- p.49 / Chapter 3.4 --- An Example --- p.55 / Chapter 3.5 --- Conclusion --- p.58 / Chapter 4 --- Conclusions --- p.62 / List of Figures --- p.64 / Bibliography --- p.65 / Biography