The problem of minimising a quadratic cost functional while regulating a dynamical system with a saturating control has been widely studied, and is known to lead to the use of non-linear controls. This thesis considers two variations on this problem, which might be considered as alternative approaches to optimal regulator problems. After a statement of the general optimal control problem in Chapter II, necessary and sufficient conditions are discussed. Chapter III considers the failure of the major necessary condition (the Maximum Principle), which leads to the idea of singular controls. These singular controls play a major role throughout Chapters IV-VI. Chapters IV and V consider the first alternative approach, in which a non-quadratic cost functional is adopted. It is chosen in such a way as to give certain desirable properties outlined in Chapter IV. This Chapter also considers two second order problems; while Chapter V considers two third order problems, and extends one to nth order systems. Chapter VI then looks at the second alternative, where a non-quadratic state penalty term is added to the quadratic term in such a way as to simplify the resulting behaviour. In this Chapter, multiple control inputs are considered, and two different types of control penalty are applied. The feedback structures obtained in this problem are used to sub-optimally control a quadratic cost problem, with a discussion of the relative merits of the sub-optimal schemes.

A feature common to predictor control schemes for plants with time delays is the use of a plant model. Any difference between plant and model is referred to as mismatch. The presence of mismatch introduces extra parameters which in a parametric optimisation problem may be exploited to produce performance improvement. A study is undertaken of the mechanism and opportunities for such improvement. When the cost functional is quadratic a matched predictor control scheme is known to be optimal. However, it is important to determine a relationship between mismatch and degradation in performance. This will indicate the amount by which plant and model may differ before the performance of the control scheme becomes unacceptable. With this aim, algebraic expressions are obtained for the mismatched input and output. An examination of these expressions shows how mismatch effects the stability and performance of the control scheme. When the plant contains measurement delays, the optimal matched control scheme requires prior knowledge of an initial state. An alternative control scheme operating without this prior knowledge is suboptimal and may be improved by mismatch. The types of mismatch that could produce improvement are determined.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Microfiche copy available in Archives and Aeronautics. / Vita. / Bibliography : leaves 302-304. / Ph.D.

The first essay considers a dynamic non-stationary inventory problem in which replenishment is made in fixed lot sizes (e.g., in full truckloads or full containers). We consider two separate cases: one with exogenous pricing and the other with endogenous pricing. In the first case (exogenous pricing), we show that when the ordering cost contains only a variable component, the reorder-point lot-size policy or (r, Q) policy is optimal for both single-stage and multi-echelon inventory systems. In the presence of a fixed cost, we establish the optimality of batch based (s, S ) policies for the single-stage inventory system. In the second case (endogenous pricing), we show that when the demand function has the additive form and there is only a variable ordering cost, the (r,Q) list-price policy is optimal for the single-stage system, where inventory replenishment follows an (r,Q) policy and the optimal price in each period depends on the order-up-to level. / The second essay analyzes a periodic-review, stochastic, inventory-control system in which the fixed order-cost is a step function of the order size. In particular, if the order size is within a specified limit, C, then the setup cost is K1; otherwise it is K2, where K2 ≥ K1. This cost structure is motivated from some industrial applications and transportation/production contracts used in practice. Under the condition that K1 ≤ K 2 ≤ K1, we introduce a new concept called C - (K1 ≤ K 2) convexity, which enables us to partially characterize the structure of an optimal ordering policy. For the general condition K 1 ≤ K2 , the analysis is facilitated with a different notion called strong K-convexity. Based on this analysis, we provide a partial characterization of the optimal policy and construct an easy-to-implement heuristic method that has near-optimal performance in random test instances. Our study extends or redevelops (with different techniques) several existing results in the literature. / The third essay studies a firm's periodic-review production/inventory ordering decisions when the next period's setup cost depends on the quantity produced/ ordered in the current period. In particular, if the current period's production/order quantity exceeds a specified threshold value, the system starts the next period in a "warm" state and no fixed setup cost is incurred; otherwise the state is considered "cold" and a positive setup cost is required for production/ ordering. We develop a dynamic programming formulation of the problem and provide a partial characterization of the optimal policy under the assumption that the demands follow a Polya or Uniform distribution. We use the structural results to develop fairly simple heuristic policies, which perform highly effectively in our computational experiments. / With increased globalization and competition in the current market, supply chain has become longer and more complicated than ever before. An effective and efficient supply chain is crucial and essential to a successful firm. In a supply chain, inventories are a very important component as the investment in inventories is enormous. This dissertation consists of three essays related to stochastic inventory management. / Yang, Yi. / Adviser: Youhua Chen. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 145-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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.

by Chen Xi. / "July 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 107-112). / 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.

Zhang Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 67-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 2 --- The Tracking Portfolio Models --- p.7 / Chapter 2.1 --- Problem Formulation --- p.8 / Chapter 2.2 --- Reformulation of Tracking Models --- p.12 / Chapter 2.3 --- A Stochastic LQ Control Approach --- p.13 / Chapter 3 --- Efficient Tracking: Deterministic Market Parameters --- p.16 / Chapter 3.1 --- Solution to Model I --- p.17 / Chapter 3.2 --- A Special Case of Model I --- p.23 / Chapter 3.3 --- Solution to Model II --- p.24 / Chapter 3.4 --- A Special Case of Model II: Mean-Variance Portfolio Selection --- p.32 / Chapter 3.5 --- Solution to Model III --- p.36 / Chapter 4 --- Efficient Tracking: Markov-Modulated Market Parameters --- p.41 / Chapter 4.1 --- Problem Formulation --- p.42 / Chapter 4.2 --- Solution to Model I with Regime Switching --- p.47 / Chapter 4.3 --- Solution to Model II with Regime Switching --- p.52 / Chapter 4.4 --- Solution to Model III with Regime Switching --- p.59 / Chapter 5 --- Conclusion --- p.64 / Bibliography --- p.66

No description available.

Mario Jodorkovsky and Adrian Segall. / Bibliography: p. 20. / "June, 1981." / U.S. Dept. of Defense contract No. N00014-75-C-1183

Thesis--Virginia Polytechnic Institute and State University, 1978. / Also available via the Internet.