Item – Theses Canada

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OCLC number
77548692
Author
Warren, Adam L.,1973-
Title
Sequential decision-making under uncertainty.
Degree
Ph. D. -- McMaster University, 2005
Publisher
Ottawa : Library and Archives Canada = Bibliothèque et Archives Canada, [2006]
Description
3 microfiches
Notes
Includes bibliographical references.
Abstract
This thesis addresses the issue of sequential decision-making under uncertainty. The results presented here are applicable to any linear decision-making system in which feedback is present in the form of periodic updates of the decision variables. However, the primary focus of this thesis is robust model-predictive control (MPC) as applied in the process industries. The performance of a model-predictive controller can suffer from model mismatch or disturbances; therefore, considerable prior research has been invested in devising robust model-predictive controllers. One approach involves detuning, which can lead to poor performance. This thesis addresses a second approach in which the controller explicitly considers the model and disturbance uncertainty in its calculations. This approach presents challenges because the controller must model the future trajectory of an uncertain system, and future control actions are taken during the trajectory. The main contribution of this thesis is a set of robust, computationally efficient MPC formulations based upon closed-loop uncertainty descriptions. These formulations model future control actions using a linear model-predictive controller, which must be solved at each controller interval within the prediction horizon. In general, modeling the future closed-loop trajectory would involve the solution of a number of quadratic programs at each controller execution. This approach would be computationally expensive. In this thesis, the MPC calculations are replaced with their equivalent stationarity conditions to provide a single set of algebraic equations for the trajectory. The closed-loop model of the system consists of the linear stationarity conditions and the linear plant model. The uncertainty description used by the proposed controllers is tailored for processes that are linear time-invariant within the prediction horizon, which gives a tight estimate of the uncertainty for many chemical processes. Furthermore, the uncertainty in the closed-loop model is characterized by a structured, ellipsoidal uncertainty description. With this formulation, the robust controllers can be cast as a second-order cone program (SOCP) or quadratic programs (QP), depending on the type of uncertainty considered by the controller. Both of these formulations can be efficiently solved using modern interior-point methods (Lobo et al., 1998). This thesis addresses several sources of uncertainty, including feedback model-mismatch, feedforward model-mismatch, stochastic unmeasured disturbances, and stochastic measured disturbances. In each case, the uncertainty description is tailored to process fundamentals, and the uncertainty description includes the effects of future control actions. The proposed controllers are able modify their behaviour as the situation in the plant changes--the robust MPC can be more aggressive, less aggressive, or the same as the nominal MPC, as the situation dictates. This thesis also explores the application of robust MPC to the production planning problem. In the presented case study, a robust MPC determines the production and advertising levels required to maintain the desired sales levels and to minimize inventory. The robust MPC must calculate the minimum amount of 'safety stock' required to ensure sales orders are met despite demand uncertainty. This calculation is done on-line, and the controller actively manages inventory--increasing inventory when uncertainty is large, and decreasing inventory when information is more exact. This allows sales orders to be met without the expense of excessive inventory.
ISBN
0494042885
9780494042885