This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.

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This thesis presents a data-driven approach to constrained control in the form of a subspace-based state-space system identification algorithm integrated into a model predictive controller. Generally this approach has been termed model-free predictive control in the literature. Previous research into this area focused on the system identification aspects resulting in an omission of many of the features that would make such a control strategy attractive to industry. These features include constraint handling, zero-offset setpoint tracking and non-stationary disturbance rejection. The link between non-stationary disturbance rejection in subspace-based state-space system identification and integral action in state-space based model predictive control was shown. Parameterization with Laguerre orthonormal functions was proposed for the reduction in computational load of the controller. Simulation studies were performed using three real-world systems demonstrating: identification capabilities in the presence of white noise and non-stationary disturbances; unconstrained and constrained control; and the benefits and costs of parameterization with Laguerre polynomials.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis addresses the problem of robustness in model predictive control (MPC) of discrete-time systems. In contrast with most previous work on robust MPC, our main focus is on robustness in the face of both imperfect state information and dynamic model uncertainty. For linear discrete-time systems with model uncertainty described by sum quadratic constraints, we propose output-feedback MPC policies that: (i) treat soft constraints using quadratic penalty functions; (ii) respect hard constraints using 'tighter' constraints; and (iii) achieve robust closed-loop stability and non-zero setpoint tracking. Our two main tools are: (1) a new linear matrix inequality condition which parameterizes a class of quadratic MPC cost functions that all lead to robust closed-loop stability; and (2) a new parameterization of soft constraints which has the advantage of leading to optimization problems of prescribable size. The stability test we use for MPC design builds on well-known results from dissipativity theory which we tailor to the case of constrained discrete-time systems. The proposed robust MPC designs are shown to converge to well-known nominal MPC designs as the model uncertainty (description) goes to zero. Furthermore, the present approach to cost function selection is independently motivated by a novel result linking MPC and minimax optimal control theory. Specifically, we show that the considered class of MPC policies are the closed-loop optimal solutions of a particular class of minimax optimal control problems. In addition, for a class of nonlinear discrete-time systems with constraints and bounded disturbance inputs, we propose state-feedback MPC policies that input-to-state stabilize the system. Our two main tools in this last part of the thesis are: (1) a class of N-step affine state-feedback policies; and (2) a result that establishes equivalence between the latter class and an associated class of N-step affine disturbance-feedback policies. Our equivalence result generalizes a recent result in the literature for linear systems to the case when N is chosen to be less than the nonlinear system's 'input-state linear horizon'.

Thèse (D.Eng.) -- Université du Québec à Chicoutimi, 2007. / La p. de t. porte en outre: Thèse présentée à l'Université du Québec à Chicoutimi comme exigence partielle du doctorat en ingénierie. Bibliogr.: f. 169-181. Document électronique également accessible en format PDF. CaQQUQ

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2005. / Bottasso, Carlo, Committee Chair ; Hodges, Dewey, Committee Member ; Bauchau, Olivier, Committee Member. Includes bibliographical references.

Thesis (Ph. D.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains viii, 104 p. : ill., map. Includes abstract. Includes bibliographical references (p. 101-108).

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / There are no leaves 76-78; manuscript misnumbered between 75 and 79. Typescript. Vita. Includes bibliographical references. Also available on the Internet.