Orientadores: Ana Friedlander, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-06T02:04:45Z (GMT). No. of bitstreams: 1 Chela_JoaoLuiz_D.pdf: 1546931 bytes, checksum: f1667806d83333df79ce853d2d25b401 (MD5) Previous issue date: 2006 / Resumo: O Problema de Programação Matemática com Restrições de Equilíbrio (MPEC) consiste em um problema de otimização, onde a definição do conjunto viável inclui o conjunto de soluções de um problema de inequações variacionais. Também é denominada MPEC à reformulação do problema como um problema de otimização clássico, obtida substituindo o problema variacional pelo sistema de Karush-Kuhn- Tucker associado. O problema variacional é também chamado neste contexto problema do segundo nível. A resolução do problema MPEC é mais difícil que a dos problemas clássicos de otimização. Esta dificuldade se deve basicamente à estrutura de dois níveis do problema MPEC. Existem diversos exemplos que mostram que a região viável pode não ser convexa e até mesmo desconexa. Mesmo no caso em que a trajetória de soluções dos problemas do segundo nível pode ser expressa como uma função dos parâmetros, a função objetivo do primeiro nível pode ser não diferenciável. Neste trabalho, propomos uma nova abordagem para resolver problemas de Programação Matemática com Restrições de Equilíbrio. Esta abordagem permite que o problema do segundo nível seja resolvido diretamente, sem reformulações nem uso de técnicas não diferenciáveis. Para isso, utilizamos um Algoritmo de Restauração Inexata baseado no trabalho de Martínez em [50]. Apresentamos resultados teóricos e experimentos numéricos, incluindo aplicações / Abstract: A Mathematical Program with Equilibrium Constraints (MPEC) is an optimization problem, where part of the variables are constrained to be solutions of a variational inequality problem parameterized by the other variables. The reformulation of a MPEC, as a classical optimizatlon problem, replacing the variational inequality problem by corresponding the K.K. T system, is also called MPEC. In this context the variational inequality problem is also called the second leveI problem. MPEC problems are harder to solve than classical optimization problems due to their two-level structure. These problems are non-convex, and the feasible region can even be a disconnected one. The objective function of the first level is in general non-differentiable, even in the case where the second level solutions can be expressed as a function of the parameters. In this work, to solve Mathematical Programming Problems we use an Algorithm of Inexact Restoration based in the work of Martínez in [50]. This approach allows to treat the second leveI problem design without reformulation and we do not need any special algorithm designed for non-differentiable optimization. We present theoretical results and numerical experiments, including an application in urban traffic problems / Doutorado / Mestre em Matemática Aplicada

Real-time optimization (RTO) is a supervisory strategy in the hierarchical industrial process automation architecture in which economically optimal set-point targets are computed for the lower level advanced control system, which is typically model predictive control (MPC). Due to highly volatile market conditions, recent developments have considered transforming the conventional steady-state RTO to dynamic RTO (DRTO) to permit economic optimization during transient operation. Published DRTO literature optimizes plant input trajectories without taking into account the presence of the plant control system, constituting an open-loop DRTO (OL-DRTO) approach. The goal of this research is to develop a design framework for a DRTO system that optimizes process economics based on a closed-loop response prediction. We focus, in particular, on DRTO applied to a continuous process operation regulated under constrained MPC. We follow a two-layer DRTO/MPC configuration due to its close tie to the industrial process automation architecture. We first analyze the effects of optimizing MPC closed-loop response dynamics at the DRTO level. A rigorous DRTO problem structure proposed in this thesis is in the form of a multilevel dynamic optimization problem, as it embeds a sequence of MPC optimization subproblems to be solved in order to generate the closed-loop prediction in the DRTO formulation, denoted here as a closed-loop DRTO (CL-DRTO) strategy. A simultaneous solution approach is applied in which the convex MPC optimization subproblems are replaced by their necessary and sufficient, Karush-Kuhn-Tucker (KKT) optimality conditions, resulting in the reformulation of the original multilevel problem as a single-level mathematical program with complementarity constraints (MPCC) with the complementarities handled using an exact penalty formulation. Performance analysis is carried out, and process conditions under which the CL-DRTO strategy significantly outperforms the traditional open-loop counterpart are identified. The multilevel DRTO problem with a rigorous inclusion of the future MPC calculations significantly increases the size and solution time of the economic optimization problem. Next, we identify and analyze multiple closed-loop approximation techniques, namely, a hybrid formulation, a bilevel programming formulation, and an input clipping formulation applied to an unconstrained MPC algorithm. Performance analysis based on a linear dynamic system shows that the proposed approximation techniques are able to substantially reduce the size and solution time of the rigorous CL-DRTO problem, while largely retaining its original performance. Application to an industrially-based case study of a polystyrene production described by a nonlinear differential-algebraic equation (DAE) system is also presented. Often large-scale industrial systems comprise multi-unit subsystems regulated under multiple local controllers that require systematic coordination between them. Utilization of closed-loop prediction in the CL-DRTO formulation is extended for application as a higher-level, centralized supervisory control strategy for coordination of a distributed MPC system. The advantage of the CL-DRTO coordination formulation is that it naturally considers interaction between the underlying MPC subsystems due to the embedded controller optimization subproblems while optimizing the overall process dynamics. In this case, we take advantage of the bilevel formulation to perform closed-loop prediction in two DRTO coordination schemes, with variations in the coordinator objective function based on dynamic economics and target tracking. Case study simulations demonstrate excellent performance in which the proposed coordination schemes minimize the impact of disturbance propagation originating from the upstream subsystem dynamics, and also reduce the magnitude of constraint violation through appropriate adjustment of the controller set-point trajectories. / Thesis / Doctor of Philosophy (PhD)

Title: Hierarchical Problems with Evolutionary Equilibrium Constraints Author: Lukáš Adam Supervisor: Prof. Jiří Outrata Abstract: In the presented thesis, we are interested in hierarchical models with evolutionary equilibrium constraints. Such models arise naturally when a time-dependent problem is to be controlled or if parameters in such a model are to be identified. We intend to discretize the problem and solve it on the basis of the so-called implicit programming approach. This technique requires knowledge of a generalized derivative of the solution mapping which assigns the state variable to the control variable/parameter. The computation of this generalized derivative amounts equivalently to the computation of (limiting) normal cone to the graph of the solution mapping. In the first part we summarize known techniques for computation of the normal cone to the set which can be represented as a finite union of convex polyhedra. Then we propose a new approach based on the so-called normally admissible stratification and simplify the obtained formulas for the case of time-dependent problems. The theoretical results are then applied first to deriving a criterion for the sensitivity analysis of the solution mapping and then to the solution of two practically motivated problems. The first one concerns optimal...