Pós-Graduação em Engenharia de Automação e Sistemas

Coorientador

Prof. Morten Hovd, Dr. – NTNU/Noruega

Videoconferência (https://NTNU.zoom.us/j/94080920248?pwd=OHUrOERmQUlESG1BbEZjbHB4WmFjZz09)

Banca

Prof. Dominique Bonvin, Dr. – EPFL/Suiça;

Profa. Cristina Stoica Maniu, Dra. – Centrale Supélec/França;

Prof. Lars Imsland, Dr. – NTNU/Noruega;

Prof. Mario Cesar Mello Massa de Campos, Dr. – SmartAutomation/RJ

These systems represent a considerable portion of the controls applications since systems are seldomly isolated in real-world applications. This thesis contributes to the field of distributed optimal control of networked systems by proposing a framework for modeling, formalizing optimal control problems (OCP), and solving the OCP. The framework relies on the augmented Lagrangian method for optimal control of differential-algebraic equations (DAEs), which has its mathematical properties improved by this thesis — necessary conditions for global, local, and suboptimal convergence are shown. The framework proposes a modeling strategy that uses a direct graph to represent the many subsystems. Each subsystem is represented as a node, where the input-output relation between the subsystem is represented as an edge.

This component-based description of the system allows for easier development and maintenance of the models. The OCP is described using the system model and a set of guidelines, leading to a decoupled cost coupled constraints (DCCC) formulation.

The proposed formulation allows for the augmented Lagrangian method for optimal control of DAEs to relax the equations that connect the subsystems. The relaxed equations are put into the objective function, transforming into a coupled cost decoupled constraint (CCDC) formulation since there are no more constraints between the subsystems. There are several strategies for solving CCDC formulations; this thesis develops algorithms based on the coordinate descent and the alternating direction multiplier method (ADMM), which are well-suited for this formulation. One downside of these techniques is that they don’t allow for two connected nodes to iterate alongside, to circumvent that a modeling artifice was used, which enables all nodes to iterate alongside. Computational experiments were performed in a benchmark system, which showed promising results. The positive results led to further investigation of the behavior of the algorithms when controlling systems with nonlinearities closer to real applications. Numerical experiments with a small-scale oil production network showed that the algorithms could properly control the plant, even with nonlinearities and discontinuities.