Scenario-based model predictive control for systems with correlated uncertainties
- Autores: Edwin Alonso González Querubín
- Directores de la Tesis: Javier Sanchis Sáez (dir. tes.), J. V. Salcedo (dir. tes.)
- Lectura: En la Universitat Politècnica de València ( España ) en 2024
- Idioma: inglés
- Tribunal Calificador de la Tesis: Juan Manuel Escaño González (presid.), Francesc Xavier Blasco Ferragud (secret.), Ramon Vilanova i Arbós (voc.)
- Programa de doctorado: Programa de Doctorado en Automática, Robótica e Informática Industrial por la Universitat Politècnica de València
- Materias:
- Enlaces
- Tesis en acceso abierto en: RiuNet
- Resumen
The vast majority of real-world processes have inherent uncertainties, which, when considered in the modelling process, can provide a representation that most accurately describes the behaviour of the real process. In most practical cases, these are considered to have stochastic behaviour and their descriptions as probability distributions are known.
Stochastic model predictive control algorithms are developed to control processes with uncertainties of a stochastic nature, where the knowledge of the statistical properties of the uncertainties is exploited by including it in the optimal control problem (OCP) statement. Contrary to other model predictive control (MPC) schemes, hard constraints are relaxed by reformulating them as probabilistic constraints to reduce conservatism. That is, violations of the original hard constraints are allowed, but such violations must not exceed a permitted level of risk.
The non-convexity of such probabilistic constraints renders the optimisation problem computationally unmanageable, thus most stochastic MPC strategies in the literature differ in how they deal with such constraints and uncertainties to turn the problem computationally tractable. On the one hand, there are deterministic strategies that, offline, convert probabilistic constraints into new deterministic ones, using the propagation of uncertainties along the prediction horizon to tighten the original hard constraints.
Scenario-based approaches, on the other hand, use the uncertainty information to randomly generate, at each sampling instant, a set of possible evolutions of uncertainties over the prediction horizon. In this fashion, they convert the probabilistic constraints into a set of deterministic constraints that must be fulfilled for all the scenarios generated. These strategies stand out for their ability to include real-time updated uncertainty information. However, this advantage comes with inconveniences such as computational effort, which grows as the number of scenarios does, and the undesired effect on the optimisation problem caused by scenarios with a low probability of occurrence when a small set of scenarios is used.
The aforementioned challenges steered this thesis toward stochastic scenario-based MPC approaches, and yielded three main contributions. The first one consists of a comparative study of an algorithm from the deterministic group with another one from the scenario-based group, where a special emphasis is made on how each of them deals with uncertainties, transforms the probabilistic constraints and on the structure of the optimisation problem, as well as pointing out their most outstanding aspects and challenges.
The second contribution is a new proposal for a MPC algorithm, which is based on conditional scenarios, developed for linear systems with correlated uncertainties. This scheme exploits the existence of such correlation to convert a large initial set of scenarios into a smaller one with their probabilities of occurrence, which preserves the characteristics of the initial set. The reduced set is used in an OCP in which the predictions of the system states and inputs are penalised according to the probabilities of the scenarios that compose them, giving less importance to the scenarios with lower probabilities of occurrence.
The third contribution consists of a procedure for the implementation of the new MPC algorithm as an energy manager in a microgrid in which the forecasts of renewables and loads are correlated.
