The work in this thesis focuses on the development of a Stochastic Model Predictive Control (SMPC) algorithm for linear systems with additive and multiplicative stochastic uncertainty subjected to linear input/state constraints. Constraints can be in the form of hard constraints, which must be satisfied at all times, or soft constraints, which can be violated up to a pre-defined limit on the frequency of violation or the expected number of violations in a given period. When constraints are included in the SMPC algorithm, the difficulty arising from stochastic model parameters manifests itself in the online optimization in two ways. Namely, the difficulty lies in predicting the probability distribution of future states and imposing constraints on closed loop responses through constraints on predictions. This problem is overcome through the introduction of layered tubes around a centre trajectory. These tubes are optimized online in order to produce a systematic and less conservative approach of handling constraints. The layered tubes centered around a nominal trajectory achieve soft constraint satisfaction through the imposition of constraints on the probabilities of one-step-ahead transition of the predicted state between the layered tubes and constraints on the probability of one-step-ahead constraint violations. An application in the field of Sustainable Development policy is used as an example. With some adaptation, the algorithm is extended the case where the uncertainty is not identically and independently distributed. Also, by including linearization errors, it is extended to non-linear systems with additive uncertainty.

Stochastic model predictive control (MPC) is a fascinating field for research and of increasing practical importance since optimal control techniques have been intensively investigated in modern control system design. With the development of computer technologies and communication networks, networked control systems (NCSs) or cyber-physical systems (CPSs) have become an interest of research due to the comprehensive integration of physical systems, such as sensors, actuators and plants, with intricate cyber components, possessing information communication and computation. In CPSs, advantages of low installation cost, high reliability, flexible modularity, improved efficiency, and greater autonomy can be obtained by the tight coordination of physical and cyber components. Several sectors, including robotics, transportation, health care, smart buildings, and smart grid, have witnessed the successful application of CPSs design. The integration of extensive cyber capability and physical plants with ubiquitous uncertainties also introduces concerns over communication efficiency, robustness and stability of the CPSs. Thus, to achieve satisfactory performance metrics of efficiency, robustness and stability, a detailed investigation into control synthesis of CPSs under the stochastic model predictive control framework is of importance. The stochastic model predictive control synthesis plays a vital role in CPSs design since the multivariable stochastic system subject to probabilistic constraints can be controlled in an optimized way. On the other hand, aperiodically sampled, or event-based, model predictive control has also been applied to CPSs extensively to improve communication efficiency. In this thesis, the control synthesis and analysis of aperiodically sampled stochastic model predictive control for CPSs is considered. Chapter 1 provides an introductory literature review of the current development of stochastic MPC, distributed stochastic MPC and event-based MPC. Chapter 2 presents a stochastic self-triggered model predictive control scheme for linear systems with additive uncertainty and with the states and inputs being subject to chance constraints. In the proposed control scheme, the succeeding sampling time instant and current control inputs are computed online by solving a formulated optimization problem. Chapter 3 discusses a stochastic self-triggered model predictive control algorithm with an adaptive prediction horizon. The communication cost is explicitly considered by adding a damping factor in the cost function. Sufficient conditions are provided to guarantee closed-loop chance constraints satisfactions. Furthermore, the recursive feasibility of the algorithm is analyzed, and the closed-loop system is shown to be stable. Chapter 4 proposes a distributed self-triggered stochastic MPC control scheme for CPSs under coupled chance constraints and additive disturbances. Based on the assumptions on stochastic disturbances, both local and coupled probabilistic constraints are transformed into the deterministic form using the tube-based method, and improved terminal constraints are constructed to guarantee the recursive feasibility of the control scheme. Theoretical analysis has shown that the overall closed-loop CPSs are quadratically stable. Numerical examples illustrate the efficacy of the proposed control method in terms of data transmission reductions. Chapter 5 concludes the thesis and suggests some promising directions for future research. / Graduate / 2022-01-15

A robust model predictive control algorithm is presented that explicitly handles multiplicative, or parametric, uncertainty in linear discrete models over a finite horizon. The uncertainty in the predicted future states and inputs is bounded by polytopes. The computational cost of running the controller is reduced by calculating matrices offline that provide a means to construct outer approximations to robust constraints to be applied online. The robust algorithm is extended to problems of uncertain models with an allowed probability of violation of constraints. The probabilistic degrees of satisfaction are approximated by one-step ahead sampling, with a greedy solution to the resulting mixed integer problem. An algorithm is given to enlarge a robustly invariant terminal set to exploit the probabilistic constraints. Exponential basis functions are used to create a Robust MPC algorithm for which the predictions are defined over the infinite horizon. The control degrees of freedom are weights that define the bounds on the state and input uncertainty when multiplied by the basis functions. The controller handles multiplicative and additive uncertainty. Robust MPC is applied to the problem of wind turbine control. Rotor speed and tower oscillations are controlled by a low sample rate robust predictive controller. The prediction model has multiplicative and additive uncertainty due to the uncertainty in short-term future wind speeds and in model linearisation. Robust MPC is compared to nominal MPC by means of a high-fidelity numerical simulation of a wind turbine under the two controllers in a wide range of simulated wind conditions.

Cette thèse propose des stratégies de gestion de l'énergie conçues pour un bus urbain électrique hybride. Le système de commande hybride devrait créer une stratégie efficace de coordination du flux d’énergie entre le moteur thermique, la batterie, les moteurs électriques et hydrauliques. Tout d'abord, une approche basée sur la programmation dynamique déterministe (DDP) a été proposée : algorithme d'optimisation simultanée de la vitesse et de la puissance pour un trajet donné (limité par la distance parcourue et le temps de parcours). Cet algorithme s’avère être gourmand en temps de calcul, il n’a pas été donc possible de l’utiliser en temps réel. Pour remédier à cet inconvénient, une base de données de profils optimaux basée sur DP (OPD-DP) a été construite pour une application en temps réel. Ensuite, une technique de programmation dynamique stochastique (SDP) a été utilisée pour générer simultanément et d’une manière optimale un profil approprié de la vitesse du Bus ainsi que sa stratégie de partage de puissance correspondante. Cette approche prend en compte à la fois la nature stochastique du comportement de conduite et les conditions de circulations urbaines (soumises à de multiples aléas). Le problème d’optimisation énergétique formulé, en tant que problème intrinsèquement multi-objectif, a été transformé en plusieurs problèmes à objectif unique avec contraintes utilisant une méthode ε-constraint afin de déterminer un ensemble de solutions optimales (le front de Pareto).En milieu urbain, en raison des conditions de circulation, des feux de circulation, un bus rencontre fréquemment des situations Stop&Go. Cela se traduit par une consommation d'énergie accrue lors notamment des démarrages. En ce sens, une stratégie de régulation de vitesse adaptative adaptée avec Stop&Go (eACCwSG) apporte un avantage indéniable. L'algorithme lisse le profil de vitesse pendant les phases d'accélération et de freinage du Bus. Une autre caractéristique importante de cet algorithme est l’aspect sécurité, étant donné que l’ACCwSG permet de maintenir une distance de sécurité afin d’éviter les collisions et d’appliquer un freinage en douceur. Comme il a été mentionné précédemment, un freinage en douceur assure le confort des passagers. / This PhD thesis proposes Energy Management Strategies conceived for a hybrid electrical urban bus. The hybrid control system should create an efficient strategy of coordinating the flow of energy between the heat engine, battery, electrical and hydraulic motors. Firstly, a Deterministic Dynamic Programming (DDP) based approach has been proposed: simultaneous speed and powersplit optimization algorithm for a given trip (constrained by the traveled distance and time limit). This algorithm turned out to be highly time consuming so it cannot be used in real-time. To overcome this drawback, an Optimal Profiles Database based on DP (OPD-DP) has been constructed for real-time application. Afterwards, a Stochastic Dynamic Programming (SDP) technique is used to simultaneously generate an optimal speed profile and related powersplit strategy. This approach takes into account a stochastic nature of the driving behavior and urban conditions. The formulated energy optimization problem, being intrinsically multi-objective problem, has been transformed into several single-objective ones with constraints using an ε-constraint method to determine a set of optimal solutions (the Pareto Front).In urban environment, due to traffic conditions, traffic lights, a bus encounters frequent Stop&Go situations. This results in increased energy consumption during the starts. In this sense, a relevant Eco Adaptive Cruise Control with Stop&Go (eACCwSG) strategy brings the undeniable benefit. The algorithm smooths speed profile during acceleration and braking phases. One more important feature of this algorithm is the safety aspect, as eACCwSG permits to maintain a safety distance in order to avoid collision and apply a smooth braking. As it was mentioned before, smooth braking ensures passengers comfort.