In this thesis, we consider the trajectory planning of an autonomous vehicle to cross an intersection within a given time interval. The vehicle communicates its sensordata to a central coordinator which then computes the trajectory for the given time horizon and sends it back to the vehicle. We consider a realistic scenario in which the communication links are unreliable, the evolution of the state has noise (e.g., due to the model simplification and environmental disturbances), and the observationis noisy (e.g., due to noisy sensing and/or delayed information). The intersection crossing is modeled as a chance constraint problem and the stochastic noise evolution is restricted by a terminal constraint. The communication impairments are modeled as packet drop probabilities and Kalman estimation techniques are used for predicting the states in the presence of state and observation noises. A robust sub-optimalsolution is obtained using convex optimization methods which ensures that the intersection is crossed by the vehicle in the given time interval with very low chance of failure.

A two-level optimal coordination control approach for energy storage and conventional generation consisting of advanced frequency control and stochastic optimal dispatch is proposed to deal with the real power balancing control problem introduced by variable renewable energy sources (RESs) in power systems. In the proposed approach, the power and energy constraints on energy storage are taken into account in addition to the traditional power system operational constraints such as generator output limits and power network constraints. The advanced frequency control level which is based on the robust control theory and the decentralized static output feedback design is responsibl e for the system frequency stabilization and restoration, whereas the stochastic optimal dispatch level which is based on the concept of stochastic model predictive control (SMPC) determines the optimal dispatch of generation resources and energy storage under uncertainties introduced by RESs as well as demand. In the advanced frequency control level, low-order decentralized robust frequency controllers for energy storage and conventional generation are simultaneously designed based on a state-space structure-preserving model of the power system and the optimal controller gains are solved via an improved linear matrix inequality algorithm. In the stochastic optimal dispatch level, various optimization decomposition techniques including both primal and dual decompositions together with two different decomposition schemes (i.e. scenario-based decomposition and temporal-based decomposition) are extensively investigated in terms of convergence speed due to the resulting large-scale and computationally demanding SMPC optimization problem. A two-stage mixed decomposition method is conceived to achieve the maximum speedup of the SMPC optimization solution process. The underlying control design philosophy across the entire work is the so-called time-scale matching principle, i.e. the conventional generators are mainly responsible to balance the low frequency components of the power variations whereas the energy storage devices because of their fast response capability are employed to alleviate the relatively high frequency components. The performance of the proposed approach is tested and evaluated by numerical simulations on both the WECC 9-bus system and the IEEE New England 39-bus system.

Threat assessment and reliable motion-prediction of surrounding vehicles are some of the major challenges encountered in autonomous vehicles' safe decision-making. Predicting a threat in advance can give an autonomous vehicle enough time to avoid crashes or near crash situations. Most vehicles on roads are human-driven, making it challenging to predict their intentions and movements due to inherent uncertainty in their behaviors. Moreover, different driver behaviors pose different kinds of threats. Various driver behavior predictive models have been proposed in the literature for motion prediction. However, these models cannot be trusted entirely due to the human drivers' highly uncertain nature. This thesis proposes a novel trust-based driver behavior prediction and stochastic reachable set threat assessment methodology for various dangerous situations on the road. This trust-based methodology allows autonomous vehicles to quantify the degree of trust in their predictions to generate the probabilistically safest trajectory. This approach can be instrumental in the near-crash scenarios where no collision-free trajectory exists. Three different driving behaviors are considered: Normal, Aggressive, and Drowsy. Hidden Markov Models are used for driver behavior prediction. A "trust" in the detected driver is established by combining four driving features: Longitudinal acceleration, lateral acceleration, lane deviation, and velocity. A stochastic reachable set-based approach is used to model these three different driving behaviors. Two measures of threat are proposed: Current Threat and Short Term Prediction Threat which quantify present and the future probability of a crash. The proposed threat assessment methodology resulted in a lower rate of false positives and negatives. This probabilistic threat assessment methodology is used to address the second challenge in autonomous vehicle safety: crash avoidance decision-making. This thesis presents a fast, proactive decision-making methodology based on Stochastic Model Predictive Control (SMPC). A proactive decision-making approach exploits the surrounding human-driven vehicles' intent to assess the future threat, which helps generate a safe trajectory in advance, unlike reactive decision-making approaches that do not account for the surrounding vehicles' future intent. The crash avoidance problem is formulated as a chance-constrained optimization problem to account for uncertainty in the surrounding vehicle's motion. These chance-constraints always ensure a minimum probabilistic safety of the autonomous vehicle by keeping the probability of crash below a predefined risk parameter. This thesis proposes a tractable and deterministic reformulation of these chance-constraints using convex hull formulation for a fast real-time implementation. The controller's performance is studied for different risk parameters used in the chance-constraint formulation. Simulation results show that the proposed control methodology can avoid crashes in most hazardous situations on the road. / Master of Science / Unexpected road situations frequently arise on the roads which leads to crashes. In an NHTSA study, it was reported that around 94% of car crashes could be attributed to driver errors and misjudgments. This could be attributed to drinking and driving, fatigue, or reckless driving on the roads. Full self-driving cars can significantly reduce the frequency of such accidents. Testing of self-driving cars has recently begun on certain roads, and it is estimated that one in ten cars will be self-driving by the year 2030. This means that these self-driving cars will need to operate in human-driven environments and interact with human-driven vehicles. Therefore, it is crucial for autonomous vehicles to understand the way humans drive on the road to avoid collisions and interact safely with human-driven vehicles on the road. Detecting a threat in advance and generating a safe trajectory for crash avoidance are some of the major challenges faced by autonomous vehicles. We have proposed a reliable decision-making algorithm for crash avoidance in autonomous vehicles. Our framework addresses two core challenges encountered in crash avoidance decision-making in autonomous vehicles: 1. The outside challenge: Reliable motion prediction of surrounding vehicles to continuously assess the threat to the autonomous vehicle. 2. The inside challenge: Generating a safe trajectory for the autonomous vehicle in case of future predicted threat. The outside challenge is to predict the motion of surrounding vehicles. This requires building a reliable model through which future evolution of their position states can be predicted. Building these models is not trivial, as the surrounding vehicles' motion depends on human driver intentions and behaviors, which are highly uncertain. Various driver behavior predictive models have been proposed in the literature. However, most do not quantify trust in their predictions. We have proposed a trust-based driver behavior prediction method which combines all sensor measurements to output the probability (trust value) of a certain driver being "drowsy", "aggressive", or "normal". This method allows the autonomous vehicle to choose how much to trust a particular prediction. Once a picture is painted of surrounding vehicles, we can generate safe trajectories in advance – the inside challenge. Most existing approaches use stochastic optimal control methods, which are computationally expensive and impractical for fast real-time decision-making in crash scenarios. We have proposed a fast, proactive decision-making algorithm to generate crash avoidance trajectories based on Stochastic Model Predictive Control (SMPC). We reformulate the SMPC probabilistic constraints as deterministic constraints using convex hull formulation, allowing for faster real-time implementation. This deterministic SMPC implementation ensures in real-time that the vehicle maintains a minimum probabilistic safety.

Trajectory planning constitutes an essential step for proper autonomous vehicles’performance. This work aims at defining and testing a stochastic approach providingsafe, length-optimal and comfortable trajectories accounting for road, model anddisturbance uncertainties. A Stochastic Model Predictive Control (SMPC) problemis formulated using a Linear Parameter Varying Bicycle Model, state-probabilisticconstraints and input constraints. The SMPC is transformed into a tractable quadraticoptimisation problem after assuming independent and gaussian uncertainties.The proposed trajectory planning methodology is intended to be implemented onlinein a Receding Horizon fashion in a real vehicle. Results are presented after computersimulatedtests have been carried out to study the influence of model uncertaintiesand SMPC parameters on the planned and executed trajectories in standard drivingsituations. Particularly, road crosswind is modelled, its effect on vehicles withdifferent steering characteristics is studied and it is considered for improved trajectoryplanning. The approach constitutes a promising method to provide robust trajectoriesto unmodeled errors reaching an equilibrium between conservativeness and quality ofthe solution. / Banplanering utgör ett väsentligt steg för riktiga autonoma fordons prestanda.Syftet med detta arbete är att definiera och testa stokastiska strategier som gersäkra, optimala och bekväma banor som tar hänsyn till vägen, modelbrus ochosäkerheter. En stokastisk Model Predictive Control (SMPC) problem är formuleratmed hjälp av Linear Parameter Varying Bicycle Model, tillstånds-sannolikhetsbivillkoroch inmatningsbivillkor. SMPC transformeras till ett lätthanterlig kvadratiskoptimeringsproblem efter oberoende gaussfördelade osäkerheter antagits.Den föreslagna banplaneringsmetoden är avsedd att implementeras online meden Receding Horizon för ett riktigt fordon. Resultatet är presenterat efterdatorsimulerade experiment har blivit genomförda för att studera påverkan avmodelosäkerheter och SMPC parametrar på den planerade och genomförda banorför standard körsituationer. I synnerhet, är sidovind modellerat, dens effekt påfordon med olika styrkaraktäristik är studerad och är tagen hänsyn till för förbättradbanplanering. Tillvägagångssättet utgör en lovande metod för att tillhandahållarobusta banor för icke-model fel som når en jämvikt mellan konservativitet och kvalitethos lösningen.

[ES] La gran mayoría de procesos del mundo real tienen incertidumbres inherentes, las cuales, al ser consideradas en el proceso de modelado, se puede obtener una representación que describa con la mayor precisión posible el comportamiento del proceso real. En la mayoría de casos prácticos, se considera que éstas tienen un comportamiento estocástico y sus descripciones como distribuciones de probabilidades son conocidas. Las estrategias de MPC estocástico están desarrolladas para el control de procesos con incertidumbres de naturaleza estocástica, donde el conocimiento de las propiedades estadísticas de las incertidumbres es aprovechado al incluirlo en el planteamiento de un problema de control óptimo (OCP). En éste, y contrario a otros esquemas de MPC, las restricciones duras son relajadas al reformularlas como restricciones de tipo probabilísticas con el fin de reducir el conservadurismo. Esto es, se permiten las violaciones de las restricciones duras originales, pero tales violaciones no deben exceder un nivel de riesgo permitido. La no-convexidad de tales restricciones probabilísticas hacen que el problema de optimización sea prohibitivo, por lo que la mayoría de las estrategias de MPC estocástico en la literatura se diferencian en la forma en que abordan tales restricciones y las incertidumbres, para volver el problema computacionalmente manejable. Por un lado, están las estrategias deterministas que, fuera de línea, convierten las restricciones probabilísticas en unas nuevas de tipo deterministas, usando la propagación de las incertidumbres a lo largo del horizonte de predicción para ajustar las restricciones duras originales. Por otra parte, las estrategias basadas en escenarios usan la información de las incertidumbres para, en cada instante de muestreo, generar de forma aleatoria un conjunto de posibles evoluciones de éstas a lo largo del horizonte de predicción. De esta manera, convierten las restricciones probabilísticas en un conjunto de restricciones deterministas que deben cumplirse para todos los escenarios generados. Estas estrategias se destacan por su capacidad de incluir en tiempo real información actualizada de las incertidumbres. No obstante, esta ventaja genera inconvenientes como su gasto computacional, el cual aumenta conforme lo hace el número de escenarios y; por otra parte, el efecto no deseado en el problema de optimización, causado por los escenarios con baja probabilidad de ocurrencia, cuando se usa un conjunto de escenarios pequeño. Los retos mencionados anteriormente orientaron esta tesis hacia los enfoques de MPC estocástico basado en escenarios, produciendo tres contribuciones principales. La primera consiste en un estudio comparativo de un algoritmo del grupo determinista con otro del grupo basado en escenarios; se hace un especial énfasis en cómo cada uno de estos aborda las incertidumbres, transforma las restricciones probabilísticas y en la estructura de su OCP, además de señalar sus aspectos más destacados y desafíos. La segunda contribución es una nueva propuesta de algoritmo MPC, el cual se basa en escenarios condicionales, diseñado para sistemas lineales con incertidumbres correlacionadas. Este esquema aprovecha la existencia de tal correlación para convertir un conjunto de escenarios inicial de gran tamaño en un conjunto de escenarios más pequeño con sus probabilidades de ocurrencia, el cual conserva las características del conjunto inicial. El conjunto reducido es usado en un OCP en el que las predicciones de los estados y entradas del sistema son penalizadas de acuerdo con las probabilidades de los escenarios que las componen, dando menor importancia a los escenarios con menores probabilidades de ocurrencia. La tercera contribución consiste en un procedimiento para la implementación del nuevo algoritmo MPC como gestor de la energía en una microrred en la que las previsiones de las energías renovables y las cargas están correlacionadas. / [CA] La gran majoria de processos del món real tenen incerteses inherents, les quals, en ser considerades en el procés de modelatge, es pot obtenir una representació que descriga amb la major precisió possible el comportament del procés real. En la majoria de casos pràctics, es considera que aquestes tenen un comportament estocàstic i les seues descripcions com a distribucions de probabilitats són conegudes. Les estratègies de MPC estocàstic estan desenvolupades per al control de processos amb incerteses de naturalesa estocàstica, on el coneixement de les propietats estadístiques de les incerteses és aprofitat en incloure'l en el plantejament d'un problema de control òptim (OCP). En aquest, i contrari a altres esquemes de MPC, les restriccions dures són relaxades en reformulades com a restriccions de tipus probabilístiques amb la finalitat de reduir el conservadorisme. Això és, es permeten les violacions de les restriccions dures originals, però tals violacions no han d'excedir un nivell de risc permès. La no-convexitat de tals restriccions probabilístiques fan que el problema d'optimització siga computacionalment immanejable, per la qual cosa la majoria de les estratègies de MPC estocàstic en la literatura es diferencien en la forma en què aborden tals restriccions i les incerteses, per a tornar el problema computacionalment manejable. D'una banda, estan les estratègies deterministes que, fora de línia, converteixen les restriccions probabilístiques en unes noves de tipus deterministes, usant la propagació de les incerteses al llarg de l'horitzó de predicció per a ajustar les restriccions dures originals. D'altra banda, les estratègies basades en escenaris usen la informació de les incerteses per a, en cada instant de mostreig, generar de manera aleatòria un conjunt de possibles evolucions d'aquestes al llarg de l'horitzó de predicció. D'aquesta manera, converteixen les restriccions probabilístiques en un conjunt de restriccions deterministes que s'han de complir per a tots els escenaris generats. Aquestes estratègies es destaquen per la seua capacitat d'incloure en temps real informació actualitzada de les incerteses. No obstant això, aquest avantatge genera inconvenients com la seua despesa computacional, el qual augmenta conforme ho fa el nombre d'escenaris i; d'altra banda, l'efecte no desitjat en el problema d'optimització, causat pels escenaris amb baixa probabilitat d'ocurrència, quan s'usa un conjunt d'escenaris xicotet. Els reptes esmentats anteriorment van orientar aquesta tesi cap als enfocaments de MPC estocàstic basat en escenaris, produint tres contribucions principals. La primera consisteix en un estudi comparatiu d'un algorisme del grup determinista amb un altre del grup basat en escenaris; on es fa un especial èmfasi en com cadascun d'aquests aborda les incerteses, transforma les restriccions probabilístiques i en l'estructura del seu problema d'optimització, a més d'assenyalar els seus aspectes més destacats i desafiaments. La segona contribució és una nova proposta d'algorisme MPC, el qual es basa en escenaris condicionals, dissenyat per a sistemes lineals amb incerteses correlacionades. Aquest esquema aprofita l'existència de tal correlació per a convertir un conjunt d'escenaris inicial de gran grandària en un conjunt d'escenaris més xicotet amb les seues probabilitats d'ocurrència, el qual conserva les característiques del conjunt inicial. El conjunt reduït és usat en un OCP en el qual les prediccions dels estats i entrades del sistema són penalitzades d'acord amb les probabilitats dels escenaris que les componen, donant menor importància als escenaris amb menors probabilitats d'ocurrència. La tercera contribució consisteix en un procediment per a la implementació del nou algorisme MPC com a gestor de l'energia en una microxarxa en la qual les previsions de les energies renovables i les càrregues estan correlacionades. / [EN] 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. / González Querubín, EA. (2024). Scenario-Based Model Predictive Control for Systems with Correlated Uncertainties [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/203887