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Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this paper, we propose a data-driven stochastic predictive control scheme for LTI systems subject to possibly unbounded additive process disturbances. Based on a stochastic extension of the fundamental lemma and leveraging polynomial chaos expansions, we construct a data-driven surrogate optimal control problem (OCP). Moreover, combined with an online selection strategy of the initial condition of the OCP, we provide sufficient conditions for recursive feasibility and for stability of the proposed data-driven predictive control scheme. Finally, two numerical examples illustrate the efficacy and closed-loop properties of the proposed scheme for process disturbances governed by different distributions.

Active power control of wind farms remains an open challenge due to inherent noise in wind power that arises from uncertain wind speed measurements and plant/model mismatch. To leverage the heteroscedastic nature of the wind power noise, heteroscedastic Bayesian optimisation (BO) is used for active power control of wind farms. BO utilises closed-loop performance data to tune the parameters of a stochastic model predictive controller (SMPC) in a systematic and data-efficient manner. This, in turn, allows for enhancing the closed-loop performance of the controller intended to decrease the power tracking error. A case study with 9 turbines in a 3x3 wind farm shows that the heteroscedastic BO approach achieves a reduced closed-loop power tracking error in terms of root-mean-square by 8.89% compared to one that relies on nominal BO and a decrease by 64.99% compared to a nominal model predictive controller (MPC) whose performance is not tuned using closed-loop data and BO.

Batteries are complex systems that need to be properly managed to guarantee safe and optimal operations. Model predictive control (MPC) is an advanced control strategy that, thanks to its characteristics, can be embedded into battery management systems (BMS) to derive optimal charging strategies. However, deterministic MPC, which relies on a nominal model only, is not adequate in a realistic scenario in which cells parameters are not known exactly. In this paper, stochastic MPC is proposed for the optimal charging of a Li-ion battery pack to account for the presence of parameter uncertainties. The adopted scheme relies on the polynomial chaos expansion paradigm for the propagation of uncertainties through the model equations and allows to satisfy safety constraints with a guaranteed probability. The results highlight the advantages of stochastic MPC over different scenarios when compared to a deterministic MPC approach.

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power.

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power.

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power.

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 decisio

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power.

In this work, a novel nonlinear approach is proposed for the stabilization of microgrids with constant power loads (CPLs). The proposed method is constructed based on the incorporation of a pseudo-extended Kalman filter into stochastic nonlinear model predictive control (MPC). In order to achieve high-performance and optimal control in DC microgrids, estimating the instantaneous power flow of the uncertain constant power loads and the available power units is essential. Thus, by utilizing the advantages of the stochastic nonlinear model predictive control and the pseudo-extended Kalman filter, an effective control solution for the stabilization of DC islanded microgrids with CPLs is established. This technique develops a constrained controller for practical application to handle the states and control input constraints explicitly; furthermore, as it estimates the current by using the pseudo-EKF, it is a current-senseless approach. As noisy measurements are taken into account for the state estimation, it leads to a less conservative control action rather than the classical robust MPC, whereas it guarantees the global asymptotic stability in the presence of noisy measurements and parameter uncertainty. To validate the performance of the proposed controller, the attained results are compared to state-of-the-art controllers. Furthermore, the implementability of the proposed method is validated using real-time simulations on dSPACE hardware.

Scenario-based stochastic model predictive control traditionally considers the optimal strategy to be the expectation of the optimal strategies across all scenarios. However, while the stochastic problem involving uncertainties can be substantiated by a large number of scenarios, the expectation of the respective optimal control strategies derived from all scenarios as the optimal control strategy to the problem is challenging to justify. We therefore propose a different approach in which we artfully have the optimization program find the common optimal strategy across all scenarios for the first prediction step at each sample time, which, if it exists, yields the true optimal strategy with greater confidence. We demonstrate the efficacy of the proposed formulation through a case study of a research villa in Borås, Sweden, that is equipped with a battery and a photovoltaic system. We compute a covariance matrix that contains time-dependent information of the data and use it to sample autocorrelated scenarios from the probabilistic forecasts that serve as the uncertain input to the energy management system. We justify the credibility of the optimal solution derived from the proposed formulation with compelling reasoning and quantitative results such as improved self-consumption of photovoltaic power.

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.

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.

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.

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.

With increasing fluctuations in electricity production due to prioritization of renewable energy sources, new applications that can adjust quickly to changes in demand/supply will be needed. Wastewater treatment use a significant amount of electricity to reduce nutrients in wastewater before discharge. The treatment process demands electricity in some selected periods which can be controlled, and hence the time of consumption is changeable. Here we suggest a novel predictive control strategy which enhances the flexibility in electricity demand by accounting for electricity price and probability of up or down regulation. The strategy is demonstrated in simulation experiments, where the concept is illustrated and the potential savings are estimated. Furthermore flexibility is investigated as a function of regulating prices, and it is shown that when difference between electricity price and regulating price increases, sodoes flexibility of the system

A numerically tractable Stochastic Model Predictive Control (SMPC) strategy using Conditional Value at Risk (CVaR) optimization for discrete-time linear time-invariant systems, with state and input constraints, subject to additive uncertainty, is presented. SMPC strategies make use of the probabilistic description of uncertainty to define chance constraints which allow a certain admissible level of constraint violation. SMPC strategies require the initial state of a system to be within a particular set, referred to as feasibility set, probabilistically, such that the derived control input, when applied to the system, gives rise to states that are also within the feasibility set satisfying all chance constraints on the system. This leads to recursive feasibility of the SMPC strategy. Such strategies are restrictive in nature when the uncertainty in the system is unbounded, as in the case of White Gaussian noise. In such a case, the feasibility set is very small and leads to a strategy that is very conservative. To reduce this conservatism, some constraint violations are permitted. However, such violations affect the closed-loop behaviour of the system leading to performance degradation. This performance degradation can be quantified as a penalty on the system for violating constraints, and intuitively, it can be thought of as a risk taken by the system in that undesirable state. An approach following the exact penalty method is proposed using the CVaR function to determine the penalty cost. The same optimal solution as the original constrained problem is obtained from a single unconstrained minimization. Since accurate computation of the expected value of risk using the CVaR function is not possible, a scenario-based approximation of the CVaR is used to obtain an overall tractable and computationally efficient SMPC strategy. An extensive simulation study of the double integrator system is provided to present the functionality of the proposed method., Electrical Engineering

Smart and optimal energy consumption in electric vehicles has high potential to improve the limited cruising range on a single battery charge. The proposed concept is a semi-autonomous ecological advanced driver assistance system which predictively plans for a safe and energy-efficient cruising velocity profile autonomously for battery electric vehicles. However, high entropy in transportation network leads to a challenging task to derive a computationally efficient and tractable model to predict the traffic flow. Stochastic optimal control has been developed to systematically find an optimal decision with the aim of performance improvement. However, most of the developed methods are not real-time algorithms. Moreover, they are mainly risk-neutral for safety-critical systems. This paper investigates on the real-time risk-sensitive nonlinear optimal control design subject to safety and ecological constraints. This system improves the efficiency of the transportation network at the microscopic level. Obtained results demonstrate the effectiveness of the proposed method in terms of states regulation and constraints satisfaction.

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer from problems and constraints that have to be solved before a mass market might be created. Key aspects that will play an important role in modern electric vehicles are range extension, energy efficiency, safety, comfort as well as communication. An overall solution approach to integrating all these aspects is the development of advanced driver assistance systems to make electric vehicles more intelligent. Driver assistance systems are based on the integration of suitable sensors and actuators as well as electronic devices and software-enabled control functionality to automatically support the human driver. Driver assistance for electric vehicles will differ from the already used systems in fuel-powered cars such as electronic stability programs, adaptive cruise control etc. in a way that they must support energy efficiency while the system itself must also have a low power consumption. In this work, an eco-driving functionality as the first step towards those new driver assistance systems for electric vehicles will be investigated. Using information about the internal state of the car, navigation information as well as advanced information about the environment coming from sensors and network connections, an algorithm will be developed that will adapt the speed of the vehicle automatically to minimize energy consumption. From an algorithmic point of view, a stochastic model predictive control approach will be applied and adapted to the special constraints of the problem. Finally, the solution will be tested in simulations as well as in first experiments with a commercial electric vehicle in the SnT Automation & Robotics Research Group (SnT ARG).

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer from problems and constraints that have to be solved before a mass market might be created. Key aspects that will play an important role in modern electric vehicles are range extension, energy efficiency, safety, comfort as well as communication. An overall solution approach to integrating all these aspects is the development of advanced driver assistance systems to make electric vehicles more intelligent. Driver assistance systems are based on the integration of suitable sensors and actuators as well as electronic devices and software-enabled control functionality to automatically support the human driver. Driver assistance for electric vehicles will differ from the already used systems in fuel-powered cars such as electronic stability programs, adaptive cruise control etc. in a way that they must support energy efficiency while the system itself must also have a low power consumption. In this work, an eco-driving functionality as the first step towards those new driver assistance systems for electric vehicles will be investigated. Using information about the internal state of the car, navigation information as well as advanced information about the environment coming from sensors and network connections, an algorithm will be developed that will adapt the speed of the vehicle automatically to minimize energy consumption. From an algorithmic point of view, a stochastic model predictive control approach will be applied and adapted to the special constraints of the problem. Finally, the solution will be tested in simulations as well as in first experiments with a commercial electric vehicle in the SnT Automation & Robotics Research Group (SnT ARG).

Smart and optimal energy consumption in electric vehicles has high potential to improve the limited cruising range on a single battery charge. The proposed concept is a semi-autonomous ecological advanced driver assistance system which predictively plans for a safe and energy-efficient cruising velocity profile autonomously for battery electric vehicles. However, high entropy in transportation network leads to a challenging task to derive a computationally efficient and tractable model to predict the traffic flow. Stochastic optimal control has been developed to systematically find an optimal decision with the aim of performance improvement. However, most of the developed methods are not real-time algorithms. Moreover, they are mainly risk-neutral for safety-critical systems. This paper investigates on the real-time risk-sensitive nonlinear optimal control design subject to safety and ecological constraints. This system improves the efficiency of the transportation network at the microscopic level. Obtained results demonstrate the effectiveness of the proposed method in terms of states regulation and constraints satisfaction.

A numerically tractable Stochastic Model Predictive Control (SMPC) strategy using Conditional Value at Risk (CVaR) optimization for discrete-time linear time-invariant systems, with state and input constraints, subject to additive uncertainty, is presented. SMPC strategies make use of the probabilistic description of uncertainty to define chance constraints which allow a certain admissible level of constraint violation. SMPC strategies require the initial state of a system to be within a particular set, referred to as feasibility set, probabilistically, such that the derived control input, when applied to the system, gives rise to states that are also within the feasibility set satisfying all chance constraints on the system. This leads to recursive feasibility of the SMPC strategy. Such strategies are restrictive in nature when the uncertainty in the system is unbounded, as in the case of White Gaussian noise. In such a case, the feasibility set is very small and leads to a strategy that is very conservative. To reduce this conservatism, some constraint violations are permitted. However, such violations affect the closed-loop behaviour of the system leading to performance degradation. This performance degradation can be quantified as a penalty on the system for violating constraints, and intuitively, it can be thought of as a risk taken by the system in that undesirable state. An approach following the exact penalty method is proposed using the CVaR function to determine the penalty cost. The same optimal solution as the original constrained problem is obtained from a single unconstrained minimization. Since accurate computation of the expected value of risk using the CVaR function is not possible, a scenario-based approximation of the CVaR is used to obtain an overall tractable and computationally efficient SMPC strategy. An extensive simulation study of the double integrator system is provided to present the functionality of the proposed method., Electrical Engineering

As the complexity and scale of chemical processes has increased, engineers have desired a process control strategy that can successfully and safely regulate modern processes. These processes are often subject to random noise and uncertainties in parameters or model structure which make regulation and control difficult. Stochastic model predictive control (SMPC) is an advanced process control strategy that can systematically seek tradeoffs between multiple (possibly competing) control objectives in the presence of constraints for multi-input multi-output systems. Furthermore, SMPC explicitly considers the stochasticity of system states and parameters, allowing for the systematic trade off of robustness and performance. Another key advantage of SMPC is the ability to implement chance constraints, which can be violated with a specified probability, instead of hard constraints which must be satisfied in all conditions. Because SMPC employs a probabilistic description of states and parameters, uncertainty propagation techniques are needed to determine the time evolution of these probability distributions. Monte Carlo methods are a widely used uncertainty propagation technique, but are too computationally expensive for real time optimization and control. Three approaches to efficient SMPC implementations are investigated in this dissertation. A SMPC algorithm with hard input constraints and joint chance constraints in the presence of (possibly) unbounded noise is presented. By recasting the nonlinear SMPC optimal control problem as a convex iterative deterministic program, the computational cost of determining the optimal control policy is significantly decreased. Two uncertainty propagation methods, the Fokker-Planck equation and adaptive polynomial chaos, are presented in the context of optimal control. The Fokker-Planck equation is a partial differential equation that can propagate the full probability distribution of uncertainties. This allows for shaping of the proba

As the complexity and scale of chemical processes has increased, engineers have desired a process control strategy that can successfully and safely regulate modern processes. These processes are often subject to random noise and uncertainties in parameters or model structure which make regulation and control difficult. Stochastic model predictive control (SMPC) is an advanced process control strategy that can systematically seek tradeoffs between multiple (possibly competing) control objectives in the presence of constraints for multi-input multi-output systems. Furthermore, SMPC explicitly considers the stochasticity of system states and parameters, allowing for the systematic trade off of robustness and performance. Another key advantage of SMPC is the ability to implement chance constraints, which can be violated with a specified probability, instead of hard constraints which must be satisfied in all conditions. Because SMPC employs a probabilistic description of states and parameters, uncertainty propagation techniques are needed to determine the time evolution of these probability distributions. Monte Carlo methods are a widely used uncertainty propagation technique, but are too computationally expensive for real time optimization and control. Three approaches to efficient SMPC implementations are investigated in this dissertation. A SMPC algorithm with hard input constraints and joint chance constraints in the presence of (possibly) unbounded noise is presented. By recasting the nonlinear SMPC optimal control problem as a convex iterative deterministic program, the computational cost of determining the optimal control policy is significantly decreased. Two uncertainty propagation methods, the Fokker-Planck equation and adaptive polynomial chaos, are presented in the context of optimal control. The Fokker-Planck equation is a partial differential equation that can propagate the full probability distribution of uncertainties. This allows for shaping of the proba

In power network management, the heat capacity of transmission lines originally arises from the line temperature constraint. The line temperatures are affected not only by the Joule heat but also by the thermal environment. This motivates us to exploit weather forecast data to improve the power management performance. The goal of this paper is to propose a stochastic model predictive control scheme for this purpose. In particular, we compensate for the probabilistic uncertainty by means of chance constraint optimization. The effectiveness of the proposed control scheme is examined through numerical simulation of power grids under the area dependent uncertainty and transmission line failure.

Water resource management has immense importance in the modern world. A large amount of water is wasted due to inefficient management of rivers, lakes and other water bodies associated with them. In order to achieve improved management of water resources, control and decision support systems can be employed. To design control systems for a river, a river model is required. Traditionally, the Saint Venant equations have been used for modelling purposes. The equations describe river flows accurately, however, they are complex, non-linear and require many unknown parameters. It is therefore difficult to use them for control design purposes. On the other hand, data-based models have proven to be very useful in control design for rivers. In this thesis, different data-based modelling methods are explored, and they are applied to the data from the upper part of Murray River in Australia. For each method, the thesis analyses the ease with which available prior knowledge can be incorporated in the modelling procedure and the ability of the obtained models to describe the river well. For efficient river control, forecasts of future water demands and flows in the unregulated tributaries are required to be taken into account. A Stochastic Model Predictive Control (S-MPC) or a randomised version of it can not only accommodate such forecasts, but it can also handle physical and environmental constraints well. However, due to uncertainties in the forecasts, the feasibility of optimisation problems cannot always be guaranteed in the presence of constraints. This thesis proposes an S-MPC based river control schemes, that not only incorporate the forecasts, but also ensure feasibility of the optimisation problems. The schemes are successfully applied in simulations to the past data from the upper part of Murray River. Another important aspect of river management is to mitigate flood risks. An ideal strategy is to reduce the risk of severe floods, and at the same time not being overl

This paper focuses on developing a stochastic model predictive control (MPC) strategy based on Gaussian Processes (GPs) for propagating system disturbances in a receding horizon way. Using a probabilistic system representation, the state trajectories considering the influence of disturbances can be obtained through the uncertainty propagation by using GPs. This fact allows obtaining the confidence intervals for state evolutions over the MPC prediction horizon that are included into the MPC objective function and constraints. The feasibility of the proposed MPC strategy considering the incorporated results of disturbance forecasting is also discussed. Simulation results obtained from the application of the proposed approach to the Barcelona drinking water network (DWN) taking real demand data into account are presented. The comparison with the well-known certainty-equivalent MPC shows the effectiveness of the proposed stochastic MPC approach.

This study focuses on developing a stochastic model predictive control (MPC) strategy based on Gaussian processes (GPs) for propagating system disturbances in a receding horizon way. Using a probabilistic system representation, the state trajectories considering the influence of disturbances can be obtained through the uncertainty propagation by using GPs. This fact allows obtaining the confidence intervals for state evolutions over the MPC prediction horizon that are included into the MPC objective function and constraints. The feasibility of the proposed MPC strategy considering the incorporated results of disturbance forecasting is also discussed. Simulation results obtained from the application of the proposed approach to the Barcelona drinking water network taking real demand data into account are presented. The comparison with the well-known certainty-equivalent MPC shows the effectiveness of the proposed stochastic MPC approach., Peer Reviewed, Postprint (author's final draft)