A randomized approach to stochastic model predictive control

In this paper, we propose a novel randomized approach to Stochastic Model Predictive Control (SMPC) for a linear system affected by a disturbance with unbounded support. As it is common in this setup, we focus on the case where the input/state of the system are subject to probabilistic constraints, i.e., the constraints have to be satisfied for all the disturbance realizations but for a set having probability smaller than a given threshold. This leads to solving at each time t a finite-horizon chance-constrained optimization problem, which is known to be computationally intractable except for few special cases. The key distinguishing feature of our approach is that the solution to this finite-horizon chance-constrained problem is computed by first extracting at random a finite number of disturbance realizations, and then replacing the probabilistic constraints with hard constraints associated with the extracted disturbance realizations only. Despite the apparent naivety of the approach, we show that, if the control policy is suitably parameterized and the number of disturbance realizations is appropriately chosen, then, the obtained solution is guaranteed to satisfy the original probabilistic constraints. Interestingly, the approach does not require any restrictive assumption on the disturbance distribution and has a wide realm of applicability

GPU-accelerated stochastic predictive control of drinking water networks

Despite the proven advantages of scenario-based stochastic model predictive control for the operational control of water networks, its applicability is limited by its considerable computational footprint. In this paper we fully exploit the structure of these problems and solve them using a proximal gradient algorithm parallelizing the involved operations. The proposed methodology is applied and validated on a case study: the water network of the city of Barcelona.Comment: 11 pages in double column, 7 figure

A stochastic output-feedback MPC scheme for distributed systems

In this paper, we present a novel stochastic output-feedback MPC scheme for distributed systems with additive process and measurement noise. The chance constraints are treated with the concept of probabilistic reachable sets, which, under an unimodality assumption on the disturbance distributions are guaranteed to be satisfied in closed-loop. By conditioning the initial state of the optimization problem on feasibility, the fundamental property of recursive feasibility is ensured. Closed-loop chance constraint satisfaction, recursive feasibility and convergence to an asymptotic average cost bound are proven. The paper closes with a numerical example of three interconnected subsystems, highlighting the chance constraint satisfaction and average cost compared to a centralized setting.Comment: 2020 American Control Conferenc

Energy management of a building cooling system with thermal storage: A randomized solution with feedforward disturbance compensation

We consider a cooling system that comprises a building composed of multiple thermally conditioned zones, a chiller plant, and a thermal storage unit. The electrical energy price is time-varying, and the goal is to minimize the electrical energy cost along some look-ahead time horizon while guaranteeing an appropriate level of comfort for the occupants of the building. To this purpose, we can appropriately set the temperatures profiles in the zones of the building and the cooling energy exchange with the storage. Since the cooling system is affected by stochastic disturbances, we adopt a stochastic formulation of the control problem, where constraints are imposed in probability and measurable disturbances are possibly compensated. The resulting chance-constrained optimization problem is then solved via a randomized approach. Numerical results show a significant reduction of the cost when the feedforward disturbance compensation scheme is adopted

Distributed Model Predictive Control of Load Frequency for Power Networks

In recent years, there has been an increase of interest in smart grid concept, to adapt the power grid to improve the reliability, efficiency and economics of the electricity production and distribution. One of the generator side problem in this is to meet the power requirement while not wasting unnecessary power, thus keeping the cost down, which must be done while the frequency is kept in a suitable range that will not damage any equipment connected to the power grid. It would theoretically be most logical to have a centralized controller that gathers the full networks data, calculates the control signals and adjusts the generators. However in practice this is not practical, mostly due to distance. The transmission of sensor data to the controller and the transmission of control signals to the generators would have to travel far, thus taking up to much time before the generators could act. This paper presents a distributed model predictive control based method to control the frequency of the power network. First, an augmented matrix model predictive controller is introduced and implemented on a two homogeneous subsystems network. Later the control method is changed to a state space model predictive controller and is then utilized on a four heterogeneous subsystems network. This controller implementation also includes state observers by Kalman filtering, constraints handler utilizing quadratic programming, and different connection topology setups to observe how the connectivity affects the outcome of the system. The effectiveness of the proposed distributed control method was compared against the corresponding centralized and decentralized controller implementation results. It is also compared to other control algorithms, specifically, an iterative gradient method, and a model predictive controller generated by the MATLAB MPC Toolbox. The results show that the usage of a distributed setup improves the outcome compared to the decentralized case, whilst keeping a more convenient setup than the centralized case. It it also shown that the level of connectivity for a chosen network topology matters for the outcome of the system, the results are improved when more connections exists

Predictive Control Strategies based on Weather Forecast in Buildings with Energy Storage System: A Review of the State-of-the Art

Energy storage systems play a crucial role in decreasing building energy consumption during peak periods and expanding the use of renewable energies in buildings and communities. To have a high system performance, the energy storage system has to be properly controlled while maintaining a comfortable thermal environment for the occupants. However, defining the optimal charging period for a storage system may be difficult since storage systems address issues with conflicting needs between cost saving and thermal comfort. Moreover, with the increase of the use of renewable energies, the complexity increases with the consideration of the renewable energy production. As a result, the decision process should be able to predict both loads and renewable energy production in order to increase the storage system efficiency. This necessity explains the increasing interest during the last decade for predictive control, i.e., control system considering the forecasting. This paper reviews the recent advancements in building predictive control with energy storage system. Special attention is paid to its limitations and abilities

Simplified Predictive Control for Load Management: A Self-Learning Approach Applied to Electrically Heated Floor

In a cold climate, the electrical power demand for space conditioning during certain periods of the day becomes a critical issue for utility companies from an environmental and financial point of view. Shifting a portion or all of this demand to off-peak periods can reduce peak demand and stress on the electrical grid. One possibility is to use an electrically heated floor as a storage system in residential houses. To shift a significant part of the consumption while maintaining occupants’ thermal comfort, predictive supervisory control strategies such as Model Predictive Control (MPC) have been developed for forecasting future energy demand. However, MPC requires a building model and an optimization algorithm. Their development is time-consuming, leading to a high implementation cost. This thesis reports the development of a new simplified predictive controller to control an electrically heated floor in order to shift and/or shave the building peak energy demand. First, a method to model an EHF in TRNSYS was proposed in order to study the potential of using an electrically heated floor (EHF) in terms of load management without predictive control. Some parametric studies on the floor assembly and its impact on the thermal comfort were conducted. Results showed that a complete night-running control strategy cannot maintain an acceptable thermal comfort in all rooms. Therefore, it is required to predict the future demand of the building in order to anticipate the charging/discharging process of the storage system. Therefore, a simplified self-learning predictive controller was proposed. The function of the proposed simplified predictive controller is to increase the rate of stored energy during off-peak periods and to decrease it during peak periods, while maintaining thermal comfort. To achieve this goal without using a detailed building model, a simplified solar prediction model using available online weather conditions forecast was proposed. The controller approach is based on a learning process; it takes building responses of previous days into consideration. The developed algorithm was applied to a single-storey building with and without basement. Results show a significant decrease in thermal discomfort, average applied powers during peak and mid-peak periods. The approach has also proven to be financially attractive to both supplier and owner