Distributed Stochastic Model Predictive Control for a Microscopic Interactive Traffic Model

Wind energy has been drawing considerable attention in recent years. However, due to the random nature of wind and high failure rate of wind energy conversion systems (WECSs), how to implement fault-tolerant WECS control is becoming a significant issue. This paper addresses the fault-tolerant control problem of a WECS with a probable actuator fault. A new stochastic model predictive control (SMPC) fault-tolerant controller with the Conditional Value at Risk (CVaR) objective function is proposed in this paper. First, the Markov jump linear model is used to describe the WECS dynamics, which are affected by many stochastic factors, like the wind. The Markov jump linear model can precisely model the random WECS properties. Second, the scenario-based SMPC is used as the controller to address the control problem of the WECS. With this controller, all the possible realizations of the disturbance in prediction horizon are enumerated by scenario trees so that an uncertain SMPC problem can be transformed into a deterministic model predictive control (MPC) problem. Finally, the CVaR object function is adopted to improve the fault-tolerant control performance of the SMPC controller. CVaR can provide a balance between the performance and random failure risks of the system. The Min-Max performance index is introduced to compare the fault-tolerant control performance with the proposed controller. The comparison results show that the proposed method has better fault-tolerant control performance.

Stochastic linear Model Predictive Control with chance constraints – A review

The domain of attraction is central to stability and recursive feasibility of model predictive control (MPC). For stochastic linear systems, this paper addresses the problem of enlarging the domain of attraction of stochastic MPC (SMPC) for offset-free tracking. The proposed SMPC strategy relies on using an artificial steady-state target to enlarge the domain of attraction while ensuring recursive feasibility. The key advantage of the proposed strategy is that it alleviates the computation of an additional robust control invariant set to greatly simplify the SMPC design. Furthermore, the proposed SMPC strategy for offset-free tracking circumvents feasibility loss due to target changes since the feasible region is independent of the desired steady-state target. The SMPC strategy is demonstrated on a benchmark DC-DC converter case study, where its performance is compared to that of standard SMPC for regulation based on tighter constraints and a recently proposed SMPC strategy with a first-step constraint.

The efficacy of control systems for distribution grids can be influenced by different sources of uncertainty. Stochastic Model Predictive Control (SMPC) can be employed to compensate for such uncertainties by integrating their probability distribution into the control problem. An efficient SMPC algorithm for online control applications is the stochastic tube SMPC, which is able to treat the evaluation of the chance constraints analytically. However, this approach is efficient only when the calculation of the constraint back-off is applied to a linear model. To address this issue, this work employs Gaussian Processes to approximate the nonlinear part of the power flow equations based on offline training, which is integrated into the SMPC formulation. The resulting SMPC is first validated and then tested on a benchmark system, comparing the results with Deterministic MPC and SMPC that excludes Gaussian Processes. The proposed SMPC proves to be more efficient in terms of cost minimization, reference tracking and voltage violation reduction.

ABSTRACTThis article proposes a parallel algorithm of stochastic model predictive control (SMPC) for linear discrete‐time systems. The proposed algorithm uses multiple threads to solve respective optimization problems at different time steps in parallel, without inter‐thread communication during each optimization. Each thread sequentially solves a stochastic optimal control problem (SOCP) for optimizing closed‐loop performance against future disturbances and a partial minimization problem for optimizing a subset of decision variables of the SOCP. The partial minimization problem computes the control input according to the last measured state to satisfy chance constraints and can be solved much faster than the original SOCP. Consequently, the proposed algorithm can reduce the implementable minimum sampling period compared to the original SMPC. A numerical example of controlling room temperature showed that the proposed algorithm achieves control performance almost identical to that of closed‐loop SMPC, which optimizes closed‐loop performance. However, the implementable minimum sampling period of the proposed algorithm is much shorter than that of the closed‐loop SMPC, even with parallelization overhead.

A stochastic model predictive control (SMPC) method is proposed for trajectory tracking of quadrotor helicopters with stochastic disturbances. The stochastic disturbances are assumed to be Gaussian white noises. The existing robust control methods generally guarantee that the tracking performances under the worst-case disturbances satisfying given conditions. However, the worst-case disturbances may have a vanishingly small probability of occurrence in practice, so these methods show great conservative. In this paper, the tracking errors caused by the disturbances are limited in the acceptable range with the given probability. The hierarchical control structure is used. In the outer loop, the position loop, SMPC controllers are designed for position tracking. In the inner loop, the attitude loop, the nonlinear dynamics are linearized by the feedback linearization strategy, and an SMPC controller is designed for attitude tracking. Finally, simulation results verify the effectiveness of the proposed method.

A methodology has been developed for optimizing building supervisory control strategies, employing building models that incorporate stochastic models of occupant behaviour and serve as the objective function evaluator in a stochastic model predictive control (SMPC) architecture. The SMPC architecture accounts for variability in building performance due to occupant behaviour and is shown to generate a sequence of automatic window opening decisions for a mixed mode building which lead to more robust building performance in the face of occupant window use than a heuristic controller. A set of receding optimization time horizons are described which enable the use of complex building models in simulated SMPC. Results of a case study show that deterministic optimization predicts a 50% increase in building performance, while stochastic optimization leads to a more conservative and more reliable 33% performance improvement, which takes into consideration the impact of occupant behaviour.

This study presents a closed‐loop hierarchical control strategy for a group of connected and autonomous hybrid electric vehicles (HEVs) with the purpose of optimising fuel economy while guaranteeing traffic mobility and vehicle safety. In the hierarchical control architecture, a decentralised stochastic model predictive control (SMPC)‐based higher level controller incorporating signal phase and timing information is formulated to optimise the velocity profile of each vehicle, and an adaptive equivalent consumption minimisation strategy based lower level controller is employed for the energy management control of the HEVs. Creatively, random errors of the control variable are considered in the SMPC framework. The errors are discretised and modelled as a Markov process and the state transition matrix of the errors is generated randomly to capture the error transition dynamics. To solve the SMPC problem more efficiently, a scenario‐based SMPC is employed. Moreover, the propulsion and recuperation efficiencies of the lower level controller are calculated at each time step with measurable variables, and fed back to the higher level controller for velocity optimisation in next time step. Simulation results validate the control effectiveness and advantages of the proposed control architecture.

The charging management of plug-in electric vehicles (PEVs) in San Francisco considering the effect of drag force on the vehicles, the real driving routes of vehicles, the social aspects of drivers' behaviour, the type of PEVs and the PEV penetration level is presented in this study. In this study, the drivers' responsiveness probability, to provide vehicle-to-grid service at the parking lot, is modelled with respect to the value of the incentive, drivers' social class and the real driving routes in San Francisco. Herein, the Monte Carlo Markov Chain is applied to estimate the hourly probability distribution function of the state of charge (SOC) of the PEV fleet in the day. The main data set applied in this study includes the real longitude and latitude of driving routes of vehicles in San Francisco, recorded in every four-minute interval of the day. In this study, a stochastic model predictive control is applied in the optimisation problem to address the variability and uncertainty issues of PEVs' SOC and renewables' power. Herein, quantum-inspired simulated annealing algorithm is applied as the optimisation technique. It is demonstrated that the type of PEVs, the PEV penetration level and even the social class of drivers can affect the problem results.

We developed a load frequency control system with stochastic model predictive control (SMPC) for power systems where the market penetration of wind power generation is high. The controller adjusts ...

A risk management system for foreign exchange (FX) brokers is described. Stochastic model predictive control (SMPC) is used to reduce positions in foreign holdings over a receding horizon, while minimising a mean-variance cost function. Computation of the broker's position incorporates elements which model client flow, transaction costs, market impact, and exchange rate. Using both synthetic and historical data, the technique is shown to outperform two simple hedging strategies on a risk-cost Pareto frontier. Prediction of client and market behaviour are shown to further enhance the hedging outcome.

This paper presents a control algorithm for autonomous overtaking problem using stochastic model predictive control. This algorithm relies on suitable prediction for the longitudinal and lateral speeds of the surrounding vehicles. Accordingly, these information are used to formulate suitable dynamics constraints for the proposed control algorithm which determines the need of overtaking action by tracking a suitable longitudinal speed reference and a lateral position reference, while avoiding the obstacles. Finally, the efficiency of the proposed algorithm is illustrated by two traffic scenarios in the environment of the reliable traffic simulator IPG CarMaker.

Robust active yaw control for offshore wind farms using stochastic predictive control based on online adaptive scenario generation

Successive Linearization based Stochastic Model Predictive Control for batch processes described by DAEs

This study focuses on demonstrating the effectiveness and efficiency of the Stochastic Sequential Model Predictive Control (MPC) framework within the context of the Hjartdøla hydropower system. Multistage MPC, while effective in managing uncertainty, poses challenges due to its high computational demands and complex optimal control problems, particularly in applications requiring long-term forecasting, such as hydropower systems. Through a comparative simulation study with multistage MPC, this paper highlights the superior feasibility and computational speed of the Stochastic Sequential MPC framework. This work contributes to the broader understanding of MPC applications in hydropower systems.