A stochastic model predictive control approach for modelling human driver steering control

In order to improve the automatic generation control (AGC) performance of thermal generators, this paper presents a stochastic model predictive control (SMPC) approach for a battery/flywheel hybrid energy storage system (HESS) to distribute power. The approach combines an adaptive Markov chain for power demand prediction of HESS, a scenario tree generation and model predictive control strategy. To develop an effective prediction model to deal with the randomness of a thermal generator in response to AGC command, a Markov chain is used to describe the randomness of the HESS power demand, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> information is used to adapt to the fluctuation of the AGC command. A scenario tree generation approach is proposed to make better use of the Markov probability matrix. Based on these efforts, an SMPC approach is proposed for HESS energy management. Simulation results show that the regulation performance of the proposed approach outperforms conventional approaches, and that its performance is close to the model predictive control strategy with prescient information of the future power demand. In addition, compared with other approaches such as rule-based strategies, it does less damage to the battery and yields higher annual average net benefits in the whole life cycle.

This paper presents a stochastic model predictive control approach combined with a time-series forecasting technique to tackle the problem of microgrid energy management in the face of uncertainty. The data-driven non-parametric chance constraint method is used to formulate chance constraints for stochastic model predictive control, while removing the dependency on probability density assumptions of uncertain variables and retaining the linear structure of the resulting optimization problem. The proposed approach is suitable for implementation on systems with limited computational power or limited memory storage, thanks to its simple linear structure and its ability to provide accurate results within pre-defined confidence levels, even when using small data batches. The proposed forecasting and stochastic model predictive control approaches are applied on a numerical example featuring a small grid-connected microgrid with PV generation, a battery storage system, and a non-controllable load, showing the ability to reduce costs by reducing the confidence level, and to satisfy pre-defined confidence levels.

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

This paper proposes a stochastic model predictive control (MPC) approach to optimize the fuel consumption in a vehicle following context. The practical solution of that problem requires solving a constrained moving horizon optimal control problem using a short-term prediction of the preceding vehicle’s velocity. In a deterministic framework, the prediction errors lead to constraint violations and to harsh control reactions. Instead, the suggested method considers errors, and limits the probability of a constraint violation. A conditional linear Gauss model is developed and trained with real measurements to estimate the probability distribution of the future velocity of the preceding vehicle. The prediction model is used to evaluate two different stochastic MPC approaches. On the one hand, an MPC with individual chance constraints is applied. On the other hand, samples are drawn from the conditional Gaussian model and used for a scenario-based optimization approach. Finally, both developed control strategies are evaluated and compared against a standard deterministic MPC. The evaluation of the controllers shows a significant reduction of the fuel consumption compared with standard adaptive cruise control algorithms.

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.

This paper presents a chance constrained stochastic model predictive control (SMPC) approach for building climate control under combined parametric and additive uncertainties. The proposed SMPCap approach enables the quantification, and manipulation, of both the mean and covariance of the stochastic system states and inputs. Its enhanced uncertainty anticipation is shown to induce improved thermal comfort in closed-loop simulations compared to the conventional deterministic MPC (DMPC) and the state-of-the-art SMPCa only accounting for additive uncertainties, at the cost of a maximum relative increase in energy use of 21.6% and 4.2%, respectively. By incorporating the SMPCap strategy in an integrated optimal control and design (IOCD) approach, its additional added value for obtaining a more appropriate, yet robust, heat supply system sizing is illustrated. Via simulations, size reductions up to 33.3% are shown to be achievable for a terraced single-family dwelling without increasing thermal discomfort compared to an IOCD approach incorporating DMPC.

Stochastic Nonlinear Model Predictive Control with Active Model Discrimination: A Closed-Loop Fault Diagnosis Application

In this paper, we consider learning-based modeling and predictive control of nonlinear systems subject to multimodal uncertainties. A Gaussian mixture Koopman operator, which learns the evolution of the observable distribution in a higher-dimensional space, is proposed to characterize the dynamics of the underlying nonlinear systems. Based on the learned probabilistic Koopman model, a stochastic model predictive control method with chance constraints is introduced for the nonlinear systems with state constraints. Finally, a simulated chemical process is used to illustrate the effectiveness of the proposed method.

This paper proposes an autonomous driving framework for unsignalized intersections. The framework consists of two modules: vehicle state inference and vehicle motion planning. A network based on Graph Convolutional Neural Network (GCN) and Gated Recurrent Unit (GRU) encoderdecoder is established. Relying on the relevant historical states of vehicles within the unsignalized intersection, the interactions among vehicles are fully taken into account, and the future trajectory distributions of all vehicles and the collision risks between each pair of vehicles are predicted together. The motion planning module, based on the prediction results of future states, adopts the Model Predictive Control (MPC) method to obtain the desired acceleration input, improving traffic efficiency while focusing on safety. We have built a simulation platform for an unsignalized intersection that simulates human interactions in the Sumo simulation software, and used it for dataset generation and simulation experiments. The results show that our framework demonstrates high efficiency and safety under different traffic volumes.

In the face of multiple failures caused by extreme disasters, the power and communication sides of the distribution network are interdependent in the fault recovery process. To improve the post-disaster recovery efficiency of the distribution network, this paper proposes a coordinated optimization strategy for distribution network reconfiguration and repair, which integrates the power and communication aspects. First, the recovery process is divided into islanding–reconfiguration and dynamic emergency repair. The coupling relationship between power and communication is considered; that is, power failure may cause communication nodes to lose power, and communication failure may affect the effective operation of remote control devices. Based on this, the fault recovery process is optimized with the objective of maximizing load transfer and direct recovery while introducing a stochastic model predictive control method to handle the uncertainty of distributed power generation by rolling optimization of typical scenarios. Finally, the effectiveness of the proposed strategy is verified using an improved IEEE33-node distribution network system. The simulation results show that the proposed method can recover power to the maximum extent and reduce loss while ensuring the safe and stable operation of the distribution system.

Stochastic Model Predictive Control (SMPC) has attracted increasing attention for autonomous driving in recent years, since it enables collision-free maneuvers and trajectory planning and can deal with uncertainties in a non-conservative way. Many promising strategies have been proposed on how to use SMPC to select appropriate maneuvers and plan safe trajectories in uncertain environments. The limitation of these approaches is that they focus on scenarios where only one vehicle is controlled by SMPC and is, thus, reacting to the surrounding vehicles; however, the surrounding vehicles do not react to the SMPC-controlled vehicle, which means there is no mutual interaction. However, when multiple autonomous vehicles are driving on the road, each individual vehicle will take the behavior of the other surrounding vehicles into account and adjust its individual decisions accordingly in trajectory planning. This paper, therefore, examines in simulations how the interactive control system of multiple SMPC-controlled vehicles behave based on a Distributed SMPC (DSMPC) framework. For a three-lane highway scenario, we first investigate the effects of the risk parameter of the collision avoidance probabilistic constraint on non-interactive and interactive vehicle systems and provide insights into how to parameterize the controllers in interactive vehicle systems.

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.