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Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.

In this paper, the attitude control problem of the spacecraft system under input/state constraints and multi-source disturbances is investigated. A novel estimation method, composite-disturbance-observer (CDO), is proposed to provide an estimate for both modeled and unmodeled disturbances in an online manner. Based on the estimates provided by the CDO, the composite stochastic model predictive control (C-SMPC) scheme is designed for attitude control. The recursive feasibility of the C-SMPC method is guaranteed by reformulating the state and input constraints. Furthermore, the sufficient conditions are established to guarantee the stability of the overall closed-loop system. Finally, the simulation on the attitude control of the spacecraft is conducted to verify the effectiveness of the proposed method.

The energy management strategy of hybrid electric vehicles is of significant importance to improve the fuel economy. In this regard, two energy management strategies are designed for power-split hybrid electric city bus (HECB), which are based on the linear time-varying stochastic model predictive control (LTV-SMPC) and stochastic model predictive control based on Pontriagin's minimum principle (PMP-SMPC). In the present study, the Markov chain and long short-term memory (LSTM) forecast demand torque and velocity respectively are applied to establish a combination forecast model. Then several processes, including linear approximation, processing simplified control model, the proposed nonlinear vehicle model is converted into a linear time-varying model. Meanwhile, the energy management problem in a linear quadratic programming problem is solved. Considering linearization error and limitations of the quadratic optimization, Pontriagin's minimum principle (PMP) is applied to optimize the nonlinear model predictive control. Based on the reference theory, the range of coordinated variables is derived, and the optimal coordination variable is searched by dichotomy to realize the rolling optimization of the model predictive control (MPC). Finally, the effectiveness of the proposed energy management strategy is verified by simulating several case studies. Obtained results show that compared with the rule-based (RB) control strategy, the fuel economy of LTV-SMPC and PMP-SMPC increases by 8.79% and 14.42%, respectively. Meanwhile, it is concluded that the two strategies have real-time computing potential.

Photovoltaic (PV) battery systems allow citizens to take part in a more sustainable energy system. Using the electric energy produced on-site usually entails a financial benefit for the consumer. Furthermore, feed-in peaks during high photovoltaic generation sometimes cause local voltage violations. Therefore, a feed-in limit applies to PV battery systems. In our study, we present a method to generate an optimal control that takes into account the forecast uncertainties. To that end, a stochastic forecast model is developed and used in a dynamic programming framework. We carry out a simulation study assuming the regulatory constraints in Germany. In this setup, our method is shown to mitigate the effects of the forecast uncertainties better than comparable methods.

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 ...

This article describes the design, implementation, and evaluation of an active lane change control algorithm for autonomous vehicles with human factor considerations. Lane changes need to be performed considering both driver acceptance and safety with surrounding vehicles. Therefore, autonomous driving systems need to be designed based on an analysis of human driving behavior. In this article, manual driving characteristics are investigated using real-world driving test data. In lane change situations, interactions with surrounding vehicles were mainly investigated. And safety indices were developed with kinematic analysis. A safety indices–based lane change decision and control algorithm has been developed. In order to improve safety, stochastic predictions of both the ego vehicle and surrounding vehicles have been conducted with consideration of sensor noise and model uncertainties. The desired driving mode is decided to cope with all lane changes on highway. To obtain desired reference and constraints, motion planning for lane changes has been designed taking stochastic prediction-based safety indices into account. A stochastic model predictive control with constraints has been adopted to determine vehicle control inputs: the steering angle and the longitudinal acceleration. The proposed active lane change algorithm has been successfully implemented on an autonomous vehicle and evaluated via real-world driving tests. Safe and comfortable lane changes in high-speed driving on highways have been demonstrated using our autonomous test vehicle.

The problem of battery health coupled with energy management brings a considerable challenge to the hybrid electric bus. To address this challenge, three contributions are made to realize optimal energy management control while prolonging battery life. First, a semi-empirical aging model of lithium iron phosphate battery is built and identified by the data fitting method, based on the battery cycling test. Besides, a severity factor map is constructed by employing the proposed aging model to characterize the relative aging of the battery under different operating conditions. Second, to make the driver demand torque more appropriate for statistical prediction, a Markov chain is formulated to predict driving behavior and also a stochastic vehicle mass estimation method is proposed to assist the prediction of required torque. Then, a stochastic multi-objective optimization problem is formulated by taking the severity factor map as a battery degradation criterion, where minimized battery degradation and fuel consumption can be simultaneously realized. Finally, a stochastic model predictive control strategy that considers battery health is established. Both simulation and hardware-in-loop tests are performed. The results demonstrate that fuel economy and battery degradation can be improved by 16.73% and 13.8% compared with rule-based strategy, respectively.

In this paper, a sampling-based stochastic model predictive control (SMPC) algorithm is proposed for discrete- time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need for reliable and robust guidance and control strategies for automated rendezvous and proximity operations between spacecraft. To this end, the proposed control algorithm is validated on a floating spacecraft experimental testbed, proving that this solution is effectively implementable in real time. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simulta- neously considered. The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Moreover, the offline sampling approach in the control design phase shifts all the intensive computations to the offline phase, thus greatly reducing the online computational cost, which usually constitutes the main limitation for the adoption of SMPC schemes, especially for low- cost on-board hardware. Numerical simulations and experiments show that the approach provides probabilistic guarantees on the success of the mission, even in rather uncertain and noisy situations, while improving the spacecraft performance in terms of fuel consumption.

The paper applies the scenario approach to stochastic model predictive control for renewable energy systems. First, the controllable and the (quasi-periodic) uncontrollable parts are decomposed. The latter is modeled by a Box-Jenkins system with appropriately chosen inputs. For the controllable part, a linear state space model is used with an affine state-feedback controller. Several numerical experiments are presented on a public lighting microgrid, e.g., about forecasting the energy balance, the effects of various controller parametrizations, reoptimization frequencies, and discarding unfavorable scenarios. The results indicate that even a low order, time-independent controller with a slow reoptimization frequency can be efficient.

Vehicle-following operation is a typical scenario in the future intelligent transportation environment. Keeping a safe distance is the most important goal in the vehicle-following scenario. For a plug-in hybrid electric bus (PHEB) running in a specific urban route, the challenge will become how to realize the optimal power split in hybrid powertrain under the premise of maintaining driving safety. Considering the above issues, this paper proposes a stochastic model predictive control (SMPC) strategy for PHEBs during vehicle-following scenario. Firstly, Markov chain-based stochastic driving model is built using real-world bus driving condition data, which is applied to predict future demand torque over a finite receding horizon. And then, a sequential quadratic programming (SQP) algorithm is adopted to solve the rolling optimization problem. Meanwhile, brake specific fuel consumption and electric motor efficiency are fitted offline to match the SMPC strategy. Furthermore, a piecewise function is given to adjust the adaptive factor that balancing fuel economy and vehicle-following in the pre-set cost function. Finally, to verify the control performance of the proposed strategy, a nonlinear model predictive control strategy with dynamic programming optimization (DP-MPC) and a rule-based (RB) strategy are employed for comparison study. Results indicate that the proposed strategy is effectiveness to the given driving condition with excellent fuel economy and vehicle-following performance. Under the driving condition of Chongqing 303 bus line in China and China typical, the fuel consumption is reduced by 20.58% and 37.89% compared with RB strategy, respectively. It is closer to the fuel consumption reduction of 16.77% and 13.11 optimized by DP-MPC. Driving safety during vehicle-following also be demonstrated in the driving condition of Chongqing 303 bus line and China typical.

Individual chance constraints can be used to systematically seek trade-offs between control performance and constraint violation for a given disturbance description. This paper presents a Stochastic Model Predictive Control (SMPC) approach with adaptive individual chance constraints that relies on online adaptation of the disturbance description using the empirical cumulative distribution (ECDF). Individual chance constraints are ensured by using a suitable worst-case confidence interval derived from the ECDF. The confidence interval may, however, be excessively conservative due to the empirical nature of the ECDF. To reduce this conservatism, the proposed approach accounts for the updated disturbance information, which is sampled online from the one-step ahead prediction error. Hence, the initial ECDF can be obtained from a reduced number of samples since the conservative handling of the chance constraint is continuously mitigated. This will also allow for using simpler models of the stochastic system disturbances. Convergence and recursive feasibility of the proposed adaptive approach are established. A DC-DC converter benchmark problem is used to illustrate the usefulness of the proposed approach.

An unmanned surface vehicles (USV) set point tracking problem is investigated in this paper. The stochastic model predictive control (SMPC) scheme is utilized to design the controller in order to reject the environment disturbances and meet the physical constraints. The design problem is formulated as a chance-constrained stochastic optimization problem, which is non-convex. Thus, the problem is computationally prohibitive. For this, the convex conditional value at risk (CVaR) approximation is introduced to convert the chance constraints into deterministic convex constraints. The converted constraints are then further transformed into the second order cone (SOC) constraints. Therefore, the proposed method is computationally tractable and hence can be implemented online. A numerical example is provided to illustrate the effectiveness of the proposed method.

In this paper, the air-fuel ratio regulation problem of compressed natural gas (CNG) engines is considered by employing stochastic model predictive control (MPC) technology. A stochastic model predictive regulator based on a discrete-time dynamic model of CNG engines is proposed, taking into account the residual gas, and the closed-loop system is deduced to be stochastically stable. A numerical simulation is performed to demonstrate the effectiveness of the proposed control scheme under two working conditions. The simulation results show that the performance of the proposed stochastic model predictive regulator is better than that of the open-loop controller.

With the increasing demand for battery electric buses, the dual-motor coupling powertrain (DMCP) shows great advantages, but it makes the energy optimization problem more complex. To solve the hybrid system optimization problem, a stochastic model predictive control (SMPC) method is proposed to exploit the potential performance of DMCP, where the most critical issue is to improve the prediction accuracy and handle the uncertainties. After analyzing the typical velocity profiles, statistical properties are used to develop a novel Signed Markov Chain Monte Carlo (SMCMC) method that can enhance the accuracy of velocity prediction by more than 50%, compared to conventional Markov Chain methods. Next, considering the uncertainties present in various driving scenarios, the development of driving cycle recognition model based on fuzzy logic control (FLC) is introduced; this method permits to identify the current category of driving cycle rapidly. Then, dynamic programming (DP) is adopted to solve the rolling optimization problems in each finite horizon online, including necessary constraints of dynamic response. Finally, simulation results demonstrate that the proposed energy management strategy can address various daily driving cycles well, and can improve the energy performance by 6% under a generalized combination of driving conditions compared to preliminary rule-based control.

This article proposes a stochastic nonlinear model predictive controller to support policymakers in determining robust optimal nonpharmaceutical strategies to tackle the COVID-19 pandemic waves. First, a time-varying SIRCQTHE epidemiological model is defined to get predictions on the pandemic dynamics. A stochastic model predictive control problem is then formulated to select the necessary control actions (i.e., restrictions on the mobility for different socioeconomic categories) to minimize the socioeconomic costs. In particular, considering the uncertainty characterizing this decision-making process, we ensure that the capacity of the healthcare system is not violated in accordance with a chance constraint approach. The effectiveness of the presented method in properly supporting the definition of diversified nonpharmaceutical strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data. The proposed approach can be easily extended to cope with other countries' characteristics and different levels of the spatial scale. IEEE

This paper presents an uncontrolled intersection-passing algorithm with an integrated approach of stochastic model-predictive control and prediction uncertainty estimation for autonomous vehicles. The proposed algorithm is designed to utilize information from sensors mounted on the autonomous vehicle and high-definition intersection maps. The proposed algorithm is composed of two modules, namely target state prediction and a motion planner. The target state prediction module has predicted the future behavior of intersection-approaching vehicles based on human driving data. The recursive covariance estimator has been utilized to estimate the prediction uncertainty for each approaching vehicle. The desired driving mode has been determined based on the uncontrolled intersection theory. The estimated prediction uncertainty has been used to define the probability distribution of the stochastic model-predictive controller to cope with time-varying uncertainty characteristics of the perception algorithm. The constrained stochastic model-predictive controller based on safety indexes has determined the desired longitudinal acceleration. The proposed robust intersection-passing algorithm has been evaluated via computer simulation based on Monte Carlo simulation with a sensor model. The simulation results showed that the proposed algorithm guarantees the minimum safety constraints and improves the ride comfort at uncontrolled intersections by estimating the uncertainty of sensors and prediction.

To maximize potential energy and cost savings, networked clusters of local buildings are formed for energy transactions. Both centralized and distributed decision approaches were explored in past decades as a way to enable efficient transactive operations. However, online distributed stochastic transactive operation has been overlooked in the literature. To bridge gaps in the research, a bi-level distributed stochastic model predictive control framework was proposed to study the transactive operations of building clusters where a system-level agent is employed to coordinate multiple building agents at the subsystem level. The energy transaction is optimized by a marginal price-based particle swarm optimizer at the system level. Given the energy transaction decisions, each building can independently solve a scenario-based two-stage stochastic model to optimally dispatch the electricity and ancillary services for optimal energy performance. The effectiveness of the proposed framework and coordination algorithm are demonstrated in deterministic, stochastic, and online operations and compared to centralized decisions using several sets of experiments. In addition, the proposed approach can realize autonomous transactive operation and be extended to community-level building clusters in a plug-and-play way.

This paper formulates a control problem for systems that are affected by uncertain inputs and are vulnerable to risks as a chance-constrained optimization problem (CCP) with two chance-constraints (CCs). The first CC encompasses requirements of the normal operations of the system, whereas the second CC ensures the avoidance of risks associated with rare events. CCPs are in general difficult to solve, and this paper proposes a scenario-based optimization, testing, and improving algorithm to find approximate solutions to such problems within a stochastic model predictive control setting in a computationally cheap manner. The proposed approach is applied to a river control problem with flood avoidance, and the controller performed well in realistic simulations of the upper part of Murray River in Australia.

This letter covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and chance constraints on their state and control input. We propose a simplified control parameterization under the framework of affine disturbance feedback, and we show that our method is equivalent to parameterization over the family of state feedback policies. Using our method, associated finite-horizon optimization can be computed efficiently, with a slight increase in conservativeness compared with conventional affine disturbance feedback parameterization.

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.

Trajectory planning in urban automated driving is challenging because of the high uncertainty resulting from the unknown future motion of other traffic participants. Robust approaches guarantee safety, but tend to result in overly conservative motion planning. Hence, we propose to use Stochastic Model Predictive Control for vehicle control in urban driving, allowing to efficiently plan the vehicle trajectory, while maintaining the risk probability sufficiently low. For motion optimization, we propose to use a two-stage hierarchical structure that plans the trajectory and the maneuver separately. A high-level layer takes advantage of a long prediction horizon and of an abstract model to plan the optimal maneuver, and a lower level is in charge of executing the selected maneuver by properly planning the vehicle's trajectory. Numerical simulations are included, showing the potential of our proposal., Comment: This work has been accepted to the IEEE 2021 International Conference on Intelligent Transportation Systems. The published version may be found at https://doi.org/10.1109/ITSC48978.2021.9564572

In this study, a hierarchical energy management system (EMS) is proposed, to coordinate different energy sources in an islanded multi-good microgrid. The first layer deals with the daily scheduling problem, while the second layer balances the generation in real-time. A novel second layer formulation, relying on model predictive control under a scenario-based stochastic approach (sMPC), is introduced and it is compared to a reference formulation, based on a central proportional-integral controller following the indications set by the first layer. The proposed sMPC explicitly accounts for uncertainty considering several scenarios of very-short term forecast errors, that act as disturbances for the system. The sMPC evaluates the control actions and the correction rules required to guarantee optimal operations through disturbance-feedback. The EMS is implemented in an experimental setup and tested for daily operations under a rolling horizon approach. The accuracy of the numerical system simulation is evaluated, resulting in an average discrepancy of 1.7%, in terms of operation cost, with respect to the experimental operations. Then, a test case comparing the proposed EMS with the reference approach shows that the adoption of sMPC allows to approach the lowest possible operation cost achievable by a second layer with an advantage of 2.7 % against the reference case. Finally, the developed sMPC leads to only 0.5% additional costs than an ideal controller working on the same control layer.

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 Boras, 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 generate 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.

The high penetration of renewable energy into distribution networks poses increasing challenges on voltage control. To address this issue, this paper presents a double-layer stochastic model predictive control algorithm to regulate voltage profile in active distribution networks. In the proposed algorithm, voltage regulation is achieved by coordination of an upper layer controller and a lower layer controller. In the upper layer, the number of operation of mechanical voltage regulation devices, including transformer with on-load tap changer and capacitor banks, is minimized in an hourly timescale. In the lower layer, the controller minimizes the active power curtailments and power losses with a control period of 5 min. The proposed double-layer stochastic model predictive voltage control utilizes not only the reactive power control, but also the active power curtailment to regulate bus voltages. In addition, mechanical voltage regulation devices and distributed generations are controlled in two different timescales. Case studies on a modified IEEE-33 bus system demonstrate that compared with traditional control and two-stage stochastic voltage control, the proposed algorithm can achieve an improvement of 8.05% and 7.43%, respectively.

We present a Buildings-to-Grid (BtG) integration framework with intermittent wind-power generation and demand flexibility management provided by buildings. First, we extend the existing BtG models by introducing uncertain wind-power generation and reformulating the interactions between the Transmission System Operator (TSO), Distribution System Operators (DSO), and buildings. We then develop a unified BtG control framework to deal with forecast errors in the wind power, by considering ancillary services from both reserves and demand-side flexibility. The resulting framework is formulated as a finite-horizon stochastic model predictive control (MPC) problem, which is generally hard to solve due to the unknown distribution of the wind-power generation. To overcome this limitation, we present a tractable robust reformulation, together with probabilistic feasibility guarantees. We demonstrate that the proposed demand flexibility management can substitute the traditional reserve scheduling services in power systems with high levels of uncertain generation. Moreover, we show that this change does not jeopardize the stability of the grid or violate thermal comfort constraints of buildings. We finally provide a large-scale Monte Carlo simulation study to confirm the impact of achievements.

We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening. We introduce an initialization of each MPC iteration which is always recursively feasibility and thereby allows that chance constraint satisfaction for the closed-loop system can readily be shown. Under an i.i.d. zero mean assumption on the additive disturbance, we furthermore provide an average asymptotic performance bound. Two examples illustrate the approach, highlighting feedback properties of the novel initialization scheme, as well as the inclusion of time-varying, correlated disturbances in a building control setting.

While Advanced Driver Assistance Systems (ADAS) are becoming the longer the more common, most interest has been devoted either to highway traffic or to special situations like parking. Against this background, this paper focuses on overtaking maneuvers on country roads, and a stochastic model predictive control (MPC) algorithm is implemented to manage this task. The behavior of the surrounding vehicles is predicted stochastically by using Bayesian networks. The overtaking algorithm is tested for various country road traffic scenarios in a stochastic traffic environment. To compare the performance of the controller to that of a real human driver a dedicated study in this stochastic traffic environment is carried out. The results of this study show that the control algorithm provides the safest trip in acceptable travel time.

While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability depending on a predefined risk parameter. However, for safety-critical systems it is not only important to bound the constraint violation probability but to reduce this probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible. We propose a novel Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed the solution is then also optimized with respect to other control objectives. Further, it is possible to account for changes over time of the support of the uncertainty. We first present a general method and then provide an approach for uncertainties with symmetric, unimodal probability density function. Recursive feasibility and convergence of the method are proved. A simulation example demonstrates the effectiveness of the proposed method., This is the pre-peer reviewed version of an article published by the International Journal of Robust and Nonlinear Control. The published version is available at https://doi.org/10.1002/rnc.5636. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions

In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either independence nor Gaussianity. We revisit the rather classical approach based on penalty functions, with the aim of designing a control scheme that meets some given probabilistic specifications. The main difference with previous approaches is that we do not recur to the notion of probabilistic recursive feasibility, and hence we do not consider separately the unfeasible case. In particular, two probabilistic design problems are envisioned. The first randomization problem aims to design \textit{offline} the constraint set tightening, following an approach inherited from tube-based MPC. For the second probabilistic scheme, a specific probabilistic validation approach is exploited for tuning the penalty parameter, to be selected \textit{offline} among a finite-family of possible values. The simple algorithm here proposed allows designing a \textit{single} controller, always guaranteeing feasibility of the online optimization problem. The proposed method is shown to be more computationally tractable than previous schemes. This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence. The efficacy of the proposed approach is demonstrated with a numerical example., Submitted as Contributed Paper to IFAC2020 Congress

Most stochastic Model Predictive Control (MPC) formulations allow constraint violations via the use of chance constraints, thus increasing control authority and improving performance when compared to their robust MPC counterparts. However, common stochastic MPC methods handle chance constraints conservatively: constraint violations are often smaller than allowed by design, thus limiting the potential improvements in control performance. This is a consequence of enforcing chance constraints overlooking the past behavior of the system and/or of an over tightening of the constraints on the predicted sequences. This work presents a stochastic MPC strategy that uses the observed amount of constraint violations to adaptively scale the tightening parameters, thus eliminating the aforementioned conservativeness. It is proven using Stochastic Approximation that, under suitable conditions, the amount of constraint violations converges in probability when using the proposed method. The effectiveness and benefits of the approach are illustrated by a simulation example.

In this letter, a guidance and tracking control strategy for fixed-wing unmanned aerial vehicle autopilots is presented. The proposed control exploits recent results on sample-based stochastic model predictive control, which allows coping in a computationally efficient way with both parametric uncertainty and additive random noise. Different application scenarios are discussed, and the implementability of the proposed approach are demonstrated through simulations. The capability of guaranteeing probabilistic robust satisfaction of the constraint specifications represents a key-feature of the proposed scheme, allowing real-time tracking of the designed trajectory with guarantees in terms of maximal deviation with respect to the planned one. The presented simulations show the effectiveness of the proposed control scheme.

Efficient river management is essential in improving water resource utilisation. However, river flows and water-levels are affected by unregulated in- and out-flows. Therefore, it is important to consider the forecasts of these unregulated flows and the uncertainties in the forecasts. The paper describes control and modelling tools from the literature that suit the river management problem. Specifically, a scenario-based Stochastic Model Predictive Control (MPC) strategy, that makes use of ensemble forecast of unregulated flows, is proposed, where the ensemble forecast contains multiple flow scenarios to characterise future flows and their uncertainties, and are obtained from catchment hydrological models.

This paper proposes a novel tri-stage online dispatch framework that coordinates the charging behaviors of electrical vehicles (EVs) within an AC/DC hybrid microgrid in the presence of uncertainties. A day-ahead scheduling model is proposed as the first stage to optimize the total operational cost for the next day (24 h). In the second stage, a receding horizon manner is adopted to adjust the day-ahead scheduling results, which can compensate for unpredictable disturbances. Both the first and second stages are operated with a time scale of one hour, which is, however, insufficient in capturing the operations of EVs. Hence, the third stage is introduced with the stochastic model predictive control (SMPC) method in a time scale of 10 min to further consider uncertainties of load, PV, EVs. The real-world behavioral data of eight private EVs in Beijing are used to evaluate the performance of our dispatch model. The simulation results show that compared with some traditional online dispatch methods, the total operational cost of the proposed dispatch framework is significantly reduced.

Economy, robustness and computational efficiency are of paramount metrics for an operation strategy of an integrated energy system (IES). To achieve the trade-off of the three metrics, a multi-layer framework is extensively exploited in existing operation strategies. This work, however, proposes a single-layer multi-timescale framework which can coordinate different operation performances associated with various timescales simultaneously. Based on the framework, an improved stochastic model predictive control (SMPC) operation strategy is further developed by embedding the proposed framework into its prediction horizon. To solve the multi-timescale optimization of the improved SMPC, the constraints and cost function are presented in the multi-timescale form, and the supplied and demands are forecast by the least square support vector machine. A simulator of an IES is thereafter constructed to mimic real system and used to evaluate the performance of the proposed strategy by operation cost, accumulative error and computation time with respect to economy, robustness and computational efficiency, respectively. Finally, the improved SMPC strategy is compared with a traditional single-layer and a hierarchical strategy by a case study. The results show that the improved strategy has the best tradeoff performance aforementioned. The multi-timescale framework can be also integrated into other operation strategies.

In a 100% clean energy town, to meet the energy balance and reduce the impact of power fluctuations on the main grid, in this paper, a hierarchical optimal energy management strategy (EMS) for a hybrid energy storage system (HESS) is proposed. The EMS consists of three layers. To meet the requirement of 100% clean energy, in the upper layer, a HESS economic operation model based on the mixed integer non-linear programming (MINLP) is presented. Then, considering the uncertainty of renewable energy and load, a power prediction model is presented in the middle layer. In addition, to reduce the power disturbance on the main grid caused by the stochastic power, a stochastic model predictive control (SMPC) strategy is implemented to optimize the power allocation of a HESS. In the lower layer, to reduce the power fluctuations of the lithium-ion battery (LiB) when mitigating minute-scale power fluctuations, a HESS optimal power allocation strategy based on Pontryagin's minimum principle (PMP) is proposed. In every control period, each layer is optimized based on the results of the previous layer. Finally, a simulation study is provided to validate the effectiveness of the proposed EMS. The results show that the proposed strategy has good performance in typical scenarios.

In the era of Industrial 4.0, the next-generation control system regards the cyber-physical system (CPS) as the core ingredient thanks to the comprehensive integration of physical systems, online computation, networking and control. A reliable, stable and resilient CPS should pledge robustness and safety. A significant concern in CPS development arises from security issues since the CPS is vulnerable to physical constraints, ubiquitous uncertainties and malicious cyber attacks. The integration of the stochastic model predictive control (MPC) framework and the resilient mechanism is a possible approach to guarantee robustness in the presence of stochastic uncertainties and enable resilience against cyber attacks. This review paper aims to offer a detailed overview of existing stochastic MPC algorithms and their CPS applications. More specifically, we first review existing stochastic MPC algorithms for both linear and nonlinear systems subject to probabilistic constraints. We then discuss how to extend the stochastic MPC framework to incorporate resilience mechanisms for constrained CPS under various malicious attacks. Finally, we present an architectural stochastic MPC-based framework for resilient CPS and identify future research challenges. This article is part of the theme issue ‘Towards symbiotic autonomous systems’.

Microgrids are a promising approach for the integration of renewable energy sources in existing networks and the energy supply of rural areas. A cost effective option for a microgrid is given by a hybrid energy system, which combines e.g. diesel generators, photovoltaic panels and batteries as considered in this paper. However, the interaction of the components and uncertainties in the load demand and photovoltaic power make the controller design challenging. This paper discusses a Stochastic Model Predictive Control approach which yields promising results regarding effectiveness and reliability as shown in a simulation study. Использование электроэнергетических микрогрид-систем является перспективным подходом к интеграции возобновляемых источников в существующие сети и энергообеспечение сельской местности. Экономическая эффективность электроэнергетических микрогрид-систем зависит от гибридной энергосистемы, объединяющей дизельные генераторы, фотоэлектрические панели и батареи. Однако взаимодействие составляющих и неопределенность графика нагрузки и фотоэлектрической энергии обусловливают необходимость создания блока управления. Рассмотрено применение стохастической модели для интеллектуального управления, что позволит обеспечить эффективность и надежность энергосистемы.

Long prediction horizons in Model Predictive Control (MPC) often prove to be efficient, however, this comes with increased computational cost. Recently, a Robust Model Predictive Control (RMPC) method has been proposed which exploits models of different granularity. The prediction over the control horizon is split into short-term predictions with a detailed model using MPC and long-term predictions with a coarse model using RMPC. In many applications robustness is required for the short-term future, but in the long-term future, subject to major uncertainty and potential modeling difficulties, robust planning can lead to highly conservative solutions. We therefore propose combining RMPC on a detailed model for short-term predictions and Stochastic MPC (SMPC), with chance constraints, on a simplified model for long-term predictions. This yields decreased computational effort due to a simple model for long-term predictions, and less conservative solutions, as robustness is only required for short-term predictions. The effectiveness of the method is shown in a mobile robot collision avoidance simulation., Comment: Accepted to the 2020 IFAC World Congress. The published version is available at https://doi.org/10.1016/j.ifacol.2020.12.515

With the penetration of electric vehicles in local markets, vehicle-induced electricity demand can cause power grid instability. Collaborative smart charging can help stabilize grid demand and mitigate those issues. This paper formulates charge scheduling when connected vehicles constitute a large portion of instantaneous demand. Allowing coordinated charging to sway electricity price, we formulate a multi-objective stochastic optimization problem to minimize cost while maximizing charge in each car. We model stochastic base electricity demand using a Gaussian Mixture Model (GMM) and solve the certainty-equivalent stochastic optimization problem. We then implement a stochastic model predictive control (SMPC) algorithm and compare performance between a naive policy, a certainty-equivalent optimized policy, and SMPC on a dataset derived from California ISO-serviced demand.