Chance-constrained Model Predictive Control Research Articles

Chance-constrained stochastic MPC of greenhouse production systems with parametric uncertainty

Greenhouse climate control is important to provide sufficient fresh food for the growing population in an economical and sustainable manner. However, the developed crop-climate models are generally complex with parametric uncertainties and far from describing the real system accurately, which affects adversely the control system’s performance. To improve optimality and guarantee robustness during the control process, we develop and implement a stochastic model predictive control (MPC) scheme for greenhouse production systems considering parametric uncertainties. By leveraging the advantages of model linearization, the proposed chance-constrained MPC method enables a more straightforward formulation of uncertainty constraints and computationally cheaper optimization in comparison to directly using the nonlinear model. Finally, the efficacy of the proposed approach is demonstrated on a greenhouse climate control case study.

Perception-aware model predictive control for constrained control in unknown environments

The operation of autonomous systems is inherently constrained by their surrounding environment, which is often time-varying and unknown a priori, necessitating perception using sensors. Hence, control strategies for autonomous systems must take into account the uncertainty of the perceived environment in making decisions, while information acquired by sensors often depends on how the system is operated, e.g., where the sensors are pointed at, or what and how much sensor information is processed. We introduce a perception-aware chance-constrained model predictive control (PAC-MPC) strategy that accounts for the uncertainty of the perceived environment, as well as the dependence of the perception quality on the control actions. The system and the environment are coupled by chance constraints due to the uncertainty in the environment estimate, which depends on control actions. We establish the constraint satisfaction and stability properties of PAC-MPC through appropriate design of the cost function and terminal set, and propose a constructive design procedure for the case of linear dynamics.

A predictive chance constraint rebalancing approach to mobility-on-demand services

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand (MoD) services. These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high. To achieve this, we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing. More precisely, first travel demand is predicted using Gaussian Process Regression (GPR) which provides uncertainty bounds on the prediction. We then formulate a stochastic model predictive control (MPC) for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds. In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user-defined confidence interval, using Chance Constrained MPC (CCMPC). The benefits of the proposed method are twofold. First, travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework, allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability. Second, CCMPC can be relaxed into a Mixed-Integer-Linear-Program (MILP) and the MILP can be solved as a corresponding Linear-Program, which always admits an integral solution. Our transportation simulations show that by tuning the confidence bound on the chance constraint, close to optimal oracle performance can be achieved, with a median customer wait time reduction of 4% compared to using only the mean prediction of the GPR.

Autonomous Needle Navigation in Retinal Microsurgery: Evaluation in ex vivo Porcine Eyes.

Important challenges in retinal microsurgery include prolonged operating time, inadequate force feedback, and poor depth perception due to a constrained top-down view of the surgery. The introduction of robot-assisted technology could potentially deal with such challenges and improve the surgeon's performance. Motivated by such challenges, this work develops a strategy for autonomous needle navigation in retinal microsurgery aiming to achieve precise manipulation, reduced end-to-end surgery time, and enhanced safety. This is accomplished through real-time geometry estimation and chance-constrained Model Predictive Control (MPC) resulting in high positional accuracy while keeping scleral forces within a safe level. The robotic system is validated using both open-sky and intact (with lens and partial vitreous removal) ex vivo porcine eyes. The experimental results demonstrate that the generation of safe control trajectories is robust to small motions associated with head drift. The mean navigation time and scleral force for MPC navigation experiments are 7.208 s and 11.97 mN, which can be considered efficient and well within acceptable safe limits. The resulting mean errors along lateral directions of the retina are below 0.06 mm, which is below the typical hand tremor amplitude in retinal microsurgery.

Overtaking decision and trajectory planning in highway via hierarchical architecture of conditional state machine and chance constrained model predictive control

An overtaking trajectory planning algorithm is an essential part of autonomous vehicles, but maximizing trip efficiency (minimum travel time) while guaranteeing safety is non-trivial. In particular, to achieve optimal trajectory results in all situations using one algorithm is challenging because overtaking is a complex maneuver in which several behaviors are combined. In this paper, an overtaking algorithm that employs a finite state machine as a high-level decision maker and chance constrained model predictive control as a trajectory planner is proposed to optimize trip efficiency and ride comfort while guaranteeing safety. By combining two methods in a hierarchical structure, the proposed algorithm takes advantage of each method to realize optimality and real-time performance. Using the conditional state machine (CSM), algorithm classifies maneuver states that can ensure safety, and sets the optimal multi-vehicle constraints in each state. The chance constrained model predictive control (MPC) plans an optimal trajectory that considers the prediction uncertainty, safety, trip efficiency and ride comfort. To rigorously evaluate both trip efficiency and safety, the performance of the proposed overtaking algorithm is evaluated in a statistical manner for various level of service (LOS) scenarios. Simulation results show that the optimal trajectory was generated in a multi-vehicle situation while ensuring higher safety than the rule-based algorithm.

Chance-constrained stochastic MPC of Astlingen urban drainage benchmark network

In urban drainage systems (UDS), a proven method for reducing the combined sewer overflow (CSO) pollution is real-time control (RTC) based on model predictive control (MPC). MPC methodologies for RTC of UDSs in the literature rely on the computation of the optimal control strategies based on deterministic rain forecast. However, in reality, uncertainties exist in rainfall forecasts which affect severely accuracy of computing the optimal control strategies. Under this context, this work aims to focus on the uncertainty associated with the rainfall forecasting and its effects. One option is to use stochastic information about the rain events in the controller; in the case of using MPC methods, the class called stochastic MPC is available, including several approaches such as the chance-constrained MPC(CC-MPC) method. In this study, we apply CC-MPC to the UDS. Moreover, we also compare the operational behavior of both the classical MPC with perfect forecast and the CC-MPC based on different stochastic scenarios of the rain forecast. The application and comparison have been based on simulations using a SWMM model of the Astlingen urban drainage benchmark network. From the simulations, it was found that CSO volumes were larger when CC-MPC had overestimating forecast biases, while for MPC they increased with any presence of forecast biases.

Optimal energy management in smart sustainable buildings – A chance-constrained model predictive control approach

Recent European environmental directives, the prevalent consumer desire to minimize electricity costs, and the grid-driven need for flexible buildings all lead to a common outcome: the smart sustainable building (SSB). Coordinated by their building energy management systems (BEMS), SSBs steer their operation towards monetary gains for their owners, and flexibility for grid operators. Another key feature is their sustainability, expressed by the mandatory nearly-zero-energy (nZE) mandate, i.e., balancing yearly energy consumption and on-site renewable energy production. In this paper, we present a generic and comprehensive (in terms of device composition) BEMS framework for SSBs. Aside from operating cost minimization, the BEMS is additionally tasked with overseeing the SSB’s environmental profile, ensuring that the nZE mandate is not jeopardized in the pursuit of monetary gains. This is achieved through a novel adaptive sustainability criterion. The inherent uncertainties of solar irradiance and ambient temperature are reflected on the occupants’ thermal comfort, the relevant limitation being cast as chance constraints. The overall mixed-integer linear programming (MILP) problem is solved through model predictive control (MPC). The main contributions lie in the joint consideration of a) a comprehensive devices set, b) weather forecast uncertainties, and c) the employment of the novel adaptive sustainability criterion. The proposed framework is validated in a nigh-exhaustive case study and evaluated with respect to cost management and ability to manage the SSB’s nZE status.

Real-time optimization strategy for single-track high-speed train rescheduling with disturbance uncertainties: A scenario-based chance-constrained model predictive control approach

To improve the operational efficiency of high-speed railway system with disturbance uncertainties, a real-time optimization rescheduling strategy is designed based on the updated information for single-track high-speed railway system in this paper. Based on the characteristics of high-speed railway lines, a mixed-integer linear optimization model is constructed, where the decision variables involve the arrival times, departure times, arrival orders, departure orders and dwelling plans. Furthermore, to satisfy real-time requirements and to enhance the robustness of solutions, a scenario-based chance-constrained model predictive control (SC-MPC) algorithm is designed for solving the train rescheduling problem. Under the designed algorithm, the original linear model is converted to a non-linear mixed-integer model. To reduce the computational burden, the nonlinear model is converted to a linear mixed-integer model by a linearization method. The proposed strategy is compared with several typical benchmark strategies via a case study on the Beijing-Shanghai high-speed railway line. The simulation results show that the train delays can be effectively reduced by the proposed strategy and the rescheduling timetable has a good robustness.

Humanoids control subjected to disturbance by chance-constrained model predictive control

Humanoids control subjected to disturbance by chance-constrained model predictive control

Chance-Constrained MPC for Voronoi-based Multi-Agent System Deployment

This paper proposes a new chance-constrained model predictive control (CCMPC) algorithm with state estimation applied to the two-dimensional deployment of a multi-vehicle system where each agent is subject to process noise and measurement noise. The bounded convex area of deployment is partitioned into time-varying Voronoi cells defined by the position of each agent. Due to the presence of noise in the system model, stochastic constraints appear in the model predictive control problem. The proposed decentralized robust CCMPC algorithm drives the multi-agent system into a static Chebyshev configuration where each agent lies on the Chebyshev center of its Voronoi cell. Simulation results show the effectiveness of the proposed control strategy on a fleet of quadrotors subject to wind perturbations and measurement noise.

Resource and Network Management for Satellite Communications Systems: A Chance-Constrained Approach

In this paper, we propose an optimization framework for the resource and network management in large-scale satellite communications (SATCOM) systems with stochastic and time-varying communication requests. Because further expansions of SATCOM systems are expected in the near future, it is of practical importance to develop management methodologies for efficiently and robustly operating large-scale SATCOM systems. To address this problem, in this paper, we formulate a SATCOM network optimization problem within the framework of the chance-constrained model predictive control. In this problem, we require that a joint chance constraint on the bandwidth loss rate is satisfied with a user-specified performance and probability. Because the joint chance constraint is nonlinear in design variables, we relax the constraint to a linear deterministic one for reformulating the original problem into a relaxed deterministic problem. We numerically verify that the proposed method outperforms a baseline methodology and therefore allows us to efficiently manage large-scale SATCOM systems.

Predictive Cruise Control Using Radial Basis Function Network-Based Vehicle Motion Prediction and Chance Constrained Model Predictive Control

Predicting future motions of surrounding vehicles and driver’s intentions are essential to avoid future potential risks. The predicting future motions, however, is very challenging because the future cannot be deterministically known a priori and there are infinitely many possible future trajectories. Prediction becomes far more challenging when trying to foresee distant future. This paper proposes a probabilistic motion prediction algorithm that can accurately compute the likelihood of multiple target lanes and trajectories of surrounding vehicles by using the artificial neural network; more specifically radial base function network (RBFN). The RBFN prediction algorithm estimates the likelihood of each lane being the driver’s target lane in categorical distributions and the corresponding future trajectories in parallel. In order to demonstrate the effectiveness of the proposed prediction algorithm, it is applied for the predictive cruise control problem. Chance-constrained model predictive control (CCMPC) is utilized because the chance constraints in CCMPC can handle collision uncertainties associated with future uncertainties from the proposed prediction algorithm. The RBFN-based CCMPC simulation is conducted for several risky cut-in scenarios and compared with the state-of-the-art Interactive Multiple Model (IMM)-based prediction algorithm. The simulation results show that the RBFN-based CCMPC achieves higher collision avoidance success rate than that of the IMM-based CCMPC while using smaller actuator inputs and providing higher passenger comforts. Furthermore, the RBFN-based CCMPC showed high robustness to false braking during near lane-change (lane-keeping) scenarios.

Integrated condition-based track maintenance planning and crew scheduling of railway networks

We develop a multi-level decision making approach for optimal condition-based maintenance planning of a railway network divided into a large number of sections with independent stochastic deterioration dynamics. At higher level, a chance-constrained Model Predictive Control (MPC) controller determines the long-term section-wise maintenance plan, minimizing condition deterioration and maintenance costs for a finite planning horizon, while ensuring that the deterioration level of each section stays below the maintenance threshold with a given probabilistic guarantee in the presence of parameter uncertainty. The resulting large MPC optimization problem containing both continuous and discrete decision variables is solved using Dantzig-Wolfe decomposition to improve the scalability of the proposed approach. At a lower level, the optimal short-term scheduling of the maintenance interventions suggested by the high-level controller and the optimal routing of the corresponding maintenance crew is formulated as a capacitated arc routing problem, which is solved exactly by transforming it into a node routing problem. The proposed approach is illustrated by a numerical case study on the optimal treatment of squats of a regional Dutch railway network. Simulation results show that the proposed approach is robust, non-conservative, and scalable.

A hierarchical energy management strategy for interconnected microgrids considering uncertainty

Coordinating the operation of neighboring microgrids is a promising solution for the problem of growing penetration of renewable-based microgrids into the power system. In this paper, a hierarchical stochastic energy management system is proposed for operation management of interconnected microgrids. At the upper-level, a central entity is responsible for coordinating the operation of microgrids. Based on the energy scheduling made at this level, the power reference values to be exchanged within the microgrids network and between the microgrids and the main grid are calculated and communicated with the local energy management systems. At the lower-level, a decision making approach based on chance-constrained model predictive control is adopted for local operation management of each microgrid taking into account different sources of uncertainties. The results show that the proposed strategy provides the microgrids with the opportunity of exploiting maximum available capacity in the network. Consequently, the microgrids dependency on the main grid will be reduced and some important performance indices such as multi-microgrid system cost and real-time power deviations will be improved.

Probabilistic Anticipation and Control in Autonomous Car Following

Human-driven and autonomously driven cars of today act often reactively to the decisions of the cars they follow, which could lead to uncomfortable, inefficient, and sometimes unsafe situations in stop and go traffic. This paper proposes methods for probabilistic anticipation of the motion of the preceding vehicle and for the control of motion of the ego vehicle. We construct: 1) a Markov chain predictor based on the observed behavior of preceding vehicle and 2) a maximum likelihood motion predictor based on historical traffic speed at different locations and times. Heuristics are proposed for combining the two predictions to determine a probability distribution on the position of the preceding vehicle over a future planning horizon. A chance-constrained model predictive control framework is employed to optimize the motion of the ego vehicle, given the probabilistic prediction of motion of preceding vehicle. Effectiveness of the proposed approach is evaluated in multiple simulation scenarios.

Model Predictive Control for Stochastic Max-Plus Linear Systems With Chance Constraints

The topic of this paper is model predictive control (MPC) for max-plus linear systems with stochastic uncertainties the distribution of which is supposed to be known. We consider linear constraints on the inputs and the outputs. Due to the uncertainties, these linear constraints are formulated as probabilistic or chance constraints, i.e., the constraints are required to be satisfied with a predefined probability level. The proposed chance constraints can be equivalently rewritten into a max-affine (i.e., the maximum of affine terms) form if the linear constraints are monotonically nondecreasing as a function of the outputs. Based on the resulting max-affine form, two methods are developed for solving the chance-constrained MPC problem for stochastic max-plus linear systems. Method 1 uses Boole's inequality to convert the multivariate chance constraint into univariate chance constraints for which the probability can be computed more efficiently. Method 2 employs Chebyshev's inequality and transforms the chance constraint into linear constraints on the inputs. The simulation results for a production system example show that the two proposed methods are faster than the Monte Carlo simulation method and yield lower closed-loop costs than the nominal MPC method.

Chance-Constrained Model Predictive Control for SAGD Process Using Robust Optimization Approximation

Control of a steam-assisted gravity drainage (SAGD) process is a challenging task, because of the presence of various uncertainties, such as geological uncertainty and steam quality uncertainty. They often lead to constraint violations and performance degradation. In this work, a chance-constrained model predictive control (CCMPC) method is presented to generate a safe and optimal control strategy, considering the presence of uncertainties. A novel robust optimization method is applied to solve the chance-constrained optimization problem under general distribution of uncertainties. Two case studies are presented to demonstrate the proposed approach. Furthermore, the modeling of SAGD process is discussed, and the proposed robust optimization-based CCMPC is tested using a reservoir simulator (Petroleum Experts) of the SAGD process. The proposed approach reduces constraint violations that are due to uncertainties and achieves satisfactory performance.

Optimal operation management of a regional network of microgrids based on chance‐constrained model predictive control

A regional network of microgrids includes a cluster of microgrids located in a neighbourhood area connecting together through power lines. In this study, the problem of operation management of networked-microgrids is considered. The main goal is to develop an efficient strategy to control local operation of each microgrid including the amount of energy to be requested from the main grid and the optimal charging/discharging patterns of batteries along with the transferred power among microgrids considering system's technical constraints. Accounting for system uncertainty due to the presence of renewable energy sources and variability of loads, the problem is formulated in the framework of chance-constrained model predictive control. Moreover, the Monte Carlo algorithm is adopted to generate discrete random scenarios to evaluate the solutions. Simulation studies have been exemplarily carried out in order to show the effectiveness of the proposed approach.

Nonlinear Model Predictive Control with Explicit Backoffs for Stochastic Systems under Arbitrary Uncertainty

The majority of work on chance constrained model predictive control (MPC) for stochastic systems adopts the concept of implicit constraint backoffs for handling state chance constraints. However, implicit backoffs cannot be computed analytically in nonlinear MPC (NMPC), so that they must be approximated and, as a result, chance constraints are not guaranteed by the closed-loop system. This paper proposes a strategy for explicit computation of constraint backoffs that allows tightly guaranteeing chance constraints in NMPC for stochastic systems with arbitrary uncertainty distributions. The proposed method relies on uncertainty propagation through closed-loop system dynamics. Thus, this paper also investigates the use of stochastic surrogate models for constructing the distribution of closed-loop quantities of interest such as state constraint functions or any general performance objectives. To this end, an extension of polynomial chaos that can handle arbitrary probability measures is proposed for a class of disturbance models representing plant-model mismatch. The proposed methods are illustrated on a benchmark continuously-stirred tank reactor problem.

Multi-level condition-based maintenance planning for railway infrastructures – A scenario-based chance-constrained approach

This paper develops a multi-level decision making approach for the optimal planning of maintenance operations of railway infrastructures, which are composed of multiple components divided into basic units for maintenance. Scenario-based chance-constrained Model Predictive Control (MPC) is used at the high level to determine an optimal long-term component-wise intervention plan for a railway infrastructure, and the Time Instant Optimization (TIO) approach is applied to transform the MPC optimization problem with both continuous and integer decision variables into a nonlinear continuous optimization problem. The middle-level problem determines the allocation of time slots for the maintenance interventions suggested at the high level to optimize the trade-off between traffic disruption and the setup cost of maintenance slots. Based on the high-level intervention plan, the low-level problem determines the optimal clustering of the basic units to be treated by a maintenance agent, subject to the time limit imposed by the maintenance slots. The proposed approach is applied to the optimal treatment of squats, with real data from the Eindhoven-Weert line in the Dutch railway network.