Scenario-based Model Predictive Control Research Articles

Conditional scenario-based energy management algorithm with uncertain correlated forecasts

This paper introduces the application of the novel approach known as Conditional Scenario-Based Model Predictive Control (CSB-MPC) into energy management in a low voltage distribution system (LVDS). The LVDS comprises renewable energy sources (RES) and an energy storage system, with correlated power generation and demand under uncertainty. This correlation is leveraged to derive a reduced set of conditional scenarios and their associated probabilities. This reduced set retains the essential characteristics of a larger set of equiprobable scenarios generated based on information about uncertainties in power generation and demand forecasts. Instead of computationally demanding methods using the larger set, a feasible Scenario-Based Mixed-Integer Linear Program (MILP) is solved by employing the reduced set. This optimisation minimises costs associated with energy consumption from the main grid and the potential waste of generated power. In the objective function, the scenarios are weighted by their probabilities to mitigate the impact of less likely forecasts, leading to efficient LVDS component utilisation and reduced operating costs. Simulation results comparing the performance of the LVDS with CSB-MPC against other MPC approaches, including classic scenario-based, chance-constrained, and deterministic methods, reveal that CSB-MPC consistently exhibits higher probabilities of operational constraint satisfaction, with differences of up to 10% or even 30%. Notably, CSB-MPC achieves these results with similar solution times to classic scenario-based MPC but with lower LVDS operating costs, between 6.62% to 11.31% less.

Obstacle Intention Awareness in Automatic Ship Collision Avoidance: Full-Scale Experiments in Confined Waters

In this article, full-scale experiments with a dynamic obstacle intention-aware Collision Avoidance System (CAS) are presented. The CAS consists of the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) for trajectory planning, dynamic obstacle avoidance, and antigrounding, with a Dynamic Bayesian Network (DBN) used for inferring obstacle intentions online. The novelty of this article lies in the utilization of intention information in deliberate collision-free planning. By inferring multiple different intention states on how and if nearby obstacles adhere to the COLREGS, the PSB-MPC can plan COLREGS-compliant avoidance maneuvers when possible, taking into account its awareness of the situation. The experiments put emphasis on hazardous situations where this intention information is both useful and necessary in order to avoid high collision risk. To the authors’ knowledge, the work is the first field experimental validation of such a probabilistic intention-aware CAS with consideration of multiple intention states. The experimental results demonstrate the validity of the proposed CAS scheme, with adherence to the traffic rules (COLREGS) 7, 8 and 13–17 in a diverse set of situations. The strengths and weaknesses of the proposed CAS are also discussed, giving insights that can be useful for researchers and practitioners in the field. Here, challenges related to detecting obstacle maneuvers and making the intention inference more robust to noise should be addressed as future work to make the scheme better suited for general usage on ships engaged in real traffic.

Scenario-based model predictive control with probabilistic human predictions for human–robot coexistence

This paper proposes a real-time motion planning scheme for safe human–robot workspace sharing relying on scenario-based nonlinear model predictive control (NMPC), a well-known approach for solving stochastic NMPC problems. A scenario tree is generated via higher-order Markov chains to provide probabilistic predictions of the human motion. Scenario-based NMPC is then used to generate point-to-point motions of the robot manipulator based on the above-mentioned human motion predictions, accounting for safety constraints via speed and separation monitoring (SSM). This means that the robot speed is always modulated to be able to stop before a possible collision with the human occurs. After proving theoretical properties on recursive feasibility and closed-loop stability of the proposed motion planning strategy, this is tested experimentally on a Kinova Gen3 robot interacting with a human operator, showing superior performance with respect to an NMPC scheme not relying on human predictions and to a fixed-path SSM strategy.

Conditional scenario-based model predictive control

This paper proposes a novel MPC approach called conditional scenario-based model predictive control (CSB-MPC), developed for discrete-time linear systems affected by parametric uncertainties and/or additive disturbances, which are correlated and with bounded support. At each control period, a primary set of equiprobable scenarios is generated and subsequently approximated to a new reduced set of conditional scenarios in which each has its respective probabilities of occurrence. This new set is considered for solving an optimal control problem in whose cost function the predicted states and inputs are penalised according to the probabilities associated with the uncertainties on which they depend in order to give more importance to predictions that involve realisations with a higher probability of occurrence. The performances of this new approach and those of a standard scenario-based MPC are compared through two numerical examples, and the results show greater probabilities of not transgressing the state constraints by the former, even when considering a smaller number of scenarios than the scenario-based MPC.

A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

ABSTRACT This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

Scenario-based model predictive control for energy scheduling in a parabolic trough concentrating solar plant with thermal storage

Optimal energy planning is a key topic in thermal solar trough plants. Obtaining a profitable energy schedule is difficult due to the stochastic nature of solar irradiance and electricity prices. This article focuses on optimal energy planning for thermal solar trough plants, particularly by developing a model predictive control algorithm based on multiple scenarios to deal with uncertainties. The results obtained using the proposed scheme have been tested and compared to other well-known approaches to energy scheduling through a realistic and reliable comparison to evaluate their performances and establish their advantages and weaknesses. Simulations were carried out for a 50 MW parabolic trough concentrating solar plant with a thermal energy storage system, considering different types of days classified according to their solar irradiance, meteorological forecast, and electrical market. Simulation results show that the proposed method outperforms other scheduling methods in dealing with uncertainties by selling energy to the grid at the right times, generating the highest income of about 7.58%.

A Hybrid Neural Network Approach for Adaptive Scenario-Based Model Predictive Control in the LPV Framework

This paper presents a hybrid neural network (NN) approach for adaptive scenario-based model predictive control (SMPC) design of nonlinear systems in the linear parametervarying (LPV) framework. In particular, a deterministic artificial neural network (ANN)-based LPV model is learned from data as the nominal model. Then, a Bayesian NN (BNN) is used to describe the mismatch between the plant and the LPV-ANN model. Adaptive scenarios are generated online based on the BNN model to reduce the conservativeness of scenario generation. Moreover, a probabilistic safety certificate is incorporated into the scenario generation by ensuring that the trajectories of scenarios contain the trajectory of the system and that all the scenarios satisfy the constraints with a high probability. Furthermore, conditions for the recursive feasibility of the SMPC are given. Experiments on the closed-loop simulations of a two-tank system demonstrate that the proposed approach can better model the behaviors of nonlinear systems than sole ANN/BNN models can, and the SMPC based on the hybrid NN (HyNN) model can improve the control performance compared to the SMPC with a fixed scenario tree.

Scenario-Based MPC for Real-Time Passenger-Centric Timetable Scheduling of Urban Rail Transit Networks

Effective timetable scheduling strategies are essential for passenger satisfaction in urban rail transit networks. Most existing passenger-centric timetable scheduling approaches generate a timetable according to deterministic passenger origin-destination (OD) demands. As passenger OD demands in urban rail transit networks generally show a high level of uncertainty, an effective timetable scheduling approach should take the uncertain passenger flows into account to generate a reliable timetable. In this paper, a scenario-based model predictive control (SMPC) approach is presented to handle uncertain passenger flows based on a passenger absorption model, where uncertainties are captured by several representative scenarios according to historical data. In each SMPC step, the optimization problem for generating the timetable can be reformulated as a mixed-integer linear programming (MILP) problem, which can be efficiently solved using current MILP solvers. A probabilistic performance level can be then determined based on the performance of SMPC under the representative scenarios. Numerical experiments based on the Beijing subway network are conducted to evaluate the efficacy of the proposed approach.

Scenario-based model predictive control of water reservoir systems

The optimal operation of water reservoir systems is a challenging task involving multiple conflicting objectives. The main source of complexity is the presence of the water inflow, which acts as an exogenous, highly uncertain disturbance on the system. When model predictive control (MPC) is employed, the optimal water release is usually computed based on the (predicted) trajectory of the inflow. This choice may jeopardize the closed-loop performance when the actual inflow differs from its forecast. In this work, we consider - for the first time - a stochastic MPC approach for water reservoirs, in which the control is optimized based on a set of plausible future inflows directly generated from past data. Such a scenario-based MPC strategy allows the controller to be more cautious, counteracting droughty periods (e.g., the lake level going below the dry limit) while at the same time guaranteeing that the agricultural water demand is satisfied. The method's effectiveness is validated through extensive Monte Carlo tests using actual inflow data from Lake Como, Italy.

A collision avoidance algorithm with intention prediction for inland waterways ships

Collision avoidance is one of the most challenging problems in developing a Maritime Autonomous Surface Ship. This paper proposes a pro-active collision avoidance algorithm for inland waterway ships. The algorithm addresses the problem of avoiding collisions with dynamic obstacles by applying a situation-based intention prediction for neighboring ships. This prediction algorithm allows own ship to be aware of future collision threats caused by the course changes of nearby ships. The prediction scheme is integrated into a scenario-based model predictive control scheme that has been modified for application in inland waterway traffic. The proposed algorithm can deal with complex traffic situations that a ship can encounter, and the performance of the proposed algorithm is evaluated in several experiment simulations.

Multi-stage scenario-based MPC for short term oil production optimization under the presence of uncertainty

This paper considers the problem of daily production optimization for a gas lift oil network under the presence of parametric uncertainty. The objective is to find the optimal distribution of injected lift gas to maximize total oil production from an oil network that contains parametric uncertainties subject to some constraints. Typically, the model-based optimization methods in such processes overlook uncertainty and go along with the optimal solution based on the nominal model. Nevertheless, the effect of uncertainty may lead to infeasibility when implemented in real applications. The proposed scenario-based optimization framework in this paper ensures robust feasibility compared to deterministic optimization. Additionally, the superiority of the method has been illustrated in comparison with the other robust optimization counterparts such as Min–Max NMPC in terms of conservativeness and execution time. The simulation results of the nominal, min–max, and scenario-based optimization are compared and discussed.

Ship Collision Avoidance Utilizing the Cross-Entropy Method for Collision Risk Assessment

In this article, a new approach for ship-ship collision probability estimation based on the Cross-Entropy (CE) method is introduced, which can be treated as an adaptive importance sampler. It has the advantage of attaining low variance estimates of small collision probabilities, which will most often be the case in realistic scenarios. Furthermore, a risk-based Collision Avoidance (COLAV) system being able to take obstacle kinematic uncertainty and intention uncertainty into account is presented, namely the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC). The collision probability estimator (CPE) is used in the risk assessment of the PSB-MPC, and tested in a simulation study, where the total system is validated. Simulation results show that the MPC is able to utilize the CPE for better risk assessment than the original version, in order to make safer decisions in close quarter situations and cases where nearby obstacles make unexpected maneuvers. It is also shown that when all vessels involved use the PSB-MPC, situations are resolved according to the traffic rules in a safe manner.

Collaborative Collision Avoidance for Autonomous Ships Using Informed Scenario-Based Model Predictive Control

There exist several collision avoidance algorithms for autonomous ships. But the majority of them do not utilize information about other ships’ intentions, except for observed position and velocity. As the attention for large-sized autonomous ships to be used in logistics is growing, autonomous ships will need to collaborate and negotiate with other ships to prevent reactive and agile collision avoidance maneuvers. As a first step towards a collaborative collision avoidance algorithm, we implemented a reactive short-range algorithm by utilizing other ships’ trajectory plans. We aimed to improve the existing Scenario-Based Model Predictive Control (SB-MPC) algorithm by including route exchange-based trajectory predictions and called it the Informed SB-MPC. Additionally, we introduce adaptive and conditional parameter selection methods for the SB-MPC design. Hereby we implemented the compliance with the COLREGs Rule 18 concerning responsibility between vessels in addition to the existing Rules 13-17. The performance of the new method is demonstrated with head-on, crossing, overtaking, and multiple ships scenarios.

Scenario-Based Model Predictive Control with Several Steps for COLREGS Compliant Ship Collision Avoidance

The main question investigated is whether additional decision steps can improve vessel behavior produced by the collision avoidance method scenario based model predictive control (SBMPC). The method, which functions by predicting alternative paths resulting from a finite number of alternative control behaviors, then selecting which behavior to apply by use of a cost function, was originally formulated to allow switching between several behaviors on the prediction horizon. However, current implementations have been limited to a single control step. To compare the single-step and multi-step SBMPC, a simulation study was performed, where different configurations for the number, positioning and possible control actions were tested. In the course of the simulation study it became clear that identifying situations producing a significant difference between the two methods was difficult to identify and the multi-step SBMPC led to only minor improvements in very few scenarios. Nevertheless, multi-step decisions can be visualized to give better situational awareness, and also have additional benefits with other trajectory parameterizations and less uncertain predictions of other ship trajectories.

Ship Collision Avoidance and Anti Grounding Using Parallelized Cost Evaluation in Probabilistic Scenario-Based Model Predictive Control

The ability to effectively process large amounts of information in reasonable time will be important for robust deliberative collision avoidance (COLAV) planning algorithms. Failure to do so can lead to collision, and can be compared to lack of proper supervision from officers on watch (OOW). The main contribution in this article is a parallelized implementation of the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC) on a Graphical Processing Unit (GPU) platform which incorporates both dynamic obstacle avoidance and anti-grounding. Simulation results demonstrate that the COLAV planner can produce collision-free trajectories with respect to grounding hazards and nearby vessels at relatively low computational cost, and which also comply to the COLREGS when deemed possible. Corresponding run-time results show that the algorithm utilizing parallel processing performs better than the alternative for increasing numbers of own-ship control behaviours, nearby static and dynamic obstacles, and dynamic obstacle prediction scenarios considered.

Scenario-based nonlinear model predictive control for building heating systems

State-of-the-art Model Predictive Control (MPC) applications for building heating adopt either a deterministic controller together with a nonlinear model or a linearized model with a stochastic MPC controller. However, deterministic MPC only considers one single realization of the disturbances and its performance strongly depends on the quality of the forecast of the disturbances, which can lead to low performance. In fact, inadequate building energy management can lead to high energy costs and CO2 emissions. On the other hand, a linearized model can fail to capture some dynamics and behavior of the building under control. In this article, we combine a stochastic scenario-based MPC (SBMPC) controller together with a nonlinear Modelica model that is able to provide a richer building description and to capture the dynamics of the building more accurately than linear models. The adopted SBMPC controller considers multiple realizations of the external disturbances obtained through a statistically accurate model, so as to consider different possible disturbance evolutions and to robustify the control action. To this purpose, we present a scenario generation method for building temperature control that can be applied to several exogenous perturbartions, e.g.solar irradiance, outside temperature, and that satisfies several important stastistical properties, in contrast with simpler and less accurate methods adopted in the literature. We show the benefits of our proposed approach through several simulations in which we compare our method against the standard ones from the literature, for several combinations of a trade-off parameter between comfort and energy cost. We show how our SBMPC controller approach outperforms the standard controllers available in the literature.

A Comparative Study of Stochastic Model Predictive Controllers

A comparative study of two state-of-the-art stochastic model predictive controllers for linear systems with parametric and additive uncertainties is presented. On the one hand, Stochastic Model Predictive Control (SMPC) is based on analytical methods and solves an optimal control problem (OCP) similar to a classic Model Predictive Control (MPC) with constraints. SMPC defines probabilistic constraints on the states, which are transformed into equivalent deterministic ones. On the other hand, Scenario-based Model Predictive Control (SCMPC) solves an OCP for a specified number of random realizations of uncertainties, also called scenarios. In this paper, Classic MPC, SMPC and SCMPC are compared through two numerical examples. Thanks to several Monte-Carlo simulations, performances of classic MPC, SMPC and SCMPC are compared using several criteria, such as number of successful runs, number of times the constraints are violated, integral absolute error and computational cost. Moreover, a Stochastic Model Predictive Control Toolbox was developed by the authors, available on MATLAB Central, in which it is possible to simulate a SMPC or a SCMPC to control multivariable linear systems with additive disturbances. This software was used to carry out part of the simulations of the numerical examples in this article and it can be used for results reproduction.

Fast approximate learning-based multistage nonlinear model predictive control using Gaussian processes and deep neural networks

Scenario-based model predictive control (MPC) methods introduce recourse into optimal control and can thus reduce the conservativeness inherent to open-loop robust MPC. However, the uncertainty scenarios are often generated offline using worst-case uncertainty bounds quantified a priori, limiting the potential gains in control performance. This paper presents a learning-based multistage MPC (msMPC) for systems with hard-to-model dynamics and time-varying plant-model mismatch. Gaussian Processes (GP) are used to learn state- and input-dependent plant-model mismatch in real-time and accordingly adapt the scenario tree online. Due to the increased computational complexity associated with incorporating the GP predictions into the optimal control problem, the learning-based msMPC (LB-msMPC) law is approximated by a deep neural network (DNN) that is cheap-to-evaluate online and has a small memory footprint, which makes it suitable for embedded applications. In addition, we present a novel algorithm for training the DNN-based controller that uses a GP description of the plant-model mismatch to generate closed-loop simulation data, which ensures the LB-msMPC law is evaluated in regions of the state space most relevant to closed-loop operation. The proposed LB-msMPC strategy is demonstrated on a cold atmospheric plasma jet with applications in (bio)materials processing. The simulation results indicate the promise of the approximate LB-msMPC strategy for control of hard-to-model systems with fast dynamics on millisecond timescales.

A Robust Scenario MPC Approach for Uncertain Multi-Modal Obstacles

Motion planning and control algorithms for autonomous vehicles need to be safe, and consider future movements of other road users to ensure collision-free trajectories. In this letter, we present a control scheme based on Model Predictive Control (MPC) with robust constraint satisfaction where the constraint uncertainty, stemming from the road users' behavior, is multimodal. The method combines ideas from tube-based and scenario-based MPC strategies in order to approximate the expected cost and to guarantee robust state and input constraint satisfaction. In particular, we design a feedback policy that is a function of the disturbance mode and allows the controller to take less conservative actions. The effectiveness of the proposed approach is illustrated through two numerical simulations, where we compare it against a standard robust MPC formulation.

On Collision Risk Assessment for Autonomous Ships Using Scenario-Based MPC

Collision Avoidance (COLAV) for autonomous ships is challenging since it relies on track estimates of nearby obstacles which are inherently uncertain in both state and intent. This uncertainty must be accounted for in the COLAV system in order to ensure both safe and efficient operation of the vessel in accordance with the traffic rules. Here, a COLAV system built on the Scenario-based Model Predictive Control (SB-MPC) with dynamic probabilistic risk treatment is presented. The system estimates the probability of collision with all nearby obstacles using a combination of Monte Carlo simulation (MCS) and a Kalman Filter (KF), taking the uncertainty in both position and velocity into account. A probabilistic collision cost is then used in the MPC to penalize risk-taking maneuvers. Simulation results show that the proposed method may provide increased robustness due to increased situational awareness, while also being able to efficiently follow the nominal path and adhere to the traffic rules.