In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus entailing a decrease in computational cost, which has been a hindrance to the application of Model Predictive Control approaches with Mixed-Integer Programming formulations in real-time. Moreover, the assignment of obstacles to clusters and the sizes of the clusters are decided within the same optimization problem that performs the trajectory planning, thus yielding optimal cluster choices. Simulation results are presented to illustrate an application of the proposal.
With the increased amount of volatile renewable energy sources connected to the electricity grid, and the phase-out of fossil fuel based power plants, there is an increased need for frequency regulation. On the demand side, frequency regulation services can be offered by buildings or districts that are equipped with electric heating or cooling systems, by exploiting their thermal inertia. Existing approaches for tapping into this potential typically rely on dynamic building models, which in practice can be challenging to obtain and maintain. As a result, practical implementations of such systems are scarce. Moreover, actively controlling buildings requires extensive control infrastructure and may cause privacy concerns in district energy systems. Motivated by this, we exploit the thermal inertia of buffer storage for reserves, reducing the building models to demand forecasts here. By combining a control scheme based on Robust Model Predictive Control, with affine policies, and heating demand forecasting based on Artificial Neural Networks with online correction methods, we offer frequency regulation reserves and maintain user comfort with a system comprising a heat pump and buffer storage. While the robust approach ensures occupant comfort, the use of affine policies reduces the effect of disturbance uncertainty on the system state. In a first-of-its-kind experiment with a real district-like building energy system, we demonstrate that the scheme is able to offer reserves in a variety of conditions and track a regulation signal while meeting the heating demand of the connected buildings. 13.4% of the consumed electricity is flexible. In additional numerical studies, we demonstrate that using affine policies significantly decreases the cost function and increases the amount of offered reserves and we investigate the suboptimality in comparison to an omniscient control system.
In this work, a revised formulation of Chance-Constrained (CC) Model Predictive Control (MPC) is presented. The focus of this work is on the mathematical formulation of the revised CC-MPC, and the reason behind the need for its revision. The revised formulation is given in the context of sewer systems, and their weir overflow structures. A linear sewer model of the Astlingen Benchmark sewer model is utilized to illustrate the application of the formulation, both mathematically and performance-wise through simulations. Based on the simulations, a comparison of performance is done between the revised CC-MPC and a comparable deterministic MPC, with a focus on overflow avoidance, computation time, and operational behavior. The simulations show similar performance for overflow avoidance for both types of MPC, while the computation time increases slightly for the CC-MPC, together with operational behaviors getting limited
Set-based integration methods allow to prove properties of differential systems, which take into account bounded disturbances. The systems (either time-discrete, time-continuous or hybrid) satisfying such properties are said to be "robust". In the context of optimal control synthesis, the set-based methods are generally extensions of numerical optimal methods of two classes: first, methods based on convex optimization; second, methods based on the dynamic programming principle. Heymann et al. have recently shown that, for certain systems of low dimension, the second numerical method can give better solutions than the first one. They have built a solver (Bocop) that implements both numerical methods. We show in this paper that a set-based extension of a method of the second class which uses a guaranteed Euler integration method, allows us to find such good solutions. Besides, these solutions enjoy the property of robustness against uncertainties on initial conditions and bounded disturbances. We demonstrate the practical interest of our method on an example taken from the numerical Bocop solver. We also give a variant of our method, inspired by the method of Model Predictive Control, that allows us to find more efficiently an optimal control at the price of losing robustness.
Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed performance criterion. Large performance gains have been reported for many applications and closed-loop stability has been recently investigated. However, computational performance still remains an open issue and only few contributions have proposed real-time algorithms tailored to EMPC. We perform a step towards computationally cheap algorithms for EMPC by proposing a new positive-definite Hessian approximation which does not hinder fast convergence and is suitable for being used within the real-time iteration (RTI) scheme. We provide two simulation examples to demonstrate the effectiveness of RTI-based EMPC relying on the proposed Hessian approximation.
To improve the driving mobility and energy efficiency of connected autonomous electrified vehicles, this paper presents an integrated longitudinal speed decision-making and energy efficiency control strategy. The proposed approach is a hierarchical control architecture, which is assumed to consist of higher-level and lower-level controls. As the core of this study, model predictive control and reinforcement learning are combined to improve the powertrain mobility and fuel economy for a group of automated vehicles. The higher-level exploits the signal phase and timing and state information of connected autonomous vehicles via vehicle to infrastructure and vehicle to vehicle communication to reduce stopping at red lights. The higher-level outputs the optimal vehicle velocity using model predictive control technique and receives the power split control from the lower-level con-troller. These two levels communicate with each other via a controller area network in the real vehicle. The lower-level utilizes a model-free reinforcement learning method to improve the fuel economy for each connected autonomous vehicle. Numerical tests illustrate that vehicle mobility can be noticeably improved (traveling time reduced by 30%) by reducing red-light idling. The effectiveness and performance of the proposed method are validated via comparison analysis among different energy efficiency controls (fuel economy promoted by 13%).
Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined risk parameter. However, considering chance constraints in an optimization problem can be challenging and computationally demanding. In this paper, we present a grid-based Stochastic Model Predictive Control approach. This approach allows to determine a simple deterministic reformulation of the chance constraints and reduces the computational effort, while considering the stochastic nature of the environment. Within the proposed method, we first divide the environment into a grid and, for each predicted step, assign each cell a probability value, which represents the probability that this cell will be occupied by surrounding vehicles. Then, the probabilistic grid is transformed into a binary grid of admissible and inadmissible cells by applying a threshold, representing a risk parameter. Only cells with an occupancy probability lower than the threshold are admissible for the controlled vehicle. Given the admissible cells, a convex hull is generated, which can then be used for trajectory planning. Simulations of an autonomous driving highway scenario show the benefits of the proposed grid-based Stochastic Model Predictive Control method.
In this paper, we formulate a Nonlinear Model Predictive Control (NMPC) to plan appropriate social distancing measures (and relaxations) in order to mitigate the COVID-19 pandemic effects, considering the contagion development in Brazil. The NMPC strategy is designed upon an adapted data-driven Susceptible-Infected-Recovered-Deceased (SIRD) contagion model, which takes into account the effects of social distancing. Furthermore, the adapted SIRD model includes time-varying auto-regressive contagion parameters, which dynamically converge according to the stage of the pandemic. This new model is identified through a three-layered procedures, with analytical regressions, Least-Squares optimization runs and auto-regressive model fits. The data-driven model is validated and shown to adequately describe the contagion curves over large forecast horizons. In this model, control input is defined as finitely parametrized values for social distancing guidelines, which directly affect the transmission and infection rates of the SARS-CoV-2 virus. The NMPC strategy generates piece-wise constant quarantine guidelines which can be relaxed/strengthen as each week passes. The implementation of the method is pursued through a search mechanism, since the control is finitely parametrized and, thus, there exist a finite number of possible control sequences. Simulation essays are shown to illustrate the results obtained with the proposed closed-loop NMPC strategy, which is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to an "open-loop"/no control condition, the number of deaths still could be reduced in up to 30 %. The forecast preview an infection peak to September 2nd, 2020, which could lead to over 1.5 million deaths if no coordinate health policy is enacted. The framework serves as guidelines for possible public health policies in Brazil.
This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed loop cost is reduced and conservativeness of Chebyshev's inequality is mitigated. Also, a larger feasible set of initial conditions can be obtained. Numerical simulations are given to show these results.
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect redundant non-linear constraints is an open problem. In this paper we present a novel methodology based on Sum of Squares for the elimination of redundant polynomial constraints. The paper also presents some relevant applications of the presented method to constrained control problems. In particular, we show how the proposed method can be used in the Model Predictive Control and in the Reference Governor frameworks to reduce the computational burden of the online algorithms. Furthermore, this method can also be used to eliminate the terminal constraints in MPC in a simple way that is independent from the cost function.
Load shedding has been one of the most widely used and effective emergency control approaches against voltage instability. With increased uncertainties and rapidly changing operational conditions in power systems, existing methods have outstanding issues in terms of either speed, adaptiveness, or scalability. Deep reinforcement learning (DRL) was regarded and adopted as a promising approach for fast and adaptive grid stability control in recent years. However, existing DRL algorithms show two outstanding issues when being applied to power system control problems: 1) computational inefficiency that requires extensive training and tuning time; and 2) poor scalability making it difficult to scale to high dimensional control problems. To overcome these issues, an accelerated DRL algorithm named PARS was developed and tailored for power system voltage stability control via load shedding. PARS features high scalability and is easy to tune with only five main hyperparameters. The method was tested on both the IEEE 39-bus and IEEE 300-bus systems, and the latter is by far the largest scale for such a study. Test results show that, compared to other methods including model-predictive control (MPC) and proximal policy optimization(PPO) methods, PARS shows better computational efficiency (faster convergence), more robustness in learning, excellent scalability and generalization capability.
In this paper we present a model-predictive control (MPC) based approach for vehicle platooning in an urban traffic setting. Our primary goal is to demonstrate that vehicle platooning has the potential to significantly increase throughput at intersections, which can create bottlenecks in the traffic flow. To do so, our approach relies on vehicle connectivity: vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. In particular, we introduce a customized V2V message set which features a velocity forecast, i.e. a prediction on the future velocity trajectory, which enables platooning vehicles to accurately maintain short following distances, thereby increasing throughput. Furthermore, V2I communication allows platoons to react immediately to changes in the state of nearby traffic lights, e.g. when the traffic phase becomes green, enabling additional gains in traffic efficiency. We present our design of the vehicle platooning system, and then evaluate performance by estimating the potential gains in terms of throughput using our results from simulation, as well as experiments conducted with real test vehicles on a closed track. Lastly, we briefly overview our demonstration of vehicle platooning on public roadways in Arcadia, CA.
Plant factories with artificial light are widely researched for food production in a controlled environment. For such control tasks, models of the energy and resource exchange in the production unit as well as those of the plant's growth process may be used. To achieve minimal operation cost, optimal control strategies can be applied to the system, taking into account the availability of resources by control reference specification. A particular advantage of model predictive control (MPC) is the incorporation of constraints that comply with actuator limitations and general plant growth conditions. In this work, a model of a production unit is derived including a description of the relation between the actuators' electrical signals and the input values to the model. Furthermore, a preliminary model based state tracking control is evaluated for production unit containing Lettuce. It could be observed that the controller is capable to track the reference while satisfying the constraint under changing weather conditions and resource availability.
We present a data-driven model predictive control (MPC) framework for systems with high state-space dimensionalities. This work is motivated by the need to exploit sensor data that appears in the form of images (e.g., 2D or 3D spatial fields reported by thermal cameras). We propose to use dynamic mode decomposition (DMD) to directly build a low-dimensional model from image data and we use such model to obtain a tractable MPC controller. We demonstrate the scalability of this approach (which we call DMD-MPC) by using a 2D thermal diffusion system. Here, we assume that the evolution of the thermal field is captured by 50x50 pixel images, which results in a 2500-dimensional state-space. We show that the dynamics of this high-dimensional space can be accurately predicted by using a 40-dimensional DMD model and we show that the field can be manipulated satisfactorily by using an MPC controller that embeds the low-dimensional DMD model. We also show that the DMD-MPC controller significantly outperforms a standard MPC controller that uses data from a finite set of spatial locations (proxy locations) to manipulate the high-dimensional thermal field. This comparison illustrates the value of information embedded in image data.
We present a general framework for risk semantics on Signal Temporal Logic (STL) specifications for stochastic dynamical systems using axiomatic risk theory. We show that under our recursive risk semantics, risk constraints on STL formulas can be expressed in terms of risk constraints on atomic predicates. We then show how this allows a (stochastic) STL risk constraint to be transformed into a risk-tightened deterministic STL constraint on a related deterministic nominal system, enabling the application of existing STL methods. For affine predicate functions and a (coherent) Distributionally Robust Value at Risk measure, we show how risk constraints on atomic predicates can be reformulated as tightened deterministic affine constraints. We demonstrate the framework using a Model Predictive Control (MPC) design with an STL risk constraint.
We present a model predictive control (MPC) framework to solve the constrained nonlinear output regulation problem. The main feature of the proposed framework is that the application does not require the solution to classical regulator (Francis-Byrnes-Isidori) equations or any other offline design procedure. In particular, the proposed formulation simply minimizes the predicted output error, possibly with some input regularization. Instead of using terminal cost/sets or a positive definite stage cost as is standard in MPC theory, we build on the theoretical results by Grimm et al. 2005 using a detectability notion. The proposed formulation is applicable if the constrained nonlinear regulation problem is (strictly) feasible, the plant is incrementally stabilizable and incrementally input-output to state stable (i-IOSS/detectable). We show that for minimum phase systems such a design ensures exponential stability of the regulator manifold. We also provide a design procedure in case of unstable zero dynamics using an incremental input regularization and a nonresonance condition. Inherent robustness properties for the noisy error/output-feedback case are established under simplifying assumptions (e.g. no state constraints). The theoretical results are illustrated with an example involving offset free tracking with noisy error feedback. The paper also contains novel results for MPC without terminal constraints with positive semidefinite input/output stage costs that are of independent interest.
The global COVID-19 pandemic (SARS-CoV-2 virus) is the defining health crisis of our century. Due to the absence of vaccines and drugs that can help to fight it, the world solution to control the spread has been to consider public social distance measures that avoids the saturation of the health system. In this context, we investigate a Model Predictive Control (MPC) framework to determine the time and duration of social distancing policies. We use Brazilian data in the period from March to May of 2020. The available data regarding the number of infected individuals and deaths suffers from sub-notification due to the absence of mass tests and the relevant presence of the asymptomatic individuals. We estimate variations of the SIR model using an uncertainty-weighted Least-Squares criterion that considers both nominal and inconsistent-data conditions. Moreover, we add to our versions of the SIR model an additional dynamic state variable to mimic the response of the population to the social distancing policies determined by the government that affects the speed of COVID-19 transmission. Our control framework is within a mixed-logical formalism, since the decision variable is forcefully binary (the existence or the absence of social distance policy). A dwell-time constraint is included to avoid harsh shifting between these two states. Finally, we present simulation results to illustrate how such optimal control policy would operate. These results point out that no social distancing should be relaxed before mid August 2020. If relaxations are necessary, they should not be performed before the beginning this date and should be in small periods, no longer than 25 days. This paradigm would proceed roughly until January/2021. The second peak of infections, which has a forecast to the beginning of October, can be reduced if the periods of no-isolation days are shortened.
Reinforcement Learning (RL) has proven a stunning ability to learn optimal policies from data without any prior knowledge on the process. The main drawback of RL is that it is typically very difficult to guarantee stability and safety. On the other hand, Nonlinear Model Predictive Control (NMPC) is an advanced model-based control technique which does guarantee safety and stability, but only yields optimality for the nominal model. Therefore, it has been recently proposed to use NMPC as a function approximator within RL. While the ability of this approach to yield good performance has been demonstrated, the main drawback hindering its applicability is related to the computational burden of NMPC, which has to be solved to full convergence. In practice, however, computationally efficient algorithms such as the Real-Time Iteration (RTI) scheme are deployed in order to return an approximate NMPC solution in very short time. In this paper we bridge this gap by extending the existing theoretical framework to also cover RL based on RTI NMPC. We demonstrate the effectiveness of this new RL approach with a nontrivial example modeling a challenging nonlinear system subject to stochastic perturbations with the objective of optimizing an economic cost.
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop deterministic problem from the current state with progressively shorter horizons, similar to Model Predictive Control (MPC), results in a feedback policy that is $O(\epsilon^4)$ near to the true global stochastic optimal policy, where $\epsilon$ is a perturbation parameter modulating the noise. We also show that the optimal deterministic feedback problem has a perturbation structure such that higher-order terms of the feedback law do not affect lower-order terms and that this structure is lost in the optimal stochastic feedback problem. Consequently, solving the Stochastic Dynamic Programming problem is highly susceptible to noise, even in low dimensional problems, and in practice, the MPC-type feedback law offers superior performance even for high noise levels.
A dual adaptive model predictive control (MPC) algorithm is presented for linear, time-invariant systems subject to bounded disturbances and parametric uncertainty in the state-space matrices. Online set-membership identification is performed to reduce the uncertainty and thus control affects both the informativity of identification and the system's performance. The main contribution of the paper is to include this dual effect in the MPC optimization problem using a predicted worst-case cost in the objective function. This allows the controller to perform active exploration, that is, the control input reduces the uncertainty in the regions of the parameter space that have most influence on the performance. Additionally, the MPC algorithm ensures robust constraint satisfaction of state and input constraints. Advantages of the proposed algorithm are shown by comparing it to a passive adaptive MPC algorithm from the literature.