We consider the problem of reasoning about networked and layered control systems using assume-guarantee specifications. As these systems are formed by the interconnection of components that operate under various clocks, we introduce a new logic, Multiclock Logic (MCL), to be able to express the requirements of components form the point of view of their local clocks. Specifying components locally promotes independent design and component reuse. We carry out a contract-based analysis of a control system implemented via two control algorithms (model predictive control and feedback linearization) running on their own processors and clocks. Then we implement each of the contracts to build a system. The system performs as desired when the requirements derived from our system-level analysis are respected. Violating the constraints required by the contract-based analysis of the system leads to error.
Data is required to develop forecasting models for use in Model Predictive Control (MPC) schemes in building energy systems. However, data is costly to both collect and exploit. Determining cost optimal data usage strategies requires understanding of the forecast accuracy and resulting MPC operational performance it enables. This study investigates the performance of both simple and state-of-the-art machine learning prediction models for MPC in multi-building energy systems using a simulated case study with historic building energy data. The impact on forecast accuracy of measures to improve model data efficiency are quantified, specifically for: reuse of prediction models, reduction of training data duration, reduction of model data features, and online model training. A simple linear multi-layer perceptron model is shown to provide equivalent forecast accuracy to state-of-the-art models, with greater data efficiency and generalisability. The use of more than 2 years of training data for load prediction models provided no significant improvement in forecast accuracy. Forecast accuracy and data efficiency were improved simultaneously by using change-point analysis to screen training data. Reused models and those trained with 3 months of data had on average 10% higher error than baseline, indicating that deploying MPC systems without prior data collection may be economic.
This paper introduces an Electric Vehicle Charging Station (EVCS) model that incorporates real-world constraints, such as slot power limitations, contract threshold overruns penalties, or early disconnections of electric vehicles (EVs). We propose a formulation of the problem of EVCS control under uncertainty, and implement two Multi-Stage Stochastic Programming approaches that leverage user-provided information, namely, Model Predictive Control and Two-Stage Stochastic Programming. The model addresses uncertainties in charging session start and end times, as well as in energy demand. A user's behavior model based on a sojourn-time-dependent stochastic process enhances cost reduction while maintaining customer satisfaction. The benefits of the two proposed methods are showcased against two baselines over a 22-day simulation using a real-world dataset. The two-stage approach demonstrates robustness against early disconnections by considering a wider range of uncertainty scenarios for optimization. The algorithm prioritizing user satisfaction over electricity cost achieves a 20% and 36% improvement in two user satisfaction metrics compared to an industry-standard baseline. Additionally, the algorithm striking the best balance between cost and user satisfaction exhibits a mere 3% relative cost increase compared to the theoretically optimal baseline - for which the nonanticipativity constraint is relaxed - while attaining 94% and 84% of the user satisfaction performance in the two used satisfaction metrics.
Handling uncertainty in model predictive control comes with various challenges, especially when considering state constraints under uncertainty. Most methods focus on either the conservative approach of robustly accounting for uncertainty or allowing a small probability of constraint violation. In this work, we propose a linear model predictive control approach that minimizes the probability that linear state constraints are violated in the presence of additive uncertainty. This is achieved by first determining a set of inputs that minimize the probability of constraint violation. Then, this resulting set is used to define admissible inputs for the optimal control problem. Recursive feasibility is guaranteed and input-to-state stability is proved under assumptions. Numerical results illustrate the benefits of the proposed model predictive control approach.
Model Predictive Control (MPC) for tracking formulation presents numerous advantages compared to standard MPC, such as a larger domain of attraction and recursive feasibility even when abrupt changes in the reference are produced. As a drawback, it includes some extra decision variables in its related optimization problem, leading to a semi-banded structure that differs from the banded structure encountered in standard MPC. This semi-banded structure prevents the direct use of the efficient algorithms available for banded problems. To address this issue, we present an algorithm based on the alternating direction method of multipliers that explicitly takes advantage of the underlying semi-banded structure of the MPC for tracking.
The potential of Machine Learning Control (MLC) in HVAC systems is hindered by its opaque nature and inference mechanisms, which is challenging for users and modelers to fully comprehend, ultimately leading to a lack of trust in MLC-based decision-making. To address this challenge, this paper investigates and explores Interpretable Machine Learning (IML), a branch of Machine Learning (ML) that enhances transparency and understanding of models and their inferences, to improve the credibility of MLC and its industrial application in HVAC systems. Specifically, we developed an innovative framework that combines the principles of Shapley values and the in-context learning feature of Large Language Models (LLMs). While the Shapley values are instrumental in dissecting the contributions of various features in ML models, LLM provides an in-depth understanding of the non-data-driven or rule-based elements in MLC; combining them, LLM further packages these insights into a coherent, human-understandable narrative. The paper presents a case study to demonstrate the feasibility of the developed IML framework for model predictive control-based precooling under demand response events in a virtual testbed. The results indicate that the developed framework generates and explains the control signals in accordance with the rule-based rationale.
Autonomous vehicle platoons present near- and long-term opportunities to enhance operational efficiencies and save lives. The past 30 years have seen rapid development in the autonomous driving space, enabling new technologies that will alleviate the strain placed on human drivers and reduce vehicle emissions. This paper introduces a testbed for evaluating and benchmarking platooning algorithms on 1/10th scale vehicles with onboard sensors. To demonstrate the testbed's utility, we evaluate three algorithms, linear feedback and two variations of distributed model predictive control, and compare their results on a typical platooning scenario where the lead vehicle tracks a reference trajectory that changes speed multiple times. We validate our algorithms in simulation to analyze the performance as the platoon size increases, and find that the distributed model predictive control algorithms outperform linear feedback on hardware and in simulation.
Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. We improve the efficiency of this general framework by proposing an algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC leverages three key techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.
Temperature control is a complex task due to its often unknown dynamics and disturbances. This paper explores the use of Neural Nonlinear AutoRegressive eXogenous (NNARX) models for nonlinear system identification and model predictive control of a temperature control unit. First, the NNARX model is identified from input-output data collected from the real plant, and a state-space representation with known measurable states consisting of past input and output variables is formulated. Second, a tailored model predictive controller is designed based on the trained NNARX network. The proposed control architecture is experimentally tested on the temperature control units manufactured by Tool-Temp AG. The results achieved are compared with those obtained using a PI controller and a linear MPC. The findings illustrate that the proposed scheme achieves satisfactory tracking performance while incurring the lowest energy cost among the compared controllers.
This paper addresses the particularities of adaptive optimal control of the uranium extraction-scrubbing operation in the PUREX process. The process dynamics are nonlinear, high dimensional, and have limited online measurements. In addition, analysis and developments are based on a qualified simulation program called PAREX, which was validated with laboratory and industrial data. The control objective is to stabilize the process at a desired solvent saturation level, guaranteeing constraints and handling disturbances. The developed control strategy relies on optimization-based methods for computing control inputs and estimates, i.e., Nonlinear Model Predictive Control (NMPC) and Nonlinear Moving Horizon Estimation (NMHE). The designs of these two associated algorithms are tailored for this process's particular dynamics and are implemented through an enhanced Particle Swarm Optimization (PSO) to guarantee constraint satisfaction. Software-in-the-loop simulations using PAREX show that the designed control scheme effectively satisfies control objectives and guarantees constraints during operation.
This work proposes a nonlinear model predictive control-based guidance strategy for unmanned surface vehicles, focused on path following. The application of this strategy, in addition to overcome drawbacks of previous line-of-sight-based guidance laws, intends to enable the application of predictive strategies also to the low-level control, responsible for tracking the references provided by the guidance strategy. The stability and robustness of the proposed strategy are theoretically discussed. Furthermore, given the non-negligible computational cost of such nonlinear predictive guidance strategy, a practical nonlinear model predictive control strategy is also applied in order to reduce the computational cost to a great extent. The effectiveness and advantages of both proposed strategies over other nonlinear guidance laws are illustrated through a complete set of simulations.
Reinforcement learning algorithms need exploration to learn. However, unsupervised exploration prevents the deployment of such algorithms on safety-critical tasks and limits real-world deployment. In this paper, we propose a new algorithm called Ensemble Model Predictive Safety Certification that combines model-based deep reinforcement learning with tube-based model predictive control to correct the actions taken by a learning agent, keeping safety constraint violations at a minimum through planning. Our approach aims to reduce the amount of prior knowledge about the actual system by requiring only offline data generated by a safe controller. Our results show that we can achieve significantly fewer constraint violations than comparable reinforcement learning methods.
Autonomous vehicles are rapidly evolving and will soon enable the application of large-scale mobility-on-demand (MoD) systems. Managing the fleets of available vehicles, commonly known as "rebalancing," is crucial to ensure that vehicles are distributed properly to meet customer demands. This paper presents an optimal control approach to optimize vehicle scheduling and rebalancing in an autonomous mobility-on-demand (AMoD) system. We use graph theory to model a city partitioned into virtual zones. Zones represent small areas of the city where vehicles can stop and pick up/drop off customers, whereas links denote corridors of the city along which autonomous vehicles can move. They are considered vertices and edges in the graph. Vehicles employed in the AMoD scheme are autonomous, and rebalancing can be executed by dispatching available empty vehicles to areas undersupplied. Rebalancing is performed on the graph's vertices, i.e., between city areas. We propose a linear, discrete-time model of an AMoD system using a transformed network. After acquiring the model, the desired number of rebalancing vehicles for the AMoD model is derived through an optimization problem. Moreover, the well-posedness of the model is illustrated. To leverage the proposed model, we implemented the model predictive control (MPC) framework to find the optimal rebalancing and scheduling policy. We show the MPC's effectiveness and how the MPC framework can be implemented in real-time for a real-world case study. The numerical results show that the MPC with a linear cost function and linear reference, which it tracks, is effective, outperforming other MPC-based and state-of-the-art algorithms across all evaluation criteria.
This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.
Determining the optimal cost function parameters of Model Predictive Control (MPC) to optimize multiple control objectives is a challenging and time-consuming task. Multiobjective Bayesian Optimization (BO) techniques solve this problem by determining a Pareto optimal parameter set for an MPC with static weights. However, a single parameter set may not deliver the most optimal closed-loop control performance when the context of the MPC operating conditions changes during its operation, urging the need to adapt the cost function weights at runtime. Deep Reinforcement Learning (RL) algorithms can automatically learn context-dependent optimal parameter sets and dynamically adapt for a Weightsvarying MPC (WMPC). However, learning cost function weights from scratch in a continuous action space may lead to unsafe operating states. To solve this, we propose a novel approach limiting the RL actions within a safe learning space representing a catalog of pre-optimized BO Pareto-optimal weight sets. We conceive a RL agent not to learn in a continuous space but to proactively anticipate upcoming control tasks and to choose the most optimal discrete actions, each corresponding to a single set of Pareto optimal weights, context-dependent. Hence, even an untrained RL agent guarantees a safe and optimal performance. Experimental results demonstrate that an untrained RL-WMPC shows Pareto-optimal closed-loop behavior and training the RL-WMPC helps exhibit a performance beyond the Pareto-front.
This paper addresses the eco-driving problem for connected vehicles on urban roads, considering localization uncertainty. Eco-driving is defined as longitudinal speed planning and control on roads with the presence of a sequence of traffic lights. We solve the problem by using a data-driven model predictive control (MPC) strategy. This approach involves learning a cost-to-go function and constraints from state-input data. The cost-to-go function represents the remaining energy-to-spend from the given state, and the constraints ensure that the controlled vehicle passes the upcoming traffic light timely while obeying traffic laws. The resulting convex optimization problem has a short horizon and is amenable for real-time implementations. We demonstrate the effectiveness of our approach through real-world vehicle experiments. Our method demonstrates $12\%$ improvement in energy efficiency compared to the traditional approaches, which plan longitudinal speed by solving a long-horizon optimal control problem and track the planned speed using another controller, as evidenced by vehicle experiments.
We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet
Model predictive control (MPC) has been used successfully in diverse applications. As its name suggests, MPC requires a model for predictive optimization. The present paper focuses on the application of MPC to a Rijke tube, in which a heating source and acoustic dynamics interact to produce self-excited oscillations. Since the dynamics of a Rijke tube are difficult to model to a high level of accuracy, the implementation of MPC requires leveraging data from the physical setup as well as knowledge about thermoacoustics, which is labor intensive and requires domain expertise. With this motivation, the present paper uses predictive cost adaptive control (PCAC) for sampled-data control of an experimental Rijke-tube setup. PCAC performs online closed-loop linear model identification for receding-horizon optimization based on the backward propagating Riccati equation. In place of analytical modeling, open-loop experiments are used to create a simple emulation model, which is used for choosing PCAC hyperparameters. PCAC is applied to the Rijke-tube setup under various experimental scenarios.
In automated driving, predicting and accommodating the uncertain future motion of other traffic participants is challenging, especially in unstructured environments in which the high-level intention of traffic participants is difficult to predict. Several possible uncertain future behaviors of traffic participants must be considered, resulting in multi-modal uncertainty. We propose a novel combination of Belief Function Theory and Stochastic Model Predictive Control for trajectory planning of the autonomous vehicle in presence of significant uncertainty about the intention estimation of traffic participants. A misjudgment of the intention of traffic participants may result in dangerous situations. At the same time, excessive conservatism must be avoided. Therefore, the measure of reliability of the estimation provided by Belief Function Theory is used in the design of collision-avoidance safety constraints, in particular to increase safety when the intention of traffic participants is not clear. We discuss two methods to leverage on Belief Function Theory: we introduce a novel belief-to-probability transformation designed not to underestimate unlikely events if the information is uncertain, and a constraint tightening mechanism using the reliability of the estimation. We evaluate our proposal through simulations comparing to state-of-the-art approaches.
Autopilots for fixed-wing aircraft are typically designed based on linearized aerodynamic models consisting of stability and control derivatives obtained from wind-tunnel testing. The resulting local controllers are then pieced together using gain scheduling. For applications in which the aerodynamics are unmodeled, the present paper proposes an autopilot based on predictive cost adaptive control (PCAC). As an indirect adaptive control extension of model predictive control, PCAC uses recursive least squares (RLS) with variable-rate forgetting for online, closed-loop system identification. At each time step, RLS-based system identification updates the coefficients of an input-output model whose order is a hyperparameter specified by the user. For MPC, the receding-horizon optimization can be performed by either the backward-propagating Riccati equation or quadratic programming. The present paper investigates the performance of PCAC for fixed-wing aircraft without the use of any aerodynamic modeling or offline/prior data collection.