This study conducts a comparative analysis of Model Predictive Control (MPC) and Proximal Policy Optimization (PPO), a Deep Reinforcement Learning (DRL) algorithm, applied to a 1-Degree of Freedom (DOF) Quanser Aero 2 system. Classical control techniques such as MPC and Linear Quadratic Regulator (LQR) are widely used due to their theoretical foundation and practical effectiveness. However, with advancements in computational techniques and machine learning, DRL approaches like PPO have gained traction in solving optimal control problems through environment interaction. This paper systematically evaluates the dynamic response characteristics of PPO and MPC, comparing their performance, computational resource consumption, and implementation complexity. Experimental results show that while LQR achieves the best steady-state accuracy, PPO excels in rise-time and adaptability, making it a promising approach for applications requiring rapid response and adaptability. Additionally, we have established a baseline for future RL-related research on this specific testbed. We also discuss the strengths and limitations of each control strategy, providing recommendations for selecting appropriate controllers for real-world scenarios.
This study proposes a machine learning-based Model Predictive Control (MPC) approach for controlling Air Handling Unit (AHU) systems by employing an Internet of Things (IoT) framework. The proposed framework utilizes an Artificial Neural Network (ANN) to provide dynamic-linear thermal model parameters considering building information and disturbances in real time, thereby facilitating the practical MPC of the AHU system. The proposed framework allows users to establish new setpoints for a closed-loop control system, enabling customization of the thermal environment to meet individual needs with minimal use of the AHU. The experimental results demonstrate the cost benefits of the proposed machine-learning-based MPC-IoT framework, achieving a 57.59\% reduction in electricity consumption compared with a clock-based manual controller while maintaining a high level of user satisfaction. The proposed framework offers remarkable flexibility and effectiveness, even in legacy systems with limited building information, making it a pragmatic and valuable solution for enhancing the energy efficiency and user comfort in pre-existing structures.
We investigate nonlinear model predictive control (MPC) with terminal conditions in the Koopman framework using extended dynamic mode decomposition (EDMD) to generate a data-based surrogate model for prediction and optimization. We rigorously show recursive feasibility and prove practical asymptotic stability w.r.t. the approximation accuracy. To this end, finite-data error bounds are employed. The construction of the terminal conditions is based on recently derived proportional error bounds to ensure the required Lyapunov decrease. Finally, we illustrate the effectiveness of the proposed data-driven predictive controller including the design procedure to construct the terminal region and controller.
This paper presents Rummaging Using Mutual Information (RUMI), a method for online generation of robot action sequences to gather information about the pose of a known movable object in visually-occluded environments. Focusing on contact-rich rummaging, our approach leverages mutual information between the object pose distribution and robot trajectory for action planning. From an observed partial point cloud, RUMI deduces the compatible object pose distribution and approximates the mutual information of it with workspace occupancy in real time. Based on this, we develop an information gain cost function and a reachability cost function to keep the object within the robot's reach. These are integrated into a model predictive control (MPC) framework with a stochastic dynamics model, updating the pose distribution in a closed loop. Key contributions include a new belief framework for object pose estimation, an efficient information gain computation strategy, and a robust MPC-based control scheme. RUMI demonstrates superior performance in both simulated and real tasks compared to baseline methods.
The expansion in automation of increasingly fast applications and low-power edge devices poses a particular challenge for optimization based control algorithms, like model predictive control. Our proposed machine-learning supported approach addresses this by utilizing a feed-forward neural network to reduce the computation load of the online-optimization. We propose approximating part of the problem horizon, while maintaining safety guarantees -- constraint satisfaction -- via the remaining optimization part of the controller. The approach is validated in simulation, demonstrating an improvement in computational efficiency, while maintaining guarantees and near-optimal performance. The proposed MPC scheme can be applied to a wide range of applications, including those requiring a rapid control response, such as robotics and embedded applications with limited computational resources.
This paper proposes a Semi-Centralized Multi-Agent Reinforcement Learning (SCMARL) approach for irrigation scheduling in spatially variable agricultural fields, where management zones address spatial variability. The SCMARL framework is hierarchical in nature, with a centralized coordinator agent at the top level and decentralized local agents at the second level. The coordinator agent makes daily binary irrigation decisions based on field-wide conditions, which are communicated to the local agents. Local agents determine appropriate irrigation amounts for specific management zones using local conditions. The framework employs state augmentation approach to handle non-stationarity in the local agents' environments. An extensive evaluation on a large-scale field in Lethbridge, Canada, compares the SCMARL approach with a learning-based multi-agent model predictive control scheduling approach, highlighting its enhanced performance, resulting in water conservation and improved Irrigation Water Use Efficiency (IWUE). Notably, the proposed approach achieved a 4.0% savings in irrigation water while enhancing the IWUE by 6.3%.
Water treatment facilities are critical infrastructure they must accommodate dynamic demand patterns without system disruption. These patterns can be scheduled, such as daily residential irrigation, or unexpected, such as demand spikes from withdrawals for fire management. The critical necessity of clean, safe, and reliable water requires water treatment control strategies that are insensitive to disturbances to guarantee that demand will be met. One essential problem in achieving this is the minimization of energy costs in the process of meeting water demand, especially as the need for decarbonization persists. This work develops a control-oriented hydraulic model of a water treatment facility with integrated pumped storage and introduces a model predictive control strategy for scheduling treatment plant system operations to minimize greenhouse gas emissions and safely meet water demand.
This paper addresses the problem of controlling constrained systems subject to disturbances in the case where controller and system are connected over a lossy network. To do so, we propose a novel framework that splits the concept of tube-based model predictive control into two parts. One runs locally on the system and is responsible for disturbance rejection, while the other runs remotely and provides optimal input trajectories that satisfy the system's state and input constraints. Key to our approach is the presence of a nominal model and an ancillary controller on the local system. Theoretical guarantees regarding the recursive feasibility and the tracking capabilities in the presence of disturbances and packet losses in both directions are provided. To test the efficacy of the proposed approach, we compare it to a state-of-the-art solution in the case of controlling a cartpole system. Extensive simulations are carried out with both linearized and nonlinear system dynamics, as well as different packet loss probabilities and disturbances. The code for this work is available at https://github.com/EricssonResearch/Robust-Tracking-MPC-over-Lossy-Networks
Safety and efficiency are crucial for autonomous driving in roundabouts, especially in the context of mixed traffic where autonomous vehicles (AVs) and human-driven vehicles coexist. This paper introduces a learning-based algorithm tailored to foster safe and efficient driving behaviors across varying levels of traffic flows in roundabouts. The proposed algorithm employs a deep Q-learning network to effectively learn safe and efficient driving strategies in complex multi-vehicle roundabouts. Additionally, a KAN (Kolmogorov-Arnold network) enhances the AVs' ability to learn their surroundings robustly and precisely. An action inspector is integrated to replace dangerous actions to avoid collisions when the AV interacts with the environment, and a route planner is proposed to enhance the driving efficiency and safety of the AVs. Moreover, a model predictive control is adopted to ensure stability and precision of the driving actions. The results show that our proposed system consistently achieves safe and efficient driving whilst maintaining a stable training process, as evidenced by the smooth convergence of the reward function and the low variance in the training curves across various traffic flows. Compared to state-of-the-art benchmarks, the proposed algorithm achieves a lower number of collisions and reduced travel time to destination.
Recent advancements in machine learning based energy management approaches, specifically reinforcement learning with a safety layer (OptLayerPolicy) and a metaheuristic algorithm generating a decision tree control policy (TreeC), have shown promise. However, their effectiveness has only been demonstrated in computer simulations. This paper presents the real-world validation of these methods, comparing against model predictive control and simple rule-based control benchmark. The experiments were conducted on the electrical installation of 4 reproductions of residential houses, which all have their own battery, photovoltaic and dynamic load system emulating a non-controllable electrical load and a controllable electric vehicle charger. The results show that the simple rules, TreeC, and model predictive control-based methods achieved similar costs, with a difference of only 0.6%. The reinforcement learning based method, still in its training phase, obtained a cost 25.5\% higher to the other methods. Additional simulations show that the costs can be further reduced by using a more representative training dataset for TreeC and addressing errors in the model predictive control implementation caused by its reliance on accurate data from various sources. The OptLayerPolicy safety layer allows safe online training of a reinforcement learning agent in the real-world, given an accurate constraint function formulation. The proposed safety layer method remains error-prone, nonetheless, it is found beneficial for all investigated methods. The TreeC method, which does require building a realistic simulation for training, exhibits the safest operational performance, exceeding the grid limit by only 27.1 Wh compared to 593.9 Wh for reinforcement learning.
This paper presents the use of robust model predictive control for the design of an intent-aware collision avoidance system for multi-agent aircraft engaged in horizontal maneuvering scenarios. We assume that information from other agents is accessible in the form of waypoints or destinations. Consequently, we consider that other agents follow their optimal Dubin's path--a trajectory that connects their current state to their intended state--while accounting for potential uncertainties. We propose using scenario tree model predictive control as a robust approach that demonstrates computational efficiency. We demonstrate that the proposed method can easily integrate intent information and offer a robust scheme that handles different uncertainties. The method is illustrated through simulation results.
This paper addresses navigation in crowded environments by integrating goal-conditioned generative models with Sampling-based Model Predictive Control (SMPC). We introduce goal-conditioned autoregressive models to generate crowd behaviors, capturing intricate interactions among individuals. The model processes potential robot trajectory samples and predicts the reactions of surrounding individuals, enabling proactive robotic navigation in complex scenarios. Extensive experiments show that this algorithm enables real-time navigation, significantly reducing collision rates and path lengths, and outperforming selected baseline methods. The practical effectiveness of this algorithm is validated on an actual robotic platform, demonstrating its capability in dynamic settings.
Model predictive control (MPC) strategies allow residential water heaters to shift load in response to dynamic price signals. Crucially, the performance of such strategies is sensitive to various algorithm design choices. In this work, we develop a framework for implementing model predictive controls on residential water heaters for load shifting applications. We use this framework to analyze how four different design factors affect control performance and thermal comfort: (i) control model fidelity, (ii) temperature sensor configuration, (iii) water draw estimation methodology, and (iv) water draw forecasting methodology. We propose new methods for estimating water draw patterns without the use of a flow meter. MPC strategies are compared under two different time-varying price signals through simulations using a high-fidelity tank model and real-world draw data. Results show that control model fidelity and the number of temperature sensors have the largest impact on electricity costs, while the water draw forecasting methodology has a significant impact on thermal comfort and the frequency of runout events. Results provide practical insight into effective MPC design for water heaters in home energy management systems.
Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original state-space to a lifted state space. In this work, we propose an input-augmented Koopman modeling and model predictive control approach. Both the states and the known inputs are lifted using two deep neural networks (DNNs), and a Koopman model with nonlinearity in inputs is trained within the higher-dimensional state-space. A Koopman-based model predictive control problem is formulated. To bypass non-convex optimization induced by the nonlinearity in the Koopman model, we further present an iterative implementation algorithm, which approximates the optimal control input via solving a convex optimization problem iteratively. The proposed method is applied to a chemical process and a biological water treatment process via simulations. The efficacy and advantages of the proposed modeling and control approach are demonstrated.
Automated and autonomous driving has made a significant technological leap over the past decade. In this process, the complexity of algorithms used for vehicle control has grown significantly. Model Predictive Control (MPC) is a prominent example, which has gained enormous popularity and is now widely used for vehicle motion planning and control. However, safety concerns constrain its practical application, especially since traditional procedures of functional safety (FS), with its universal standard ISO26262, reach their limits. Concomitantly, the new aspect of safety-of-the-intended-function (SOTIF) has moved into the center of attention, whose standard, ISO21448, has only been released in 2022. Thus, experience with SOTIF is low and few case studies are available in industry and research. Hence this paper aims to make two main contributions: (1) an analysis of the SOTIF for a generic MPC-based trajectory planner and (2) an interpretation and concrete application of the generic procedures described in ISO21448 for determining functional insufficiencies (FIs) and triggering conditions (TCs). Particular novelties of the paper include an approach for the out-of-context development of SOTIF-related elements (SOTIF-EooC), a compilation of important FIs and TCs for a MPC-based trajectory planner, and an optimized safety concept based on the identified FIs and TCs for the MPC-based trajectory planner.
Imagining potential outcomes of actions before execution helps agents make more informed decisions, a prospective thinking ability fundamental to human cognition. However, mainstream model-free Reinforcement Learning (RL) methods lack the ability to proactively envision future scenarios, plan, and guide strategies. These methods typically rely on trial and error to adjust policy functions, aiming to maximize cumulative rewards or long-term value, even if such high-reward decisions place the environment in extremely dangerous states. To address this, we propose the Prospective (ProSpec) RL method, which makes higher-value, lower-risk optimal decisions by imagining future n-stream trajectories. Specifically, ProSpec employs a dynamic model to predict future states (termed "imagined states") based on the current state and a series of sampled actions. Furthermore, we integrate the concept of Model Predictive Control and introduce a cycle consistency constraint that allows the agent to evaluate and select the optimal actions from these trajectories. Moreover, ProSpec employs cycle consistency to mitigate two fundamental issues in RL: augmenting state reversibility to avoid irreversible events (low risk) and augmenting actions to generate numerous virtual trajectories, thereby improving data efficiency. We validated the effectiveness of our method on the DMControl benchmarks, where our approach achieved significant performance improvements. Code will be open-sourced upon acceptance.
This paper presents an estimation and control framework that enables the targeted reentry of a drag-modulated spacecraft in the presence of atmospheric density uncertainty. In particular, an extended Kalman filter (EKF) is used to estimate the in-flight density errors relative to the atmospheric density used to generate the nominal guidance trajectory. This information is leveraged within a model predictive control (MPC) strategy to improve tracking performance, reduce control effort, and increase robustness to actuator saturation compared to the state-of-the-art approach. The estimation and control framework is tested in a Monte Carlo simulation campaign with historical space weather data. These simulation efforts demonstrate that the proposed framework is able to stay within 100 km of the guidance trajectory at all points in time for 98.4% of cases. The remaining 1.6% of cases were pushed away from the guidance by large density errors, many due to significant solar storms and flares, that could not physically be compensated for by the drag control device. For the successful cases, the proposed framework was able to guide the spacecraft to the desired location at the entry interface altitude with a mean error of 12.1 km and 99.7% of cases below 100 km.
Inspired by the success of the Transformer architecture in natural language processing and computer vision, we investigate the use of Transformers in Reinforcement Learning (RL), specifically in modeling the environment's dynamics using Transformer Dynamics Models (TDMs). We evaluate the capabilities of TDMs for continuous control in real-time planning scenarios with Model Predictive Control (MPC). While Transformers excel in long-horizon prediction, their tokenization mechanism and autoregressive nature lead to costly planning over long horizons, especially as the environment's dimensionality increases. To alleviate this issue, we use a TDM for short-term planning, and learn an autoregressive discrete Q-function using a separate Q-Transformer (QT) model to estimate a long-term return beyond the short-horizon planning. Our proposed method, QT-TDM, integrates the robust predictive capabilities of Transformers as dynamics models with the efficacy of a model-free Q-Transformer to mitigate the computational burden associated with real-time planning. Experiments in diverse state-based continuous control tasks show that QT-TDM is superior in performance and sample efficiency compared to existing Transformer-based RL models while achieving fast and computationally efficient inference.
Reconfigurable Intelligent Surface (RIS) technology has gained significant attention due to its ability to enhance the performance of wireless communication systems. The main advantage of RIS is that it can be strategically placed in the environment to control wireless signals, enabling improvements in coverage, capacity, and energy efficiency. In this paper, we investigate a scenario in which a drone, equipped with a RIS, travels from an initial point to a target destination. In this scenario, the aerial RIS (ARIS) is deployed to establish a direct link between the base station and obstructed users. Our objective is to maximize the energy efficiency of the ARIS while taking into account its dynamic model including its velocity and acceleration along with the phase shift of the RIS. To this end, we formulate the energy efficiency problem under the constraints of the dynamic model of the drone. The studied problem is challenging to solve. To address this, we proceed as follows. First, we introduce an efficient solution that involves decoupling the phase shift optimization and the trajectory design. Specifically, the closed-form expression of the phase-shift is obtained using a convex approximation, which is subsequently integrated into the trajectory design problem. We then employ tools inspired by economic model predictive control (EMPC) to solve the resulting trajectory optimization. Our simulation results show a significant improvement in energy efficiency against the scenario where the dynamic model of the UAV is ignored.
Shaping thermoplastic sheets into three-dimensional products is challenging since overheating results in failed manufactured parts and wasted material. To this end, we propose an indirect data-driven predictive control approach using Model Predictive Control (MPC) capable of handling temperature constraints and heating-power saturation while delivering enhanced precision, overshoot control, and settling times compared to state-of-the-art methods. We employ a Non-linear Auto-Regressive with Exogenous inputs (NARX) model to define a linear control-oriented model at each operating point. Using a high-fidelity simulator, several simulation studies have been conducted to evaluate the proposed method's robustness and performance under parametric uncertainty, indicating overshoot and average steady-state error less than $2^\circ \mathrm{C}$ and $0.7^\circ \mathrm{C}$ ($7^\circ \mathrm{C}$ and $2^\circ \mathrm{C}$) for the nominal (worst-case) scenario. Finally, we applied the proposed method to a lab-scale thermoforming platform, resulting in a close response to the simulation analysis with overshoot and average steady-state error metrics less than $5.3^\circ \mathrm{C}$ and $1^\circ \mathrm{C}$, respectively.