We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can provide guarantees for a large class of distributions, including time-varying distributions. Specifically, we first provide a new characterization of sub-Gaussian random vectors using matrix variance proxies, which can more accurately represent the predicted state distribution. We then derive tail bounds under linear propagation for the new characterization, enabling tractable computation of probabilistic reachable sets of linear systems. Lastly, we utilize these probabilistic reachable sets to formulate a stochastic MPC scheme that provides closed-loop guarantees for general sub-Gaussian noise. We further demonstrate our approach in simulations, including a challenging task of surgical planning from image observations.
Signal Temporal Logic (STL) robustness is a common objective for optimal robot control, but its dependence on history limits the robot's decision-making capabilities when used in Model Predictive Control (MPC) approaches. In this work, we introduce Signal Temporal Logic robustness-to-go (Ro-To-Go), a new quantitative semantics for the logic that isolates the contributions of suffix trajectories. We prove its relationship to formula progression for Metric Temporal Logic, and show that the robustness-to-go depends only on the suffix trajectory and progressed formula. We implement robustness-to-go as the objective in an MPC algorithm and use formula progression to efficiently evaluate it online. We test the algorithm in simulation and compare it to MPC using traditional STL robustness. Our experiments show that using robustness-to-go results in a higher success rate.
The increase in renewable energy sources (RES) has reduced power system inertia, making frequency stabilization more challenging and highlighting the need for fast frequency response (FFR) resources. While building energy management systems (BEMS) equipped with distributed energy resources (DERs) can provide FFR, individual BEMS alone cannot fully meet demand. To address this, we propose a community energy management system (CEMS) operational model that minimizes energy costs and generates additional revenue, which is provided FFR through coordinated DERs and building loads under photovoltaic (PV) generation uncertainty. The model incorporates a hierarchical control framework with three levels: Level 1 allocates maximum FFR capacity, Level 2 employs scenario-based stochastic model predictive control (SMPC) to adjust DER operations and ensure FFR provision despite PV uncertainties, and Level 3 performs rapid load adjustments in response to frequency fluctuations detected by a frequency meter. Simulation results on a campus building cluster demonstrate the effectiveness of the proposed model, achieving a 10\% reduction in energy costs and a 24\% increase in FFR capacity, all while maintaining occupant comfort and enhancing frequency stabilization.
A large body of simulation research suggests that model predictive control (MPC) and reinforcement learning (RL) for heating, ventilation, and air-conditioning (HVAC) in residential and commercial buildings could reduce energy costs, pollutant emissions, and strain on power grids. Despite this potential, neither MPC nor RL has seen widespread industry adoption. Field demonstrations could accelerate MPC and RL adoption by providing real-world data that support the business case for deployment. Here we review 24 papers that document field demonstrations of MPC and RL in residential buildings and 80 in commercial buildings. After presenting demographic information -- such as experiment scopes, locations, and durations -- this paper analyzes experiment protocols and their influence on performance estimates. We find that 71% of the reviewed field demonstrations use experiment protocols that may lead to unreliable performance estimates. Over the remaining 29% that we view as reliable, the weighted-average cost savings, weighted by experiment duration, are 16% in residential buildings and 13% in commercial buildings. While these savings are potentially attractive, making the business case for MPC and RL also requires characterizing the costs of deployment, operation, and maintenance. Only 13 of the 104 reviewed papers report these costs or discuss related challenges. Based on these observations, we recommend directions for future field research, including: Improving experiment protocols; reporting deployment, operation, and maintenance costs; designing algorithms and instrumentation to reduce these costs; controlling HVAC equipment alongside other distributed energy resources; and pursuing emerging objectives such as peak shaving, arbitraging wholesale energy prices, and providing power grid reliability services.
Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. In this paper, we develop a formulation for multistage economic MPC which directly minimizes an economic objective function. The multistage economic MPC framework is extended for systems with a cyclic steady state (CSS) and stability is guaranteed by employing a Lyapunov-based stability constraint. The multistage economic MPC framework is validated on two natural gas network case studies to minimize the net energy consumption during gas transmission. In both instances, the multistage economic MPC effectively manages uncertain demands by preventing constraint violations and guides the network to its optimal cyclic operating conditions. The Lyapunov function remains bounded in both instances, validating the robust stability of the controller.
This paper addresses the challenge of amplitude-unbounded false data injection (FDI) attacks targeting the sensor-to-controller (S-C) channel in cyber-physical systems (CPSs). We introduce a resilient tube-based model predictive control (MPC) scheme. This scheme incorporates a threshold-based attack detector and a control sequence buffer to enhance system security. We mathematically model the common FDI attacks and derive the maximum duration of such attacks based on the hypothesis testing principle. Following this, the minimum feasible sequence length of the control sequence buffer is obtained. The system is proven to remain input-to-state stable (ISS) under bounded external disturbances and amplitude-unbounded FDI attacks. Moreover, the feasible region under this scenario is provided in this paper. Finally, the proposed algorithm is validated by numerical simulations and shows superior control performance compared to the existing methods.
The paper proposes a novel Economic Model Predictive Control (EMPC) scheme for Autonomous Surface Vehicles (ASVs) to simultaneously address path following accuracy and energy constraints under environmental disturbances. By formulating lateral deviations as energy-equivalent penalties in the cost function, our method enables explicit trade-offs between tracking precision and energy consumption. Furthermore, a motion-dependent decomposition technique is proposed to estimate terminal energy costs based on vehicle dynamics. Compared with the existing EMPC method, simulations with real-world ocean disturbance data demonstrate the controller's energy consumption with a 0.06 energy increase while reducing cross-track errors by up to 18.61. Field experiments conducted on an ASV equipped with an Intel N100 CPU in natural lake environments validate practical feasibility, achieving 0.22 m average cross-track error at nearly 1 m/s and 10 Hz control frequency. The proposed scheme provides a computationally tractable solution for ASVs operating under resource constraints.
This study proposes a coordinated ramp metering control framework in large networks based on scalable nonlinear traffic dynamics model discovery. Existing coordinated ramp metering control methods often require accurate traffic dynamics models in real time, however, for large-scale highway networks, since these models are always nonlinear, they are extremely challenging to obtain. To overcome this limitation, this study utilizes the Sparse Identification of Nonlinear Dynamics with Control (SINDYc) to derive the accurate nonlinear traffic dynamics model from observed data. The discovered dynamics model is then integrated into a Model Predictive Control (MPC) coordinated ramp metering controller, enabling optimized control actions that enhance traffic flow and efficiency. The proposed framework is tested on a large-scale highway network that includes three intersecting highways and eight on-ramps, which outperforms the existing approaches, demonstrating its effectiveness and potential for real-time application. This framework can offer a scalable and robust solution for improving real-time traffic management in complex urban environments.
Quadrupedal robots exhibit remarkable adaptability in unstructured environments, making them well-suited for formation control in real-world applications. However, keeping stable formations while ensuring collision-free navigation presents significant challenges due to dynamic obstacles, communication constraints, and the complexity of legged locomotion. This paper proposes a distributed model predictive control framework for multi-quadruped formation control, integrating Control Lyapunov Functions to ensure formation stability and Control Barrier Functions for decentralized safety enforcement. To address the challenge of dynamically changing team structures, we introduce Scale-Adaptive Permutation-Invariant Encoding (SAPIE), which enables robust feature encoding of neighboring robots while preserving permutation invariance. Additionally, we develop a low-latency Data Distribution Service-based communication protocol and an event-triggered deadlock resolution mechanism to enhance real-time coordination and prevent motion stagnation in constrained spaces. Our framework is validated through high-fidelity simulations in NVIDIA Omniverse Isaac Sim and real-world experiments using our custom quadrupedal robotic system, XG. Results demonstrate stable formation control, real-time feasibility, and effective collision avoidance, validating its potential for large-scale deployment.
A key challenge in tuning Model Predictive Control (MPC) cost function parameters is to ensure that the system performance stays consistently above a certain threshold. To address this challenge, we propose a novel method, COAT-MPC, Constrained Optimal Auto-Tuner for MPC. With every tuning iteration, COAT-MPC gathers performance data and learns by updating its posterior belief. It explores the tuning parameters' domain towards optimistic parameters in a goal-directed fashion, which is key to its sample efficiency. We theoretically analyze COAT-MPC, showing that it satisfies performance constraints with arbitrarily high probability at all times and provably converges to the optimum performance within finite time. Through comprehensive simulations and comparative analyses with a hardware platform, we demonstrate the effectiveness of COAT-MPC in comparison to classical Bayesian Optimization (BO) and other state-of-the-art methods. When applied to autonomous racing, our approach outperforms baselines in terms of constraint violations and cumulative regret over time.
In this paper, we present a novel model to characterize individual tendencies in repeated decision-making scenarios, with the goal of designing model-based control strategies that promote virtuous choices amidst social and external influences. Our approach builds on the classical Friedkin and Johnsen model of social influence, extending it to include random factors (e.g., inherent variability in individual needs) and controllable external inputs. We explicitly account for the temporal separation between two processes that shape opinion dynamics: individual decision-making and social imitation. While individual decisions occur at regular, frequent intervals, the influence of social imitation unfolds over longer periods. The inclusion of random factors naturally leads to dynamics that do not converge in the classical sense. However, under specific conditions, we prove that opinions exhibit ergodic behavior. Building on this result, we propose a constrained asymptotic optimal control problem designed to foster, on average, social acceptance of a target action within a network. To address the transient dynamics of opinions, we reformulate this problem within a Model Predictive Control (MPC) framework. Simulations highlight the significance of accounting for these transient effects in steering individuals toward virtuous choices while managing policy costs.
For quadrotors, achieving safe and autonomous flight in complex environments with wind disturbances and dynamic obstacles still faces significant challenges. Most existing methods address wind disturbances in either trajectory planning or control, which may lead to hazardous situations during flight. The emergence of dynamic obstacles would further worsen the situation. Therefore, we propose an efficient and reliable framework for quadrotors that incorporates wind disturbance estimations during both the planning and control phases via a generalized proportional integral observer. First, we develop a real-time adaptive spatial-temporal trajectory planner that utilizes Hamilton-Jacobi (HJ) reachability analysis for error dynamics resulting from wind disturbances. By considering the forward reachability sets propagation on an Euclidean Signed Distance Field (ESDF) map, safety is guaranteed. Additionally, a Nonlinear Model Predictive Control (NMPC) controller considering wind disturbance compensation is implemented for robust trajectory tracking. Simulation and real-world experiments verify the effectiveness of our framework. The video and supplementary material will be available at https://github.com/Ma29-HIT/SEAL/.
The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.
Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell's power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.
Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding to reduce the open-loop trajectory dimensionality by over 95%, and integrating it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, we enable intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization NMPC, demonstrates the methodology's practical effectiveness in real-world applications.
In reinforcement learning (RL), world models serve as internal simulators, enabling agents to predict environment dynamics and future outcomes in order to make informed decisions. While previous approaches leveraging discrete latent spaces, such as DreamerV3, have demonstrated strong performance in discrete action settings and visual control tasks, their comparative performance in state-based continuous control remains underexplored. In contrast, methods with continuous latent spaces, such as TD-MPC2, have shown notable success in state-based continuous control benchmarks. In this paper, we demonstrate that modeling discrete latent states has benefits over continuous latent states and that discrete codebook encodings are more effective representations for continuous control, compared to alternative encodings, such as one-hot and label-based encodings. Based on these insights, we introduce DCWM: Discrete Codebook World Model, a self-supervised world model with a discrete and stochastic latent space, where latent states are codes from a codebook. We combine DCWM with decision-time planning to get our model-based RL algorithm, named DC-MPC: Discrete Codebook Model Predictive Control, which performs competitively against recent state-of-the-art algorithms, including TD-MPC2 and DreamerV3, on continuous control benchmarks. See our project website www.aidanscannell.com/dcmpc.
Partitioning is a fundamental challenge for non-centralized control of large-scale systems, such as hierarchical, decentralized, distributed, and coalitional strategies. The problem consists of finding a decomposition of a network of dynamical systems into system units for which local controllers can be designed. Unfortunately, despite its critical role, a generalized approach to partitioning applicable to every system is still missing from the literature. This paper introduces a novel partitioning framework that integrates an algorithmic selection of fundamental system units (FSUs), considered indivisible entities, with an aggregative procedure, either algorithmic or optimization-based, to select composite system units (CSUs) made of several FSUs. A key contribution is the introduction of a global network metric, the partition index, which quantitatively balances intra- and inter-CSU interactions, with a granularity parameter accounting for the size of CSUs, allowing for their selection at different levels of aggregation. The proposed method is validated through case studies in distributed model predictive control (DMPC) for linear and hybrid systems, showing significant reductions in computation time and cost while maintaining or improving control performance w.r.t. conventional strategies.
Inspired by the recent successes of Inverse Optimization (IO) across various application domains, we propose a novel offline Reinforcement Learning (ORL) algorithm for continuous state and action spaces, leveraging the convex loss function called ``sub-optimality loss" from the IO literature. To mitigate the distribution shift commonly observed in ORL problems, we further employ a robust and non-causal Model Predictive Control (MPC) expert steering a nominal model of the dynamics using in-hindsight information stemming from the model mismatch. Unlike the existing literature, our robust MPC expert enjoys an exact and tractable convex reformulation. In the second part of this study, we show that the IO hypothesis class, trained by the proposed convex loss function, enjoys ample expressiveness and achieves competitive performance comparing with the state-of-the-art (SOTA) methods in the low-data regime of the MuJoCo benchmark while utilizing three orders of magnitude fewer parameters, thereby requiring significantly fewer computational resources. To facilitate the reproducibility of our results, we provide an open-source package implementing the proposed algorithms and the experiments.
The use of autonomous underwater vehicles (AUVs) for surveying, mapping, and inspecting unexplored underwater areas plays a crucial role, where maneuverability and power efficiency are key factors for extending the use of these platforms, making six degrees of freedom (6-DOF) holonomic platforms essential tools. Although Proportional-Integral-Derivative (PID) and Model Predictive Control controllers are widely used in these applications, they often require accurate system knowledge, struggle with repeatability when facing payload or configuration changes, and can be time-consuming to fine-tune. While more advanced methods based on Deep Reinforcement Learning (DRL) have been proposed, they are typically limited to operating in fewer degrees of freedom. This paper proposes a novel DRL-based approach for controlling holonomic 6-DOF AUVs using the Truncated Quantile Critics (TQC) algorithm, which does not require manual tuning and directly feeds commands to the thrusters without prior knowledge of their configuration. Furthermore, it incorporates power consumption directly into the reward function. Simulation results show that the TQC High-Performance method achieves better performance to a fine-tuned PID controller when reaching a goal point, while the TQC Energy-Aware method demonstrates slightly lower performance but consumes 30% less power on average.
In tropical countries with high humidity, air conditioning can account for up to 60% of a building's energy use. For commercial buildings with centralized systems, the efficiency of the chiller plant is vital, and model predictive control provides an effective strategy for optimizing operations through dynamic adjustments based on accurate load predictions. Artificial neural networks are effective for modelling nonlinear systems but are prone to overfitting due to their complexity. Effective feature engineering can mitigate this issue. While weather data are crucial for load prediction, they are often used as raw numerical inputs without advanced processing. Clustering features is a technique that can reduce model complexity and enhance prediction accuracy. Although previous studies have explored clustering algorithms for load prediction, none have applied them to multidimensional weather data, revealing a research gap. This study presents a cooling load prediction model that combines a neural network with Kalman filtering and K-means clustering. Applied to real world data from a commercial skyscraper in Singapore's central business district, the model achieved a 46.5% improvement in prediction accuracy. An optimal chiller sequencing strategy was also developed through genetic algorithm optimization of the predictive load, potentially saving 13.8% in energy. Finally, the study evaluated the integration of thermal energy storage into the chiller plant design, demonstrating potential reductions in capital and operational costs of 26% and 13%, respectively.