Model Predictive Control (MPC) is a powerful control strategy widely utilized in domains like energy management, building control, and autonomous systems. However, its effectiveness in real-world settings is challenged by the need to incorporate context-specific predictions and expert instructions, which traditional MPC often neglects. We propose InstructMPC, a novel framework that addresses this gap by integrating real-time human instructions through a Large Language Model (LLM) to produce context-aware predictions for MPC. Our method employs a Language-to-Distribution (L2D) module to translate contextual information into predictive disturbance trajectories, which are then incorporated into the MPC optimization. Unlike existing context-aware and language-based MPC models, InstructMPC enables dynamic human-LLM interaction and fine-tunes the L2D module in a closed loop with theoretical performance guarantees, achieving a regret bound of $O(\sqrt{T\log T})$ for linear dynamics when optimized via advanced fine-tuning methods such as Direct Preference Optimization (DPO) using a tailored loss function.
We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example.
Persistence of excitation (PE) of the system input is a fundamental requirement for the successful operation of data-driven model predictive control, as it ensures that the input--output data contains sufficient information about the underlying system dynamics. Nonetheless, this property is usually assumed rather than guaranteed. This paper introduces a novel data-driven predictive control formulation that maintains persistence of excitation. The technical development that permits this is the characterization of the nonexciting input set i.e. the set of inputs that lead to loss of PE, and the consequent derivation of a pair of disjoint, linear inequality constraints on the input that, if satisfied, maintain PE. When used in the predictive control formulation, these constraints lead to a mixed-integer optimal control problem with a single binary variable or, equivalently, a pair of disjoint quadratic programming problems that can be efficiently and reliably solved in parallel. Numerical examples show how these constraints are able to maintain persistence of excitation on the input during the controller's operation.
We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the applicability of flatness-based planning and control methods. To address this, we propose a framework for learning flatness-preserving residual dynamics in systems whose nominal model admits a pure-feedback form. We show that residuals with a lower-triangular structure preserve both the flatness of the system and the original flat outputs. Moreover, we provide a constructive procedure to recover the flatness diffeomorphism of the augmented system from that of the nominal model. We then introduce a learning algorithm that fits such residuals from trajectory data using smooth function approximators. Our approach is validated in simulation on a 2D quadrotor subject to unmodeled aerodynamic effects. We demonstrate that the resulting learned flat model enables tracking performance comparable to nonlinear model predictive control ($5\times$ lower tracking error than the nominal flat model) while also achieving over a $20\times$ speedup in computation.
Noise pollution from heat pumps (HPs) has been an emerging concern to their broader adoption, especially in densely populated areas. This paper explores a model predictive control (MPC) approach for building climate control, aimed at minimizing the noise nuisance generated by HPs. By exploiting a piecewise linear approximation of HP noise patterns and assuming linear building thermal dynamics, the proposed design can be generalized to handle various HP acoustic patterns with mixed-integer linear programming (MILP). Additionally, two computationally efficient options for defining the noise cost function in the proposed MPC design are discussed. Numerical experiments on a high-fidelity building simulator are performed to demonstrate the viability and effectiveness of the proposed design. Simulation results show that the proposed approach can effectively reduce the noise pollution caused by HPs with negligible energy cost increase.
The 3rd AI Olympics with RealAIGym competition poses the challenge of developing a global policy that can swing up and stabilize an underactuated 2-link system Acrobot and/or Pendubot from any configuration in the state space. This paper presents an optimal control-based approach using a real-time Nonlinear Model Predictive Control (MPC). The results show that the controller achieves good performance and robustness and can reliably handle disturbances.
We study the control of stochastic discrete-time linear multi-agent systems (MAS) subject to additive stochastic noise and collaborative signal temporal logic (STL) specifications to be satisfied with a desired probability. Given available disturbance datasets, we leverage conformal prediction (CP) to address the underlying chance-constrained multi-agent STL synthesis problem in a distribution-free manner. By introducing nonconformity scores as functions of prediction regions (PRs) of error trajectories, we develop an iterative PR-scaling and disturbance-feedback synthesis approach to bound training error trajectory samples. These bounds are then calibrated using a separate dataset, providing probabilistic guarantees via CP. Subsequently, we relax the underlying stochastic optimal control problem by tightening the robustness functions of collaborative tasks based on their Lipschitz constants and the computed error bounds. To address scalability, we exploit the compositional structure of the multi-agent STL formula and propose a model-predictive-control-like algorithm, where agent-level problems are solved in a distributed fashion. Lastly, we showcase the benefits of the proposed method in comparison with [1] via an illustrative example.
Communication remains a key factor limiting the applicability of distributed model predictive control (DMPC) in realistic settings, despite advances in wireless communication. DMPC schemes can require an overwhelming amount of information exchange between agents as the amount of data depends on the length of the predication horizon, for which some applications require a significant length to formally guarantee nominal asymptotic stability. This work aims to provide an approach to reduce the communication effort of DMPC by reducing the size of the communicated data between agents. Using an autoencoder, the communicated data is reduced by the encoder part of the autoencoder prior to communication and reconstructed by the decoder part upon reception within the distributed optimization algorithm that constitutes the DMPC scheme. The choice of a learning-based reduction method is motivated by structure inherent to the data, which results from the data's connection to solutions of optimal control problems. The approach is implemented and tested at the example of formation control of differential-drive robots, which is challenging for optimization-based control due to the robots' nonholonomic constraints, and which is interesting due to the practical importance of mobile robotics. The applicability of the proposed approach is presented first in form of a simulative analysis showing that the resulting control performance yields a satisfactory accuracy. In particular, the proposed approach outperforms the canonical naive way to reduce communication by reducing the length of the prediction horizon. Moreover, it is shown that numerical experiments conducted on embedded computation hardware, with real distributed computation and wireless communication, work well with the proposed way of reducing communication even in practical scenarios in which full communication fails.
Improving energy efficiency of building heating systems is essential for reducing global energy consumption and greenhouse gas emissions. Traditional control methods in buildings rely on static heating curves based solely on outdoor temperature measurements, neglecting system state and free heat sources like solar gain. Model predictive control (MPC) not only addresses these limitations but further optimizes heating control by incorporating weather forecasts and system state predictions. However, current industrial MPC solutions often use simplified physics-inspired models, which compromise accuracy for interpretability. While purely data-driven models offer better predictive performance, they face challenges like overfitting and lack of transparency. To bridge this gap, we propose a Bayesian Long Short-Term Memory (LSTM) architecture for indoor temperature modeling. Our experiments across 100 real-world buildings demonstrate that the Bayesian LSTM outperforms an industrial physics-based model in predictive accuracy, enabling potential for improved energy efficiency and thermal comfort if deployed in heating MPC solutions. Over deterministic black-box approaches, the Bayesian framework provides additional advantages by improving generalization ability and allowing interpretation of predictions via uncertainty quantification. This work advances data-driven heating control by balancing predictive performance with the transparency and reliability required for real-world heating MPC applications.
Autonomous Micro Aerial Vehicles (MAVs), particularly quadrotors, have shown significant potential in assisting humans with tasks such as construction and package delivery. These applications benefit greatly from the use of cables for manipulation mechanisms due to their lightweight, low-cost, and simple design. However, designing effective control and planning strategies for cable-suspended systems presents several challenges, including indirect load actuation, nonlinear configuration space, and highly coupled system dynamics. In this paper, we introduce a novel event-triggered distributed Nonlinear Model Predictive Control (NMPC) method specifically designed for cooperative transportation involving multiple quadrotors manipulating a cable-suspended payload. This approach addresses key challenges such as payload manipulation, inter-robot separation, obstacle avoidance, and trajectory tracking, all while optimizing the use of computational and communication resources. By integrating an event-triggered mechanism, our NMPC method reduces unnecessary computations and communication, enhancing energy efficiency and extending the operational range of MAVs. The proposed method employs a lightweight state vector parametrization that focuses on payload states in all six degrees of freedom, enabling efficient planning of trajectories on the SE(3) manifold. This not only reduces planning complexity but also ensures real-time computational feasibility. Our approach is validated through extensive simulation, demonstrating its efficacy in dynamic and resource-constrained environments.
Safety assurance in multi-agent systems with coupled dynamics is a fundamental yet challenging problem, especially when agents exhibit uncertain and state-dependent behaviors. Classical robust control often assumes worst-case disturbances, leading to overly conservative actions. In this work, we propose a learning-based framework that combines conformal prediction with model predictive control (MPC) to ensure probabilistic safety under action-level uncertainty. Unlike prior approaches that predict future states, we directly model the control action of the uncontrollable agent as a stochastic function of the joint state, trained via neural networks and calibrated using conformal prediction. This enables us to construct dynamic, probabilistically guaranteed reachable tubes for the uncontrollable agent. These tubes are then embedded into an MPC formulation to synthesize control actions for the controllable agent that ensure safe interactions over a finite planning horizon. We provide formal stepwise and cumulative safety guarantees, and demonstrate the effectiveness of our approach through a pedestrian-vehicle interaction scenario. Compared to baseline methods, our framework achieves higher safety rates while maintaining high performance in terms of speed and responsiveness.
This paper proposes a path planning algorithm for multi-agent unmanned aircraft systems (UASs) to autonomously cover a search area, while considering obstacle avoidance, as well as the capabilities and energy consumption of the employed unmanned aerial vehicles. The path planning is optimized in terms of energy efficiency to prefer low energy-consuming maneuvers. In scenarios where a UAS is low on energy, it autonomously returns to its initial position for a safe landing, thus preventing potential battery damage. To accomplish this, an energy-aware multicopter model is integrated into a path planning algorithm based on model predictive control and mixed integer linear programming. Besides factoring in energy consumption, the planning is improved by dynamically defining feasible regions for each UAS to prevent obstacle corner-cutting or over-jumping.
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a computationally tractable procedure to approximate these projections from data, and show how the effect of control can be incorporated. For a 180-dimensional robotic system, we demonstrate that our reduced-order models outperform previous state-of-the-art approaches by up to fivefold in trajectory tracking accuracy under model predictive control.
We present a nonlinear data-driven Model Predictive Control (MPC) algorithm for deep brain stimulation (DBS) for the treatment of Parkinson's disease (PD). Although DBS is typically implemented in open-loop, closed-loop DBS (CLDBS) uses the amplitude of neural oscillations in specific frequency bands (e.g. beta 13-30 Hz) as a feedback signal, resulting in improved treatment outcomes with reduced side effects and slower rates of patient habituation to stimulation. To date, CLDBS has only been implemented in vivo with simple control algorithms, such as proportional or proportional-integral control. Our approach employs a multi-step predictor based on differences of input-convex neural networks to model the future evolution of beta oscillations. The use of a multi-step predictor enhances prediction accuracy over the optimization horizon and simplifies online computation. In tests using a simulated model of beta-band activity response and data from PD patients, we achieve reductions of more than 20% in both tracking error and control activity in comparison with existing CLDBS algorithms. The proposed control strategy provides a generalizable data-driven technique that can be applied to the treatment of PD and other diseases targeted by CLDBS, as well as to other neuromodulation techniques.
The reinforcement learning (RL) and model predictive control (MPC) communities have developed vast ecosystems of theoretical approaches and computational tools for solving optimal control problems. Given their conceptual similarities but differing strengths, there has been increasing interest in synergizing RL and MPC. However, existing approaches tend to be limited for various reasons, including computational cost of MPC in an RL algorithm and software hurdles towards seamless integration of MPC and RL tools. These challenges often result in the use of "simple" MPC schemes or RL algorithms, neglecting the state-of-the-art in both areas. This paper presents MPCritic, a machine learning-friendly architecture that interfaces seamlessly with MPC tools. MPCritic utilizes the loss landscape defined by a parameterized MPC problem, focusing on "soft" optimization over batched training steps; thereby updating the MPC parameters while avoiding costly minimization and parametric sensitivities. Since the MPC structure is preserved during training, an MPC agent can be readily used for online deployment, where robust constraint satisfaction is paramount. We demonstrate the versatility of MPCritic, in terms of MPC architectures and RL algorithms that it can accommodate, on classic control benchmarks.
Data-enabled predictive control (DeePC) has emerged as a powerful technique to control complex systems without the need for extensive modeling efforts. However, relying solely on offline collected data trajectories to represent the system dynamics introduces certain drawbacks. Therefore, we present a novel semi-data-driven model predictive control (SD-MPC) framework that combines (limited) model information with DeePC to address a range of these drawbacks, including sensitivity to noisy data, lack of robustness, and a high computational burden. In this work we focus on the performance of DeePC in operating regimes not captured by the offline collected data trajectories and demonstrate how incorporating an underlying parametric model can counteract this issue. SD-MPC exhibits equivalent closed-loop performance as DeePC for deterministic linear time-invariant systems. Simulations demonstrate the general control performance of the proposed SD-MPC for both a linear time-invariant system and a nonlinear system modeled as a linear parameter-varying system. These results provide numerical evidence of the enhanced robustness of SD-MPC over classical DeePC.
Dynamic metabolic control can enhance bioprocess flexibility and expand the available optimization degrees of freedom via real-time modulation of metabolic enzyme expression. This allows target metabolic fluxes to be dynamically tuned throughout the process. However, identifying optimal dynamic control policies is challenging due to the presence of potential metabolic burden, cytotoxic effects, and the generally high-dimensional solution space, making exhaustive experimentation impractical. Here, we propose an approach based on reinforcement learning to derive optimal dynamic metabolic control policies by allowing an agent or controller to interact with a surrogate dynamic model $\textit{in silico}$. To incorporate and test robustness, we apply domain randomization, enabling the controller to generalize across system uncertainties. Our approach provides an alternative to conventional model-based control such as model predictive control, which requires differentiating the models with respect to decision variables; an often impractical task when dealing with complex stochastic, nonlinear, stiff, or piecewise-defined dynamics. In contrast, our approach only requires forward integration, making the task computationally much simpler with off-the-shelf solvers. We demonstrate our approach with a case study on the dynamic control of acetyl-CoA carboxylase in $\textit{Escherichia coli}$ for fatty acid biosynthesis. The derived dynamic metabolic control policies outperform static control, achieving up to 40 % higher titers while remaining robust under uncertainty.
This paper presents an online energy management system for an energy hub where electric vehicles are charged combining on-site photovoltaic generation and battery energy storage with the power grid, with the objective to decide on the battery (dis)charging to minimize the costs of operation. To this end, we devise a scenario-based stochastic model predictive control (MPC) scheme that leverages probabilistic 24-hour-ahead forecasts of charging load, solar generation and day-ahead electricity prices to achieve a cost-optimal operation of the energy hub. The probabilistic forecasts leverage conformal prediction providing calibrated distribution-free confidence intervals starting from a machine learning model that generates no uncertainty quantification. We showcase our controller by running it over a 280-day evaluation in a closed-loop simulated environment to compare the observed cost of two scenario-based MPCs with two deterministic alternatives: a version with point forecast and a version with perfect forecast. Our results indicate that, compared to the perfect forecast implementation, our proposed scenario-based MPCs are 11\% more expensive, and 1\% better than their deterministic point-forecast counterpart.
This paper proposes tackling safety-critical stochastic Reinforcement Learning (RL) tasks with a samplebased, model-based approach. At the core of the method lies a Model Predictive Control (MPC) scheme that acts as function approximation, providing a model-based predictive control policy. To ensure safety, a probabilistic Control Barrier Function (CBF) is integrated into the MPC controller. A sample-based approach with guarantees is employed to approximate the effects of stochasticies in the optimal control formulation and to guarantee the probabilistic CBF condition. A learnable terminal cost formulation is included in the MPC objective to counterbalance the additional computational burden due to sampling. An RL algorithm is deployed to learn both the terminal cost and the CBF constraint. Results from our numerical experiment on a constrained LTI problem corroborate the effectiveness of the proposed methodology in reducing computation time while preserving control performance and safety.
Motion Cueing Algorithms (MCAs) encode the movement of simulated vehicles into movement that can be reproduced with a motion simulator to provide a realistic driving experience within the capabilities of the machine. This paper introduces a novel learning-based MCA for serial robot-based motion simulators. Building on the differentiable predictive control framework, the proposed method merges the advantages of Nonlinear Model Predictive Control (NMPC) - notably nonlinear constraint handling and accurate kinematic modeling - with the computational efficiency of machine learning. By shifting the computational burden to offline training, the new algorithm enables real-time operation at high control rates, thus overcoming the key challenge associated with NMPC-based motion cueing. The proposed MCA incorporates a nonlinear joint-space plant model and a policy network trained to mimic NMPC behavior while accounting for joint acceleration, velocity, and position limits. Simulation experiments across multiple motion cueing scenarios showed that the proposed algorithm performed on par with a state-of-the-art NMPC-based alternative in terms of motion cueing quality as quantified by the RMSE and correlation coefficient with respect to reference signals. However, the proposed algorithm was on average 400 times faster than the NMPC baseline. In addition, the algorithm successfully generalized to unseen operating conditions, including motion cueing scenarios on a different vehicle and real-time physics-based simulations.