Distributed model predictive control (DMPC) is promising in achieving optimal cooperative control in multirobot systems (MRS). However, real-time DMPC implementation relies on numerical optimization tools to periodically calculate local control sequences online. This process is computationally demanding and lacks scalability for large-scale, nonlinear MRS. This article proposes a novel distributed learning-based predictive control (DLPC) framework for scalable multirobot control. Unlike conventional DMPC methods that calculate open-loop control sequences, our approach centers around a computationally fast and efficient distributed policy learning algorithm that generates explicit closed-loop DMPC policies for MRS without using numerical solvers. The policy learning is executed incrementally and forward in time in each prediction interval through an online distributed actor-critic implementation. The control policies are successively updated in a receding-horizon manner, enabling fast and efficient policy learning with the closed-loop stability guarantee. The learned control policies could be deployed online to MRS with varying robot scales, enhancing scalability and transferability for large-scale MRS. Furthermore, we extend our methodology to address the multirobot safe learning challenge through a force field-inspired policy learning approach. We validate our approach's effectiveness, scalability, and efficiency through extensive experiments on cooperative tasks of large-scale wheeled robots and multirotor drones. Our results demonstrate the rapid learning and deployment of DMPC policies for MRS with scales up to 10,000 units.
This article describes a new, efficient way of finding control and state trajectories in optimal control problems by reformulation as a system of differential-algebraic equations (DAEs). The optimal control and state vectors can be obtained via simulation of the resulting DAE system with the selected DAE solver, eliminating the need for an optimization solver. Our simulation-based approach is demonstrated and benchmarked against various optimization-based algorithms via four case studies associated with the optimization and control of a Stefan problem for cell therapy. The simulation-based approach is faster than every optimization-based method by more than an order of magnitude while giving similar/better accuracy in all cases. The solution obtained from the simulation-based approach is guaranteed to be optimal provided that at least one constraint or algebraic equation resulting from the reformulation remains active at all times. The proposed technique offers an efficient and reliable framework for optimal control, serving as a promising alternative to the traditional techniques in applications where speed is crucial, e.g., real-time online model predictive control.
This paper presents a novel approach for vibration control of satellite-based flexible beam-type antennas using Nonlinear Model Predictive Control (NMPC) and Deep Learning techniques. The developed control system leverages piezoelectric (PZT) actuators and sensors to manage the coupled attitude and structural dynamics of the satellite, improving precision and stability. We propose a detailed coupled dynamics model that integrates both satellite attitude and beam structural dynamics, considering the effects of PZT-based actuators. Through MATLAB/Simulink simulations, we demonstrate the effectiveness of the combined NMPC and Deep Learning framework in reducing structural vibrations, achieving faster response times, and enhancing overall control accuracy. The results indicate that the proposed system provides a robust solution for controlling flexible beam-type satellite antennas in space environments.
Model predictive control has emerged as an effective approach for real-time optimal control of connected and automated vehicles. However, nonlinear dynamics of vehicle and traffic systems make accurate modeling and real-time optimization challenging. Learning-based control offer a promising alternative, as they adapt to environment without requiring an explicit model. For learning control framework, an augmented state space system design is necessary since optimal control depends on both the ego vehicle's state and predicted states of other vehicles. This work develops a traffic adaptive augmented state space system that allows the control strategy to intelligently adapt to varying traffic conditions. This design ensures that while different vehicle trajectories alter initial conditions, the system dynamics remain independent of specific trajectories. Additionally, a physics-informed learning control framework is presented that combines value function from Bellman's equation with derivative of value functions from Pontryagin's Maximum Principle into a unified loss function. This method aims to reduce required training data and time while enhancing robustness and efficiency. The proposed control framework is applied to car-following scenarios in real-world data calibrated simulation environments. The results show that this learning control approach alleviates real-time computational requirements while achieving car-following behaviors comparable to model-based methods, resulting in 9% energy savings in scenarios not previously seen in training dataset.
Piezoelectric fast steering mirrors (PFSM) are widely utilized in beam precision-pointing systems but encounter considerable challenges in achieving high-precision tracking of fast trajectories due to nonlinear hysteresis and mechanical dual-axis cross-coupling. This paper proposes a model predictive control (MPC) approach integrated with a hysteresis inverse based on the Hammerstein modeling structure of the PFSM. The MPC is designed to decouple the rate-dependent dual-axis linear components, with an augmented error integral variable introduced in the state space to eliminate steady-state errors. Moreover, proofs of zero steady-state error and disturbance rejection are provided. The hysteresis inverse model is then cascaded to compensate for the rate-independent nonlinear components. Finally, PFSM tracking experiments are conducted on step, sinusoidal, triangular, and composite trajectories. Compared to traditional model-free and existing model-based controllers, the proposed method significantly enhances tracking accuracy, demonstrating superior tracking performance and robustness to frequency variations. These results offer valuable insights for engineering applications.
We consider the problem of optimizing the economic performance of nonlinear constrained systems subject to uncertain time-varying parameters and bounded disturbances. In particular, we propose an adaptive economic model predictive control (MPC) framework that: (i) directly minimizes transient economic costs, (ii) addresses parametric uncertainty through online model adaptation, (iii) determines optimal setpoints online, and (iv) ensures robustness by using a tube-based approach. The proposed design ensures recursive feasibility, robust constraint satisfaction, and a transient performance bound. In case the disturbances have a finite energy and the parameter variations have a finite path length, the asymptotic average performance is (approximately) not worse than the performance obtained when operating at the best reachable steady-state. We highlight performance benefits in a numerical example involving a chemical reactor with unknown time-invariant and time-varying parameters.
Airborne Wind Energy (AWE) is an emerging technology designed to harness the power of high-altitude winds, offering a solution to several limitations of conventional wind turbines. AWE is based on flying devices (usually gliders or kites) that, tethered to a ground station and driven by the wind, convert its mechanical energy into electrical energy by means of a generator. Such systems are usually controlled by manoeuvering the kite so as to follow a predefined path prescribed by optimal control techniques, such as model-predictive control. These methods are strongly dependent on the specific model at use and difficult to generalize, especially in unpredictable conditions such as the turbulent atmospheric boundary layer. Our aim is to explore the possibility of replacing these techniques with an approach based on Reinforcement Learning (RL). Unlike traditional methods, RL does not require a predefined model, making it robust to variability and uncertainty. Our experimental results in complex simulated environments demonstrate that AWE agents trained with RL can effectively extract energy from turbulent flows, relying on minimal local information about the kite orientation and speed relative to the wind.
Monthly demand charges form a significant portion of the electric bill for microgrids with variable renewable energy generation. A battery energy storage system (BESS) is commonly used to manage these demand charges. Economic model predictive control (EMPC) with a reference trajectory can be used to dispatch the BESS to optimize the microgrid operating cost. Since demand charges are incurred monthly, EMPC requires a full-month reference trajectory for asymptotic stability guarantees that result in optimal operating costs. However, a full-month reference trajectory is unrealistic from a renewable generation forecast perspective. Therefore, to construct a practical EMPC with a reference trajectory, an EMPC formulation considering both non-coincident demand and on-peak demand charges is designed in this work for 24 to 48 h prediction horizons. The corresponding reference trajectory is computed at each EMPC step by solving an optimal control problem over 24 to 48 h reference (trajectory) horizon. Furthermore, BESS state of charge regulation constraints are incorporated to guarantee the BESS energy level in the long term. Multiple reference and prediction horizon lengths are compared for both shrinking and rolling horizons with real-world data. The proposed EMPC with 48 h rolling reference and prediction horizons outperforms the traditional EMPC benchmark with a 2% reduction in the annual cost, proving its economic benefits.
Model Predictive Control (MPC) has demonstrated significant potential in improving energy efficiency in building climate control, outperforming traditional controllers commonly used in modern building management systems. Among MPC variants, data-driven predictive control (DPC) offers the advantage of modeling building dynamics directly from data, thereby substantially reducing commissioning efforts. However, inevitable model uncertainties and measurement noise can result in comfort violations, even with dedicated MPC setups. This work introduces a disturbance-adaptive DPC (DAD-DPC) framework designed to ensure asymptotic satisfaction of predefined violation bounds under sufficient conditions. The framework employs a fully data-driven pipeline based on Willems' Fundamental Lemma and conformal prediction for application in building climate control. The proposed DAD-DPC framework was validated using four building cases, leveraging a high-fidelity simulation platform, BOPTEST, and an actual building testbed, Polydome. For a 5% violation bound, the framework achieved energy consumption increases of 2.82%, 2.24%, 3.75%, and 5.09% while reducing comfort violations by 77.62%, 79.51%, 73.26%, and 39.76%, respectively, compared to other controller configurations. These results demonstrate the framework's ability to effectively balance energy consumption and comfort violations, offering a practical solution for building climate control applications.
Modern power grids are evolving to become more interconnected, include more electric vehicles (EVs), and utilize more renewable energy sources (RES). Increased interconnectivity provides an opportunity to manage EVs and RES by using price signaling to shift EV loads towards periods of high RES output. This work uses ERCOT's 2035 RES installation plans and projections for Texas's EV fleet to examine and compare how both open-loop control and model predictive control (MPC) schemes can leverage time varying rates for EV charging to utilize excess RES supply that may otherwise be underutilized in a highly weather-dependent grid. The results show that while open-loop control increases RES usage, MPC increases RES usage even further by responding to RES outputs that differ from forecasts due to the inherent uncertainty of weather predictions. If MPC is used with time steps that are too frequent, however, difficulties arise; EV owners may find it too onerous to keep up with changing price structures, and frequent over-corrections to charging profiles can lead to a ``rebound peak" phenomenon. Therefore, control schemes should balance maximizing RES usage with ensuring customer participation.
Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen initial guesses, this non-convexity often leads to suboptimal performance resulting from local optima. To overcome this limitation, we propose a novel diffusion model-based approach for near-globally optimal NMPC consisting of an offline and an online phase. The offline phase employs a local optimizer to sample from the distribution of optimal NMPC control sequences along generated system trajectories through random initial guesses. Subsequently, the generated diverse dataset is used to train a diffusion model to reflect the multi-modal distribution of optima. In the online phase, the trained model is leveraged to efficiently perform a variant of random shooting optimization to obtain near-globally optimal control sequences without relying on any initial guesses or online NMPC solving. The effectiveness of our approach is illustrated in a numerical simulation indicating high performance benefits compared to direct neural network approximations of NMPC and significantly lower computation times than online solving NMPC using global optimizers.
We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples.
This paper proposes a distributed data-driven framework to address the challenge of dynamics learning from a large amount of training data for optimal control purposes, named distributed deep Koopman learning for control (DDKC). Suppose a system states-inputs trajectory and a multi-agent system (MAS), the key idea of DDKC is to assign each agent in MAS an offline partial trajectory, and each agent approximates the unknown dynamics linearly relying on the deep neural network (DNN) and Koopman operator theory by communicating information with other agents to reach a consensus of the approximated dynamics for all agents in MAS. Simulations on a surface vehicle first show that the proposed method achieves the consensus in terms of the learned dynamics and the learned dynamics from each agent can achieve reasonably small estimation errors over the testing data. Furthermore, simulations in combination with model predictive control (MPC) to drive the surface vehicle for goal-tracking and station-keeping tasks demonstrate the learned dynamics from DDKC are precise enough to be used for the optimal control design.
We prove input-to-state stability (ISS) of perturbed Newton methods for generalized equations arising from Nash equilibrium (NE) and generalized NE (GNE) problems. This ISS property allows the use of inexact computation in equilibrium-seeking to enable fast solution tracking in dynamic systems and plays a critical role in the analysis of interconnected plant-optimizer feedback systems such as model predictive control (MPC) with iterative optimization algorithms. For NE problems, we address the local convergence of perturbed Newton methods from the variational inequality (VI) stability analysis and point out that the ISS of the perturbed Josephy-Newton can be established under less restrictive stability/regularity conditions compared to the existing results established for nonlinear optimizations. Agent-distributed Josephy-Newton methods are then developed to enable agent-wise local computations. For GNE problems, since they cannot be reduced to VI problems in general, we use semismooth Newton methods to solve the semismooth equations arising from the Karush-Kuhn-Tucker (KKT) systems of the GNE problem and show that the ISS of the perturbed semismooth Newton methods can be established under a quasi-regularity condition. Agent-distributed updates are also developed for the GNE-seeking. To illustrate the use of the ISS in dynamic systems, applications to constrained game-theoretic MPC (CG-MPC) are studied. A real-time CG-MPC solver with both time- and agent- distributed computations is developed and is proven to have bounded solution tracking errors.
This paper proposes a geomagnetic and inertial combined navigation approach based on the flexible correction-model predictive control algorithm (Fc-MPC). This approach aims to overcome the limitations of existing combined navigation methods that require prior geomagnetic maps and the inertial navigation drift of long-range missions. The proposed method uses geomagnetic gradient information and the model predictive control (MPC) algorithm with heading control and state constraints, eliminating the dependence on prior geomagnetic maps. Instead, the proposed method achieves real-time measurements of the geomagnetic declination, geomagnetic inclination, and inertial navigation data and introduces uniform compensation conditions to adjust and correct the predictive results in real-time. Simulation and real experiment results demonstrate that the proposed Fc-MPC algorithm significantly improves the precision, efficiency, and stability of the geomagnetic and inertial combined navigation system.
Recent work in Offline Reinforcement Learning (RL) has shown that a unified Transformer trained under a masked auto-encoding objective can effectively capture the relationships between different modalities (e.g., states, actions, rewards) within given trajectory datasets. However, this information has not been fully exploited during the inference phase, where the agent needs to generate an optimal policy instead of just reconstructing masked components from unmasked ones. Given that a pretrained trajectory model can act as both a Policy Model and a World Model with appropriate mask patterns, we propose using Model Predictive Control (MPC) at test time to leverage the model's own predictive capability to guide its action selection. Empirical results on D4RL and RoboMimic show that our inference-phase MPC significantly improves the decision-making performance of a pretrained trajectory model without any additional parameter training. Furthermore, our framework can be adapted to Offline to Online (O2O) RL and Goal Reaching RL, resulting in more substantial performance gains when an additional online interaction budget is provided, and better generalization capabilities when different task targets are specified. Code is available: https://github.com/wkh923/m3pc.
We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies asymptotical stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.
Autonomous driving heavily relies on perception systems to interpret the environment for decision-making. To enhance robustness in these safety critical applications, this paper considers a Deep Ensemble of Deep Neural Network regressors integrated with Conformal Prediction to predict and quantify uncertainties. In the Adaptive Cruise Control setting, the proposed method performs state and uncertainty estimation from RGB images, informing the downstream controller of the DNN perception uncertainties. An adaptive cruise controller using Conformal Tube Model Predictive Control is designed to ensure probabilistic safety. Evaluations with a high-fidelity simulator demonstrate the algorithm's effectiveness in speed tracking and safe distance maintaining, including in Out-Of-Distribution scenarios.
The physical coupling between robots has the potential to improve the capabilities of multi-robot systems in challenging manufacturing processes. However, the path tracking accuracy of physically coupled robots is not studied adequately, especially considering the uncertain kinematic parameters, the mechanical elasticity, and the built-in controllers of off-the-shelf robots. This paper addresses these issues with a novel differential-algebraic system model which is verified against measurement data from real execution. The uncertain kinematic parameters are estimated online to adapt the model. Consequently, an adaptive model predictive controller is designed as a coordinator between the robots. The controller achieves a path tracking error reduction of 88.6% compared to the state-of-the-art benchmark in the simulation.
This paper proposes a novel robust model predictive control (RMPC) method for the stabilization of constrained systems subject to additive disturbance (AD) and multiplicative disturbance (MD). Concentric containers are introduced to facilitate the characterization of MD, and varying tubes are constructed to bound reachable states. By restricting states and the corresponding inputs in containers with free sizes and a fixed shape, feasible MDs, which are the products of model uncertainty with states and inputs, are restricted into polytopes with free sizes. Then, tubes with different centers and shapes are constructed based on the nominal dynamics and the knowledge of AD and MD. The free sizes of containers allow for a more accurate characterization of MD, while the fixed shape reduces online computational burden, making the proposed method less conservative and computationally efficient. Moreover, the shape of containers is optimized to further reduce conservativeness. Compared to the RMPC method using homothetic tubes, the proposed method has a larger region of attraction while involving fewer decision variables and constraints in the online optimization problem.