In this paper we propose a framework towards achieving two intertwined objectives: (i) equipping reinforcement learning with active exploration and deliberate information gathering, such that it regulates state and parameter uncertainties resulting from modeling mismatches and noisy sensory; and (ii) overcoming the computational intractability of stochastic optimal control. We approach both objectives by using reinforcement learning to compute the stochastic optimal control law. On one hand, we avoid the curse of dimensionality prohibiting the direct solution of the stochastic dynamic programming equation. On the other hand, the resulting stochastic optimal control reinforcement learning agent admits caution and probing, that is, optimal online exploration and exploitation. Unlike fixed exploration and exploitation balance, caution and probing are employed automatically by the controller in real-time, even after the learning process is terminated. We conclude the paper with a numerical simulation, illustrating how a Linear Quadratic Regulator with the certainty equivalence assumption may lead to poor performance and filter divergence, while our proposed approach is stabilizing, of an acceptable performance, and computationally convenient.
The replacement of fossil fuels in combination with an increasing share of renewable energy sources leads to an increased focus on decentralized microgrids. One option is the local production of green hydrogen in combination with fuel cell vehicles (FCVs). In this paper, we develop a control strategy based on Model Predictive Control (MPC) for an energy management system (EMS) of a hydrogen plant, which is currently under installation in Offenbach, Germany. The plant includes an electrolyzer, a compressor, a low pressure storage tank, and six medium pressure storage tanks with complex heuristic physical coupling during the filling and extraction of hydrogen. Since these heuristics are too complex to be incorporated into the optimal control problem (OCP) explicitly, we propose a novel approach to do so implicitly. First, the MPC is executed without considering them. Then, the so-called allocator uses a heuristic model (of arbitrary complexity) to verify whether the MPC's plan is valid. If not, it introduces additional constraints to the MPC's OCP to implicitly respect the tanks' pressure levels. The MPC is executed again and the new plan is applied to the plant. Simulation results with real-world measurement data of the facility's energy management and realistic fueling scenarios show its advantages over rule-based control.
This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way to understand system behavior and design control algorithms that account for underlying dynamics and changing parameters. The PVKO builds on a conventional Koopman model by incorporating local time-invariant linear systems through interpolation within the lifted space. This paper outlines a procedure for identifying the PVKO and designing a model predictive control using the identified PVKO model. Simulation results demonstrate that the proposed approach improves model accuracy and enables predictions based on future parameter information. The feasibility and stability of the proposed control approach are analyzed, and their effectiveness is demonstrated through simulation.
Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations.
Railway running gears with independently rotating wheels (IRW) can significantly improve wear figures, comfort, and safety in railway transportation, but certain measures for wheelset stabilization are required. This is one reason why the application of traditional wheelsets is still common practice in industry. Apart from lateral guidance, the longitudinal control is of crucial importance for railway safety. In the current contribution, an integrated controller for joined lateral and longitudinal control of a high-speed railway running gear with driven IRW is designed. To this end, a novel adhesion-based traction control law is combined with linear time-variant and nonlinear model predictive control (MPC) schemes for lateral guidance. The MPC schemes are able to use tabulated track geometry data and preview information about set points to minimize the lateral displacement error. Co-simulation results with a detailed multi-body simulation show the effectiveness of the approach compared with state-of-the-art techniques in various scenarios, including curving, varying velocities up to 400 km/h and abruptly changing wheel-rail adhesion conditions.
In this paper, a multi-model predictive control approach is used to automate the co-administration of propofol and remifentanil from bispectral index measurement during general anesthesia. To handle the parameter uncertainties in the non-linear output function, multiple Extended Kalman Filters are used to estimate the state of the system in parallel. The best model is chosen using a model-matching criterion and used in a non-linear MPC to compute the next drug rates. The method is compared with a conventional non-linear MPC approach and a PID from the literature. The robustness of the controller is evaluated using Monte-Carlo simulations on a wide population introducing uncertainties in the models. Both simulation setup and controller codes are accessible in open source for further use. Our preliminary results show the potential interest in using a multi-model method to handle parameter uncertainties.
Model Predictive Control (MPC) is typically characterized for being computationally demanding, as it requires solving optimization problems online; a particularly relevant point when considering its implementation in embedded systems. To reduce the computational burden of the optimization algorithm, most solvers perform as many offline operations as possible, typically performing the computation and factorization of its expensive matrices offline and then storing them in the embedded system. This improves the efficiency of the solver, with the disadvantage that online changes on some of the ingredients of the MPC formulation require performing these expensive computations online. This article presents an efficient algorithm for the factorization of the key matrix used in several first-order optimization methods applied to linear MPC formulations, allowing its prediction model and cost function matrices to be updated online at the expense of a small computational cost. We show results comparing the proposed approach with other solvers from the literature applied to a linear time-varying system.
When we rely on deep-learned models for robotic perception, we must recognize that these models may behave unreliably on inputs dissimilar from the training data, compromising the closed-loop system's safety. This raises fundamental questions on how we can assess confidence in perception systems and to what extent we can take safety-preserving actions when external environmental changes degrade our perception model's performance. Therefore, we present a framework to certify the safety of a perception-enabled system deployed in novel contexts. To do so, we leverage robust model predictive control (MPC) to control the system using the perception estimates while maintaining the feasibility of a safety-preserving fallback plan that does not rely on the perception system. In addition, we calibrate a runtime monitor using recently proposed conformal prediction techniques to certifiably detect when the perception system degrades beyond the tolerance of the MPC controller, resulting in an end-to-end safety assurance. We show that this control framework and calibration technique allows us to certify the system's safety with orders of magnitudes fewer samples than required to retrain the perception network when we deploy in a novel context on a photo-realistic aircraft taxiing simulator. Furthermore, we illustrate the safety-preserving behavior of the MPC on simulated examples of a quadrotor. We open-source our simulation platform and provide videos of our results at our project page: https://tinyurl.com/fallback-safe-mpc.
Model predictive control (MPC) is a powerful tool for planning and controlling dynamical systems due to its capacity for handling constraints and taking advantage of preview information. Nevertheless, MPC performance is highly dependent on the choice of cost function tuning parameters. In this work, we demonstrate an approach for online automatic tuning of an MPC controller with an example application to an ecological cruise control system that saves fuel by using a preview of road grade. We solve the global fuel consumption minimization problem offline using dynamic programming and find the corresponding MPC cost function by solving the inverse optimization problem. A neural network fitted to these offline results is used to generate the desired MPC cost function weight during online operation. The effectiveness of the proposed approach is verified in simulation for different road geometries.
We present Ungar, an open-source library to aid the implementation of high-dimensional optimal control problems (OCPs). We adopt modern template metaprogramming techniques to enable the compile-time modeling of complex systems while retaining maximum runtime efficiency. Our framework provides syntactic sugar to allow for expressive formulations of a rich set of structured dynamical systems. While the core modules depend only on the header-only Eigen and Boost.Hana libraries, we bundle our codebase with optional packages and custom wrappers for automatic differentiation, code generation, and nonlinear programming. Finally, we demonstrate the versatility of Ungar in various model predictive control applications, namely, four-legged locomotion and collaborative loco-manipulation with multiple one-armed quadruped robots. Ungar is available under the Apache License 2.0 at https://github.com/fdevinc/ungar.
Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality reduction introduces model uncertainty which can potentially compromise the stability and safety of the original high-dimensional system. In this work, we propose a novel reduced-order model predictive control (ROMPC) scheme to solve constrained optimal control problems for nonlinear, high-dimensional systems. To address the challenges of using ROMs in predictive control schemes, we derive an error bounding system that dynamically accounts for model reduction error. Using these bounds, we design a robust MPC scheme that ensures robust constraint satisfaction, recursive feasibility, and asymptotic stability. We demonstrate the effectiveness of our proposed method in simulations on a high-dimensional soft robot with nearly 10,000 states.
This paper addresses the particularities of the uranium extraction-scrubbing operation in a spent nuclear fuel treatment process (PUREX-Plutonium Uranium Refining by Extraction) through the use of set-point tracking MPC (Model Predictive Control). The presented controller uses the feed solution flow rate as the manipulated variable to control the saturation of the solvent at the extraction step. In addition, it guarantees not to loose uranium in the raffinates, and ensures equipment limitations during operation time. Simulation results show that the tracking NMPC effectively ensures accurate set point tracking and constraints guarantee. As a result, the system can be driven to its optimal working condition, avoid and recover from constraint violations. The control performance was compared with PID and openloop controllers.
We propose a Nonlinear Model Predictive Control approach to spacecraft rendezvous in non-Keplerian Lunar orbits. The approach is based on the Pontryagin Minimum Principle and allows the accomplishment of minimum-propellant maneuvers. The relative motion between the chaser and the target is described by the nonlinear and unstable dynamics of the circular restricted three body-problem. In the proposed formulation, we design a minimum-propellant controller, which leads to a bang-bang behavior of the control signal. Under suitable assumptions, simplified dynamics is employed as prediction model, in order to reduce the complexity of the controller algorithm but, at the same time, without penalizing the controller tracking performance. The proposed approach's effectiveness is validated by a simulation example.
Most of the real-time implementations of the stabilizing optimal control actions suffer from the necessity to provide high computational effort. This paper presents a cutting-edge approach for real-time evaluation of linear-quadratic model predictive control (MPC) that employs a novel generalized stopping criterion, achieving asymptotic stability in the presence of input constraints. The proposed method evaluates a fixed number of iterations independent of the initial condition, eliminating the necessity for computationally expensive methods. We demonstrate the effectiveness of the introduced technique by its implementation of two widely-used first-order optimization methods: the projected gradient descent method (PGDM) and the alternating directions method of multipliers (ADMM). The numerical simulation confirmed a significantly reduced number of iterations, resulting in suboptimality rates of less than 2\,\%, while the effort reductions exceeded 80\,\%. These results nominate the proposed criterion for an efficient real-time implementation method of MPC controllers.
Because neuronal networks are intricate systems composed of interconnected neurons, their control poses challenges owing to their nonlinearity and complexity. In this paper, we propose a method to design control input to a neuronal network to manipulate the firing patterns of modules within the network. We propose a methodology for designing a control input based on temporal deep unfolding-based model predictive control (TDU-MPC), a control methodology based on the deep unfolding technique actively investigated in the context of wireless signal processing. During the method development, we address the unique characteristics of neuron dynamics, such as zero gradients in firing times, by approximating input currents using a sigmoid function. The effectiveness of the proposed method is confirmed via numerical simulations. In networks with 15 and 30 neurons, the control was achieved to switch the firing frequencies of two modules without directly applying control inputs. This study includes a tailored methodology for networked neurons, the extension of TDU-MPC to nonlinear systems with reset dynamics, and the achievement of desired firing patterns in neuronal networks.
Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation cost, stemming from the need to solve an optimisation problem at each control interval. There are several methods to reduce this cost. This survey focusses on approaches where a neural network is used to approximate an existing controller. Herein, relevant and unique neural approximation methods for linear, nonlinear, and robust MPC are presented and compared. Comparisons are based on the theoretical guarantees that are preserved, the factor by which the original controller is sped up, and the size of problem that a framework is applicable to. Research contributions include: a taxonomy that organises existing knowledge, a summary of literary gaps, discussion on promising research directions, and simple guidelines for choosing an approximation framework. The main conclusions are that (1) new benchmarking tools are needed to help prove the generalisability and scalability of approximation frameworks, (2) future breakthroughs most likely lie in the development of ties between control and learning, and (3) the potential and applicability of recently developed neural architectures and tools remains unexplored in this field.
A stochastic Model Predictive Control strategy for control systems with communication networks between the sensor node and the controller and between the controller and the actuator node is proposed. Data packets are subject to random delays and packet loss is possible; acknowledgments for received packets are not provided. The expected value of a quadratic cost is minimized subject to linear constraints; the set of all initial states for which the resulting optimization problem is guaranteed to be feasible is provided. The state vector of the controlled plant is shown to converge to zero with probability one.
This paper proposes a novel control design for voltage tracking of an islanded AC microgrid in the presence of {nonlinear} loads and parametric uncertainties at the primary level of control. The proposed method is based on the Tube-Based Robust Model Predictive Control (RMPC), an online optimization-based method which can handle the constraints and uncertainties as well. The challenge with this method is the conservativeness imposed by designing the tube based on the worst-case scenario of the uncertainties. This weakness is amended in this paper by employing a combination of a learning-based Gaussian Process (GP) regression and RMPC. The advantage of using GP is that both the mean and variance of the loads are predicted at each iteration based on the real data, and the resulted values of mean and the bound of confidence are utilized to design the tube in RMPC. The theoretical results are also provided to prove the recursive feasibility and stability of the proposed learning based RMPC. Finally, the simulation results are carried out on both single and multiple DG (Distributed Generation) units.
Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital twins. In particular, data-driven approaches require little expert knowledge of the particular process and its model, and provide reduced models of a well-defined generic structure. Herein, we apply our recently proposed data-driven reduction strategy based on Koopman theory [Schulze et al. (2022), Comput. Chem. Eng.] to generate a low-order control model of an air separation unit (ASU). The reduced Koopman model combines autoencoders and linear latent dynamics and is constructed using machine learning. Further, we present an NMPC implementation that uses derivative computation tailored to the fixed block structure of reduced Koopman models. Our reduction approach with tailored NMPC implementation enables real-time NMPC of an ASU at an average CPU time decrease by 98 %.
Ensuring safety and meeting temporal specifications are critical challenges for long-term robotic tasks. Signal temporal logic (STL) has been widely used to systematically and rigorously specify these requirements. However, traditional methods of finding the control policy under those STL requirements are computationally complex and not scalable to high-dimensional or systems with complex nonlinear dynamics. Reinforcement learning (RL) methods can learn the policy to satisfy the STL specifications via hand-crafted or STL-inspired rewards, but might encounter unexpected behaviors due to ambiguity and sparsity in the reward. In this paper, we propose a method to directly learn a neural network controller to satisfy the requirements specified in STL. Our controller learns to roll out trajectories to maximize the STL robustness score in training. In testing, similar to Model Predictive Control (MPC), the learned controller predicts a trajectory within a planning horizon to ensure the satisfaction of the STL requirement in deployment. A backup policy is designed to ensure safety when our controller fails. Our approach can adapt to various initial conditions and environmental parameters. We conduct experiments on six tasks, where our method with the backup policy outperforms the classical methods (MPC, STL-solver), model-free and model-based RL methods in STL satisfaction rate, especially on tasks with complex STL specifications while being 10X-100X faster than the classical methods.