This work presents a Model Predictive Control (MPC) for the artificial pancreas, which is able to autonomously manage basal insulin injections in type 1 diabetic patients. Specifically, the MPC goal is to maintain the patients' blood glucose level inside the safe range of 70-180 mg/dL, acting on the insulin amount and respecting all the imposed constraints, taking into consideration also the Insulin On Board (IOB), to avoid excess of insulin infusion. MPC uses a model to make predictions of the system behaviour. In this work, due to the complexity of the diabetes disease that complicates the identification of a general physiological model, a data-driven learning method is employed instead. The Componentwise H\"{o}lder Kinky Inference (CHoKI) method is adopted, to have a customized controller for each patient. For the data collection phase and also to test the proposed controller, the virtual patients of the FDA-accepted UVA/Padova simulator are exploited. The proposed MPC is also tested on a modified version of the simulator, that takes into consideration also the variability of the insulin sensitivity. The final results are satisfying since the proposed controller reduces the time in hypoglycemia (which is more dangerous) if compared to the outcome obtained with the standard constant basal insulin therapy provided by the simulator, satisfying also the time in range requirements and avoiding long-term hyperglycemia events.
We propose in this paper an optimal control framework for renewable energy communities (RECs) equipped with controllable assets. Such RECs allow its members to exchange production surplus through an internal market. The objective is to control their assets in order to minimise the sum of individual electricity bills. These bills account for the electricity exchanged through the REC and with the retailers. Typically, for large companies, another important part of the bills are the costs related to the power peaks; in our framework, they are determined from the energy exchanges with the retailers. We compare rule-based control strategies with the two following control algorithms. The first one is derived from model predictive control techniques, and the second one is built with reinforcement learning techniques. We also compare variants of these algorithms that neglect the peak power costs. Results confirm that using policies accounting for the power peaks lead to a significantly lower sum of electricity bills and thus better control strategies at the cost of higher computation time. Furthermore, policies trained with reinforcement learning approaches appear promising for real-time control of the communities, where model predictive control policies may be computationally expensive in practice. These findings encourage pursuing the efforts toward development of scalable control algorithms, operating from a centralised standpoint, for renewable energy communities equipped with controllable assets.
In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows to track a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows to estimate the rotor effective wind speeds at downstream turbines based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.
State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState
Model predictive control (MPC) has been shown to significantly improve the energy efficiency of buildings while maintaining thermal comfort. Data-driven approaches based on neural networks have been proposed to facilitate system modelling. However, such approaches are generally nonconvex and result in computationally intractable optimization problems. In this work, we design a readily implementable energy management method for small commercial buildings. We then leverage our approach to formulate a real-time demand bidding strategy. We propose a data-driven and mixed-integer convex MPC which is solved via derivative-free optimization given a limited computational time of 5 minutes to respect operational constraints. We consider rooftop unit heating, ventilation, and air conditioning systems with discrete controls to accurately model the operation of most commercial buildings. Our approach uses an input convex recurrent neural network to model the thermal dynamics. We apply our approach in several demand response (DR) settings, including a demand bidding, a time-of-use, and a critical peak rebate program. Controller performance is evaluated on a state-of-the-art building simulation. The proposed approach improves thermal comfort while reducing energy consumption and cost through DR participation, when compared to other data-driven approaches or a set-point controller.
Quadrotors are increasingly used in the evolving field of aerial robotics for their agility and mechanical simplicity. However, inherent uncertainties, such as aerodynamic effects coupled with quadrotors' operation in dynamically changing environments, pose significant challenges for traditional, nominal model-based control designs. We propose a multi-task meta-learning method called Encoder-Prototype-Decoder (EPD), which has the advantage of effectively balancing shared and distinctive representations across diverse training tasks. Subsequently, we integrate the EPD model into a model predictive control problem (Proto-MPC) to enhance the quadrotor's ability to adapt and operate across a spectrum of dynamically changing tasks with an efficient online implementation. We validate the proposed method in simulations, which demonstrates Proto-MPC's robust performance in trajectory tracking of a quadrotor being subject to static and spatially varying side winds.
Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learning-enabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBF-based switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.
Applications in robotics or other size-, weight- and power-constrained autonomous systems at the edge often require real-time and low-energy solutions to large optimization problems. Event-based and memory-integrated neuromorphic architectures promise to solve such optimization problems with superior energy efficiency and performance compared to conventional von Neumann architectures. Here, we present a method to solve convex continuous optimization problems with quadratic cost functions and linear constraints on Intel's scalable neuromorphic research chip Loihi 2. When applied to model predictive control (MPC) problems for the quadruped robotic platform ANYmal, this method achieves over two orders of magnitude reduction in combined energy-delay product compared to the state-of-the-art solver, OSQP, on (edge) CPUs and GPUs with solution times under ten milliseconds for various problem sizes. These results demonstrate the benefit of non-von-Neumann architectures for robotic control applications.
Application of nonlinear model predictive control (NMPC) to problems with hybrid dynamical systems, disjoint constraints, or discrete controls often results in mixed-integer formulations with both continuous and discrete decision variables. However, solving mixed-integer nonlinear programming problems (MINLP) in real-time is challenging, which can be a limiting factor in many applications. To address the computational complexity of solving mixed integer nonlinear model predictive control problem in real-time, this paper proposes an approximate mixed integer NMPC formulation based on value function approximation. Leveraging Bellman's principle of optimality, the key idea here is to divide the prediction horizon into two parts, where the optimal value function of the latter part of the prediction horizon is approximated offline using expert demonstrations. Doing so allows us to solve the MINMPC problem with a considerably shorter prediction horizon online, thereby reducing the online computation cost. The paper uses an inverted pendulum example with discrete controls to illustrate this approach.
The application of supervised learning techniques in combination with model predictive control (MPC) has recently generated significant interest, particularly in the area of approximate explicit MPC, where function approximators like deep neural networks are used to learn the MPC policy via optimal state-action pairs generated offline. While the aim of approximate explicit MPC is to closely replicate the MPC policy, substituting online optimization with a trained neural network, the performance guarantees that come with solving the online optimization problem are typically lost. This paper considers an alternative strategy, where supervised learning is used to learn the optimal value function offline instead of learning the optimal policy. This can then be used as the cost-to-go function in a myopic MPC with a very short prediction horizon, such that the online computation burden reduces significantly without affecting the controller performance. This approach differs from existing work on value function approximations in the sense that it learns the cost-to-go function by using offline-collected state-value pairs, rather than closed-loop performance data. The cost of generating the state-value pairs used for training is addressed using a sensitivity-based data augmentation scheme.
This research proposes an innovative approach to detumble satellites' triple-axis angular velocities with only one single-axis magnetic torquer. Since magnetic torque is generated perpendicularly to magnetorquers, no intended control torque along the magnetorquer can be produced, which makes systems underactuated. Our paper introduces a control method using Model Predictive Control (MPC) and compares it with B-dot control algorithm. By applying these control laws to Kyushu University Light Curve Inversion (Q-Li) Demonstration Satellite in numerical simulations, we describe the applicability of these control laws to underactuated systems.
Among various satellite actuators, magnetic torquers have been widely equipped for stabilization and attitude control of small satellites. Although magnetorquers are generally used with other actuators, such as momentum wheels, this paper explores a control method where only a magnetic actuation is available. We applied a nonlinear optimal control method, Nonlinear Model Predictive Control (NMPC), to small satellites, employing the generalized minimal residual (GMRES) method, which generates continuous control inputs. Onboard magnetic actuation systems often find it challenging to produce smooth magnetic moments as a control input; hence, we employ the Pulse Width Modulation (PWM) method, which discretizes a control input and reduces the burden on actuators. In our case, the PWM approach discretizes control torques generated by the NMPC scheme. This study's main contributions are investigating the NMPC and the GMRES method applied to small spacecraft and presenting the PWM control system's feasibility.
Practical and accurate traffic models play an important role in capturing real traffic dynamics and then in achieving effective control performance. This paper studies traffic signal control in a traffic network with multiple interconnected intersections, where the target is to balance the vehicle density on each lane by controlling the green times of each phase at every intersection. Different from traditional road-based modeling schemes, a two-lane intersection model is first proposed to model the flow propagation in a more accurate way. A distributed model predictive control (MPC) method is then presented to assign the green times. To enable the real-time feasibility of the proposed approach, the alternating direction method of multipliers (ADMM) is incorporated with the distributed MPC scheme for solving the problem. Finally, the simulation studies performed in VISSIM for a six-intersection traffic network in Dalian, China, show the effectiveness and characteristics of the proposed method.
Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging model predictive control techniques. In this paper, we extend this framework such that in addition, robust asymptotic stability of the closed-loop system can be guaranteed by enforcing a decrease of an implicit Lyapunov function which is constructed using a predicted system trajectory. Differently from previous results, we show robust asymptotic stability with respect to a predefined disturbance set on an extended state consisting of the system state and a warmstart input sequence. The proposed strategy is applied to an automotive lane keeping example in simulation.
Distributed model predictive control (MPC) is currently being investigated as a solution to the important control challenge presented by networks of hybrid dynamical systems. However, a benchmark problem for distributed hybrid MPC is absent from the literature. We propose distributed control of a platoon of autonomous vehicles as a comparison benchmark problem. The problem provides a complex and adaptable case study, upon which existing and future approaches to distributed MPC for hybrid systems can be evaluated. Two hybrid modeling frameworks are presented for the vehicle dynamics. Five hybrid MPC controllers are then evaluated and extensively assessed on the fleet of vehicles. Finally, we comment on the need for new efficient and high performing distributed MPC schemes for hybrid systems.
The vast majority of products we use daily are supplied to us through complex global supply chains that transform raw materials into finished goods and distribute them to end consumers. This paper proposes a modeling methodology for dynamic competitive supply chains based on game theory and model predictive control. We model each manufacturer in the supply chain as a rational utility maximizing agent that selects their actions by finding an open-loop generalized Nash equilibrium of a multi-stage game. To react to competitors and the state of the market, every agent re-plans their actions in a receding horizon manner based on estimates of market and supplier parameters thereby creating an approximate closed-loop equilibrium policy. We demonstrate through numerical simulations that this modeling approach is computationally tractable and generates economically interpretable behaviors in a variety of settings such as demand spikes, supply shocks, and information asymmetry.
Downstream wind turbines operating behind upstream turbines face significant performance challenges due to reduced wind speeds and increased turbulence. This leads to decreased wind energy production and higher dynamic loads on downwind turbines. Consequently, real-time monitoring and control have become crucial for improving wind farm performance. One promising solution involves optimizing wind farm layouts in real-time, taking advantage of the added flexibility offered by floating offshore wind turbines (FOWTs). This study explores a dynamic layout optimization strategy to minimize wake effects in wind farms while meeting power requirements. Two scenarios are considered: power maximization and power set-point tracking. The methodology involves a centralized wind farm controller optimizing the layout, followed by wind turbine controllers to meet the prescribed targets. Each FOWT employs model predictive control to adjust aerodynamic thrust force. The control strategy integrates a dynamic wind farm model that considers floating platform motion and wake transport in changing wind conditions. In a case study with a 1x3 wind farm layout of 5 MW FOWTs, the results show a 25% increase in stable energy production compared to a static layout in one hour for the first scenario. In the second scenario, desired power production was swiftly and consistently achieved.
Model Predictive Control (MPC) can be applied to safety-critical control problems, providing closed-loop safety and performance guarantees. Implementation of MPC controllers requires solving an optimization problem at every sampling instant, which is challenging to execute on embedded hardware. To address this challenge, we propose a framework that combines a tightened soft constrained MPC formulation with supervised learning to approximate the MPC value function. This combination enables us to obtain a corresponding optimal control law, which can be implemented efficiently on embedded platforms. The framework ensures stability and constraint satisfaction for various nonlinear systems. While the design effort is similar to that of nominal MPC, the proposed formulation provides input-to-state stability (ISS) with respect to the approximation error of the value function. Furthermore, we prove that the value function corresponding to the soft constrained MPC problem is Lipschitz continuous for Lipschitz continuous systems, even if the optimal control law may be discontinuous. This serves two purposes: First, it allows to relate approximation errors to a sufficiently large constraint tightening to obtain constraint satisfaction guarantees. Second, it paves the way for an efficient supervised learning procedure to obtain a continuous value function approximation. We demonstrate the effectiveness of the method using a nonlinear numerical example.
This paper proposes a robust model predictive control-based solution for the recently introduced series active variable geometry suspension (SAVGS) to improve the ride comfort and road holding of a quarter car. In order to close the gap between the nonlinear multi-body SAVGS model and its linear equivalent, a new uncertain system characterization is proposed that captures unmodeled dynamics, parameter variation, and external disturbances. Based on the newly proposed linear uncertain model for the quarter car SAVGS system, a constrained optimal control problem (OCP) is presented in the form of a linear matrix inequality (LMI) optimization. More specifically, utilizing semidefinite relaxation techniques a state-feedback robust model predictive control (RMPC) scheme is presented and integrated with the nonlinear multi-body SAVGS model, where state-feedback gain and control perturbation are computed online to optimise performance, while physical and design constraints are preserved. Numerical simulation results with different ISO-defined road events demonstrate the robustness and significant performance improvement in terms of ride comfort and road holding of the proposed approach, as compared to the conventional passive suspension, as well as, to actively controlled SAVGS by a previously developed conventional H-infinity control scheme.
The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91\%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.