We consider the problem of hydrogen storage integration in microgrids to improve the electricity supply resilience. Nonlinear effects from electrochemical models of electrolyzers and fuel cells for hydrogen storage are considered, making scheduling under the nonlinear model intractable and the conventional linear approximation infeasible. A piecewise linear model approximation with feasibility projection is proposed, resulting in a computationally efficient model predictive control for hydrogen storage operation. Several resilience performance measures, such as loss-of-load, duration-of-outage, and system cost, are used in performance evaluation. Simulations for the proposed optimization demonstrated a 13%-48% reduction in duration-of-outage, a 6.4%-21.7% reduction in system cost, and a 95% reduction in loss-of-load for critical loads compared to the scheduling algorithm involving linear model approximation. The performance gap of the proposed optimization to the benchmark involving the accurate nonlinear electrochemical model is less than 1% in most metrics.
Autoscaling is a critical mechanism in cloud computing, enabling the autonomous adjustment of computing resources in response to dynamic workloads. This is particularly valuable for co-located, long-running applications with diverse workload patterns. The primary objective of autoscaling is to regulate resource utilization at a desired level, effectively balancing the need for resource optimization with the fulfillment of Service Level Objectives (SLOs). Many existing proactive autoscaling frameworks may encounter prediction deviations arising from the frequent fluctuations of cloud workloads. Reactive frameworks, on the other hand, rely on realtime system feedback, but their hysteretic nature could lead to violations of stringent SLOs. Hybrid frameworks, while prevalent, often feature independently functioning proactive and reactive modules, potentially leading to incompatibility and undermining the overall decision-making efficacy. In addressing these challenges, we propose OptScaler, a collaborative autoscaling framework that integrates proactive and reactive modules through an optimization module. The proactive module delivers reliable future workload predictions to the optimization module, while the reactive module offers a self-tuning estimator for real-time updates. By embedding a Model Predictive Control (MPC) mechanism and chance constraints into the optimization module, we further enhance its robustness. Numerical results have demonstrated the superiority of our workload prediction model and the collaborative framework, leading to over a 36% reduction in SLO violations compared to prevalent reactive, proactive, or hybrid autoscalers. Notably, OptScaler has been successfully deployed at Alipay, providing autoscaling support for the world-leading payment platform.
Nonlinear dynamics bring difficulties to controller design for control-affine systems such as tractor-trailer vehicles, especially when the parameters in the dynamics are unknown. To address this constraint, we propose a derivative-based lifting function construction method, show that the corresponding infinite dimensional Koopman bilinear model over the lifting function is equivalent to the original control-affine system. Further, we analyze the propagation and bounds of state prediction errors caused by the truncation in derivative order. The identified finite dimensional Koopman bilinear model would serve as predictive model in the next step. Koopman Bilinear Model Predictive control (K-BMPC) is proposed to solve the trajectory tracking problem. We linearize the bilinear model around the estimation of the lifted state and control input. Then the bilinear Model Predictive Control problem is approximated by a quadratic programming problem. Further, the estimation is updated at each iteration until the convergence is reached. Moreover, we implement our algorithm on a tractor-trailer system, taking into account the longitudinal and side slip effects. The open-loop simulation shows the proposed Koopman bilinear model captures the dynamics with unknown parameters and has good prediction performance. Closed-loop tracking results show the proposed K-BMPC exhibits elevated tracking precision with the commendable computational efficiency. The experimental results demonstrate the feasibility of K-BMPC.
In the backdrop of an increasingly pressing need for effective urban and highway transportation systems, this work explores the synergy between model-based and learning-based strategies to enhance traffic flow management by use of an innovative approach to the problem of ramp metering control that embeds Reinforcement Learning (RL) techniques within the Model Predictive Control (MPC) framework. The control problem is formulated as an RL task by crafting a suitable stage cost function that is representative of the traffic conditions, variability in the control action, and violations of the constraint on the maximum number of vehicles in queue. An MPC-based RL approach, which leverages the MPC optimal problem as a function approximation for the RL algorithm, is proposed to learn to efficiently control an on-ramp and satisfy its constraints despite uncertainties in the system model and variable demands. Simulations are performed on a benchmark small-scale highway network to compare the proposed methodology against other state-of-the-art control approaches. Results show that, starting from an MPC controller that has an imprecise model and is poorly tuned, the proposed methodology is able to effectively learn to improve the control policy such that congestion in the network is reduced and constraints are satisfied, yielding an improved performance that is superior to the other controllers.
This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot effectively cope with highly noisy measurements, resulting in unstable control performance. To address this challenge, the present study extends current physics-informed machine learning capabilities for modeling nonlinear dynamics with control and integrates them into a model predictive control framework. To demonstrate the capability of the proposed method we test and validate with two noisy nonlinear dynamic systems: the chaotic Lorenz 3 system, and turning machine tool. Analysis of the results illustrate that the proposed method outperforms state-of-the-art benchmarks as measured by both modeling accuracy and control performance for nonlinear dynamic systems under high-noise conditions.
Deriving precise system dynamic models through traditional numerical methods is often a challenging endeavor. The performance of Model Predictive Control is heavily contingent on the accuracy of the system dynamic model. Consequently, this study employs Echo State Networks to acquire knowledge of the unmodeled dynamic characteristics inherent in the system. This information is then integrated with the nominal model, functioning as a form of model compensation. The present paper introduces a control framework that combines ESN with MPC. By perpetually assimilating the disparities between the nominal and real models, control performance experiences augmentation. In a demonstrative example, a second order dynamic system is subjected to simulation. The outcomes conclusively evince that ESNbased MPC adeptly assimilates unmodeled dynamic attributes, thereby elevating the system control proficiency.
In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz.
Neural network-based optimization and control methods, often referred to as black-box approaches, are increasingly gaining attention in energy and manufacturing systems, particularly in situations where first-principles models are either unavailable or inaccurate. However, their non-convex nature significantly slows down the optimization and control processes, limiting their application in real-time decision-making processes. To address this challenge, we propose a novel Input Convex Long Short-Term Memory (IC-LSTM) network to enhance the computational efficiency of neural network-based optimization. Through two case studies employing real-time neural network-based optimization for optimizing energy and chemical systems, we demonstrate the superior performance of IC-LSTM-based optimization in terms of runtime. Specifically, in a real-time optimization problem of a real-world solar photovoltaic energy system at LHT Holdings in Singapore, IC-LSTM-based optimization achieved at least 4-fold speedup compared to conventional LSTM-based optimization. These results highlight the potential of IC-LSTM networks to significantly enhance the efficiency of neural network-based optimization and control in practical applications. Source code is available at https://github.com/killingbear999/ICLSTM.
Ensuring safety of nonlinear systems under model uncertainty and external disturbances is crucial, especially for real-world control tasks. Predictive methods such as robust model predictive control (RMPC) require solving nonconvex optimization problems online, which leads to high computational burden and poor scalability. Reinforcement learning (RL) works well with complex systems, but pays the price of losing rigorous safety guarantee. This paper presents a theoretical framework that bridges the advantages of both RMPC and RL to synthesize safety filters for nonlinear systems with state- and action-dependent uncertainty. We decompose the robust invariant set (RIS) into two parts: a target set that aligns with terminal region design of RMPC, and a reach-avoid set that accounts for the rest of RIS. We propose a policy iteration approach for robust reach-avoid problems and establish its monotone convergence. This method sets the stage for an adversarial actor-critic deep RL algorithm, which simultaneously synthesizes a reach-avoid policy network, a disturbance policy network, and a reach-avoid value network. The learned reach-avoid policy network is utilized to generate nominal trajectories for online verification, which filters potentially unsafe actions that may drive the system into unsafe regions when worst-case disturbances are applied. We formulate a second-order cone programming (SOCP) approach for online verification using system level synthesis, which optimizes for the worst-case reach-avoid value of any possible trajectories. The proposed safety filter requires much lower computational complexity than RMPC and still enjoys persistent robust safety guarantee. The effectiveness of our method is illustrated through a numerical example.
There has been a growing interest in realizing the resilient consensus of the multi-agent system (MAS) under cyber-attacks, which aims to achieve the consensus of normal agents (i.e., agents without attacks) in a network, depending on the neighboring information. The literature has developed mean-subsequence-reduced (MSR) algorithms for the MAS with F adversarial attacks and has shown that the consensus is achieved for the normal agents when the communication network is at least (2F+1)-robust. However, such a stringent requirement on the communication network needs to be relaxed to enable more practical applications. Our objective is, for the first time, to achieve less stringent conditions on the network, while ensuring the resilient consensus for the general linear MAS subject to control input constraints. In this work, we propose a distributed resilient consensus framework, consisting of a pre-designed consensus protocol and distributed model predictive control (DMPC) optimization, which can help significantly reduce the requirement on the network robustness and effectively handle the general linear constrained MAS under adversarial attacks. By employing a novel distributed adversarial attack detection mechanism based on the history information broadcast by neighbors and a convex set (i.e., resilience set), we can evaluate the reliability of communication links. Moreover, we show that the recursive feasibility of the associated DMPC optimization problem can be guaranteed. The proposed consensus protocol features the following properties: 1) by minimizing a group of control variables, the consensus performance is optimized; 2) the resilient consensus of the general linear constrained MAS subject to F-locally adversarial attacks is achieved when the communication network is (F+1)-robust. Finally, numerical simulation results are presented to verify the theoretical results.
This article presents a new optimal control-based interactive motion planning algorithm for an autonomous vehicle interacting with a human-driven vehicle. The ego vehicle solves a joint optimization problem for its motion planning involving costs and coupled constraints of both vehicles and applies its own actions. The non-convex feasible region and lane discipline are handled by introducing integer decision variables and the resulting optimization problem is a mixed-integer quadratic program (MIQP) which is implemented via model predictive control (MPC). Furthermore, the ego vehicle imputes the cost of human-driven neighboring vehicle (NV) using an inverse optimal control method based on Karush-Kuhn-Tucker (KKT) conditions and adapts the joint optimization cost accordingly. We call the algorithm adaptive interactive mixed-integer MPC (aiMPC). Its interaction with human subjects driving the NV in a mandatory lane change scenario is tested in a developed software-and-human-in-the-loop simulator. Results show the effectiveness of the presented algorithm in terms of enhanced mobility of both the vehicles compared to baseline methods.
We tackle the challenge of learning to charge Electric Vehicles (EVs) with Out-of-Distribution (OOD) data. Traditional scheduling algorithms typically fail to balance near-optimal average performance with worst-case guarantees, particularly with OOD data. Model Predictive Control (MPC) is often too conservative and data-independent, whereas Reinforcement Learning (RL) tends to be overly aggressive and fully trusts the data, hindering their ability to consistently achieve the best-of-both-worlds. To bridge this gap, we introduce a novel OOD-aware scheduling algorithm, denoted OOD-Charging. This algorithm employs a dynamic "awareness radius", which updates in real-time based on the Temporal Difference (TD)-error that reflects the severity of OOD. The OOD-Charging algorithm allows for a more effective balance between consistency and robustness in EV charging schedules, thereby significantly enhancing adaptability and efficiency in real-world charging environments. Our results demonstrate that this approach improves the scheduling reward reliably under real OOD scenarios with remarkable shifts of EV charging behaviors caused by COVID-19 in the Caltech ACN-Data.
Control related data, such as system states and inputs or controller specifications, is often sensitive. Meanwhile, the increasing connectivity of cloud-based or networked control results in vast amounts of such data, which poses a privacy threat, especially when evaluation on external platforms is considered. In this context, a cipher based on a random affine transformation gained attention, which is supposed to enable privacy-preserving evaluations of quadratic programs (QPs) with little computational overhead compared to other methods. This paper deals with the security of such randomly transformed QPs in the context of model predictive control (MPC). In particular, we show how to construct attacks against this cipher and thereby underpin concerns regarding its security in a practical setting. To this end, we exploit invariants under the transformations and common specifications of MPC-related QPs. Our numerical examples then illustrate that these two ingredients suffice to extract information from ciphertexts.
In this paper, we present a Deep Reinforcement Learning (RL)-driven Adaptive Stochastic Nonlinear Model Predictive Control (SNMPC) to optimize uncertainty handling, constraints robustification, feasibility, and closed-loop performance. To this end, we conceive an RL agent to proactively anticipate upcoming control tasks and to dynamically determine the most suitable combination of key SNMPC parameters - foremost the robustification factor $\kappa$ and the Uncertainty Propagation Horizon (UPH) $T_u$. We analyze the trained RL agent's decision-making process and highlight its ability to learn context-dependent optimal parameters. One key finding is that adapting the constraints robustification factor with the learned policy reduces conservatism and improves closed-loop performance while adapting UPH renders previously infeasible SNMPC problems feasible when faced with severe disturbances. We showcase the enhanced robustness and feasibility of our Adaptive SNMPC (aSNMPC) through the real-time motion control task of an autonomous passenger vehicle to follow an optimal race line when confronted with significant time-variant disturbances. Experimental findings demonstrate that our look-ahead RL-driven aSNMPC outperforms its Static SNMPC (sSNMPC) counterpart in minimizing the lateral deviation both with accurate and inaccurate disturbance assumptions and even when driving in previously unexplored environments.
Automatic control of greenhouse crop production is of great interest owing to the increasing energy and labor costs. In this work, we use two-level control, where the upper level generates suitable reference trajectories for states and control inputs based on day-ahead predictions. These references are tracked in the lower level using Nonlinear Model Predictive Control (NMPC). In order to apply NMPC, a model of the greenhouse dynamics is essential. However, the complex nature of the underlying model including discontinuities and nonlinearities results in intractable computational complexity and long sampling times. As a remedy, we employ NMPC as a data generator to learn the tracking control policy using deep neural networks. Then, the references are tracked using the trained Deep Neural Network (DNN) to reduce the computational burden. The efficiency of our approach under real-time disturbances is demonstrated by means of a simulation study.
This paper addresses the control of diesel engine nitrogen oxides (NOx) and Soot emissions through the application of Model Predictive Control (MPC). The developments described in the paper are based on a high-fidelity model of the engine airpath and torque response in GT-Power, which is extended with a feedforward neural network (FNN)-based model of engine out (feedgas) emissions identified from experimental engine data to enable the controller co-simulation and performance verification. A Recurrent Neural Network (RNN) is then identified for use as a prediction model in the implementation of a nonlinear economic MPC that adjusts intake manifold pressure and EGR rate set-points to the inner loop airpath controller as well as the engine fueling rate. Based on GT-Power engine model and FNN emissions model, the closed-loop simulations of the control system and the plant model, over different driving cycles, demonstrate the capability to shape engine out emissions response by adjusting weights and constraints in economic MPC formulation.
This paper presents the results of developing a multi-layer Neural Network (NN) to represent diesel engine emissions and integrating this NN into control design. Firstly, a NN is trained and validated to simultaneously predict oxides of nitrogen (N Ox) and Soot using both transient and steady-state data. Based on the input-output correlation analysis, inputs to NN with the highest influence on the emissions are selected while keeping the NN structure simple. Secondly, a co-simulation framework is implemented to integrate the NN emissions model with a model of a diesel engine airpath system built in GT-Power and used to identify a low-order linear parameter-varying (LPV) model for emissions prediction. Finally, an economic supervisory model predictive controller (MPC) is developed using the LPV emissions model to adjust setpoints to an inner-loop airpath tracking MPC. Simulation results are reported illustrating the capability of the resulting controller to reduce N Ox, meet the target Soot limit, and track the adjusted intake manifold pressure and exhaust gas recirculation (EGR) rate targets.
We consider the problem of safely coordinating ensembles of identical autonomous agents to conduct complex missions with conflicting safety requirements and under noisy control inputs. Using non-smooth control barrier functions (CBFs) and stochastic model-predictive control as springboards, and by adopting an extrinsic approach where the ensemble is treated as a unified dynamic entity, we devise a method to synthesize safety-aware control inputs for uncertain collectives. Drawing upon stochastic CBF theory and recent developments in Boolean CBF composition, our method proceeds by smoothing a Boolean-composed CBF and solving a stochastic optimization problem where each agent's forcing term is restricted to the affine subspace of control inputs certified by the combined CBF. For the smoothing step, we employ a polynomial approximation scheme, providing evidence for its advantage in generating more conservative yet sufficiently-filtered control inputs than the smoother but more aggressive equivalents produced from an approximation technique based on the log-sum-exp function. To further demonstrate the utility of the proposed method, we present an upper bound for the expected CBF approximation error, along with results from simulations of a single-integrator collective under velocity perturbations. Lastly, we compare these results with those obtained using a naive state-feedback controller lacking safety filters.
Deformable object manipulation stands as one of the most captivating yet formidable challenges in robotics. While previous techniques have predominantly relied on learning latent dynamics through demonstrations, typically represented as either particles or images, there exists a pertinent limitation: acquiring suitable demonstrations, especially for long-horizon tasks, can be elusive. Moreover, basing learning entirely on demonstrations can hamper the model's ability to generalize beyond the demonstrated tasks. In this work, we introduce a demonstration-free hierarchical planning approach capable of tackling intricate long-horizon tasks without necessitating any training. We employ large language models (LLMs) to articulate a high-level, stage-by-stage plan corresponding to a specified task. For every individual stage, the LLM provides both the tool's name and the Python code to craft intermediate subgoal point clouds. With the tool and subgoal for a particular stage at our disposal, we present a granular closed-loop model predictive control strategy. This leverages Differentiable Physics with Point-to-Point correspondence (DiffPhysics-P2P) loss in the earth mover distance (EMD) space, applied iteratively. Experimental findings affirm that our technique surpasses multiple benchmarks in dough manipulation, spanning both short and long horizons. Remarkably, our model demonstrates robust generalization capabilities to novel and previously unencountered complex tasks without any preliminary demonstrations. We further substantiate our approach with experimental trials on real-world robotic platforms. Our project page: https://qq456cvb.github.io/projects/donut.
Autonomous racing creates challenging control problems, but Model Predictive Control (MPC) has made promising steps toward solving both the minimum lap-time problem and head-to-head racing. Yet, accurate models of the system are necessary for model-based control, including models of vehicle dynamics and opponent behavior. Both dynamics model error and opponent behavior can be modeled with Gaussian Process (GP) regression. GP models can be updated iteratively from data collected using the controller, but the strength of the GP model depends on the diversity of the training data. We propose a novel active exploration mechanism for iterative GP regression that purposefully collects additional data at regions of higher uncertainty in the GP model. In the exploration, a MPC collects diverse data by balancing the racing objectives and the exploration criterion; then the GP is re-trained. The process is repeated iteratively; in later iterations, the exploration is deactivated, and only the racing objectives are optimized. Thus, the MPC can achieve better performance by leveraging the improved GP model. We validate our approach in the highly realistic racing simulation platform Gran Turismo Sport of Sony Interactive Entertainment Inc for a minimum lap time challenge, and in numerical simulation of head-to-head. Our active exploration mechanism yields a significant improvement in the GP prediction accuracy compared to previous approaches and, thus, an improved racing performance.