The paper presents a movement strategy for Connected and Automated Vehicles (CAVs) in a lane-free traffic environment with vehicle nudging by use of an optimal control approach. State-dependent constraints on control inputs are considered to ensure that the vehicle moves within the road boundaries and to prevent collisions. An objective function, comprising various weighted sub-objectives, is designed, whose minimization leads to vehicle advancement at the desired speed, when possible, while avoiding obstacles. A nonlinear optimal control problem (OCP) is formulated for the minimization of the objective function subject to constraints for each vehicle. A computationally efficient Feasible Direction Algorithm (FDA) is called, on event-triggered basis, to compute in real-time the numerical solution for finite time-horizons within a Model Predictive Control (MPC) framework. The approach is applied to each vehicle on the road, while running simulations on a lane-free ring-road, for a wide range of vehicle densities and different types of vehicles. From the simulations, which create myriads of driving episodes for each involved vehicle, it is observed that the proposed approach is highly efficient in delivering safe, comfortable and efficient vehicle trajectories, as well as high traffic flow outcomes. The approach is under investigation for further use in various lane-free road infrastructures for CAV traffic.
In this work, we consider the task of improving the accuracy of dynamic models for model predictive control (MPC) in an online setting. Although prediction models can be learned and applied to model-based controllers, these models are often learned offline. In this offline setting, training data is first collected and a prediction model is learned through an elaborated training procedure. However, since the model is learned offline, it does not adapt to disturbances or model errors observed during deployment. To improve the adaptiveness of the model and the controller, we propose an online dynamics learning framework that continually improves the accuracy of the dynamic model during deployment. We adopt knowledge-based neural ordinary differential equations (KNODE) as the dynamic models, and use techniques inspired by transfer learning to continually improve the model accuracy. We demonstrate the efficacy of our framework with a quadrotor, and verify the framework in both simulations and physical experiments. Results show that our approach can account for disturbances that are possibly time-varying, while maintaining good trajectory tracking performance.
A plug-and-play model predictive control (PnP MPC) scheme is proposed for varying-topology networks to track piecewise constant references. The proposed scheme allows subsystems to occasionally join and leave the network while preserving asymptotic stability and recursive feasibility and comprises two main phases. In the redesign phase, passivity-based control is used to ensure that asymptotic stability of the network is preserved. In the transition phase, reconfigurable terminal ingredients are used to ensure that the distributed MPC problem is initially feasible after the PnP operation. The efficacy of the proposed scheme is evaluated by applying it to a network of mass-spring-damper systems and comparing it to a benchmark scheme. It is found that the novel redesign phase results in faster PnP operations, whereas the novel transition phase increases flexibility by accepting more requests.
A distributed model predictive control scheme is developed for tracking piecewise constant references where the terminal set is reconfigured online, whereas the terminal controller is computed offline. Unlike many standard existing schemes, this scheme yields large feasible regions without performing offline centralized computations. Although the resulting optimal control problem (OCP) is a semidefinite program (SDP), an SDP scalability method based on diagonal dominance is used to approximate the derived SDP by a second-order cone program. The OCPs of the proposed scheme and its approximation are amenable to distributed optimization. Both schemes are evaluated using a power network example and compared to a scheme where the terminal controller is reconfigured online as well. It is found that fixing the terminal controller results in better performance, noticeable reduction in computational cost and similar feasible region compared to the case in which this controller is reconfigured online.
This paper presents cooperative target defense guidance strategies using nonlinear model predictive control (NMPC) framework for a target-attacker-defender (TAD) game. The TAD game consists of an attacker and a cooperative target-defender pair. The attacker's objective is to capture the target, whereas the target-defender team acts together such that the defender can intercept the attacker and ensure target survival. We assume that the cooperative target-defender pair do not have perfect knowledge of the attacker states, and hence the states are estimated using an Extended Kalman Filter (EKF). The capture analysis based on the Apollonius circles is performed to identify the target survival regions. The efficacy of the NMPC-based solution is evaluated through extensive numerical simulations. The results show that the NMPC-based solution offers robustness to the different unknown attacker models and has better performance than CLOS and A-CLOS based strategies.
Self-triggered control, a well-documented technique for reducing the communication overhead while ensuring desired system performance, is gaining increasing popularity. However, existing methods for self-triggered control require explicit system models that are assumed perfectly known a priori. An end-to-end control paradigm known as data-driven control learns control laws directly from data, and offers a competing alternative to the routine system identification-then-control method. In this context, the present paper puts forth data-driven self-triggered control schemes for unknown linear systems using data collected offline. Specifically, for output feedback control systems, a data-driven model predictive control (MPC) scheme is proposed, which computes a sequence of control inputs while generating a predicted system trajectory. A data-driven self-triggering law is designed using the predicted trajectory, to determine the next triggering time once a new measurement becomes available. For state feedback control systems, instead of capitalizing on MPC to predict the trajectory, a data-fitting problem using the pre-collected input-state data is solved, whose solution is employed to construct the self-triggering mechanism. Both feasibility and stability are established for the proposed self-triggered controllers, which are validated using numerical examples.
This paper considers the problem of online multi-robot motion planning with general nonlinear dynamics subject to unknown external disturbances. We propose dSLAP, a distributed safe learning and planning framework that allows the robots to safely navigate through the environments by coupling online learning and motion planning. Gaussian process regression is used to online learn the disturbances with uncertainty quantification. The planning algorithm ensures collision avoidance against the learning uncertainty and utilizes set-valued analysis to achieve fast adaptation in response to the newly learned models. A set-valued model predictive control problem is then formulated and solved to return a control policy that balances between actively exploring the unknown disturbances and reaching goal regions. Sufficient conditions are established to guarantee the safety of the robots in the absence of backup policy. Monte Carlo simulations are conducted for evaluation.
Human drivers have limited and time-varying cognitive resources when making decisions in real-world traffic scenarios, which often leads to unique and stochastic behaviors that can not be explained by perfect rationality assumption, a widely accepted premise in modeling driving behaviors that presume drivers rationally make decisions to maximize their own rewards under all circumstances. To explicitly address this disadvantage, this study presents a novel driver behavior model that aims to capture the resource rationality and stochasticity of the human driver's behaviors in realistic longitudinal driving scenarios. The resource rationality principle can provide a theoretic framework to better understand the human cognition processes by modeling human's internal cognitive mechanisms as utility maximization subject to cognitive resource limitations, which can be represented as finite and time-varying preview horizons in the context of driving. An inverse resource rational-based stochastic inverse reinforcement learning approach (IRR-SIRL) is proposed to learn a distribution of the planning horizon and cost function of the human driver with a given series of human demonstrations. A nonlinear model predictive control (NMPC) with a time-varying horizon approach is used to generate driver-specific trajectories by using the learned distributions of the planning horizon and the cost function of the driver. The simulation experiments are carried out using human demonstrations gathered from the driver-in-the-loop driving simulator. The results reveal that the proposed inverse resource rational-based stochastic driver model can address the resource rationality and stochasticity of human driving behaviors in a variety of realistic longitudinal driving scenarios.
Control of warm-water supply for dialysis treatment in a hospital environment is typical of safety-critical control problems. In order to guarantee the continuity of warm-water supply satisfying physical specifications for a wide range of operating conditions, it is inevitable to consider the nonlinearity involved in a dynamic model of a warm-water supply system for the control design. In this paper, we propose to incorporate control specifications described by signal temporal logic, which is a temporal logic with semantics over finite-time signals in formal methods, into the so-called Koopman-Model Predictive Control (MPC) as a novel technique of nonlinear MPC based on the Koopman operator framework for nonlinear systems. This enables us to generate a sequence of optimal inputs such that the controlled state of a nonlinear system can satisfy the specifications. The proposal is applied to the temperature regulation of warm-water supply, and its effectiveness is established numerically.
Many works have recently explored Sim-to-real transferable visual model predictive control (MPC). However, such works are limited to one-shot transfer, where real-world data must be collected once to perform the sim-to-real transfer, which remains a significant human effort in transferring the models learned in simulations to new domains in the real world. To alleviate this problem, we first propose a novel model-learning framework called Kalman Randomized-to-Canonical Model (KRC-model). This framework is capable of extracting task-relevant intrinsic features and their dynamics from randomized images. We then propose Kalman Randomized-to-Canonical Model Predictive Control (KRC-MPC) as a zero-shot sim-to-real transferable visual MPC using KRC-model. The effectiveness of our method is evaluated through a valve rotation task by a robot hand in both simulation and the real world, and a block mating task in simulation. The experimental results show that KRC-MPC can be applied to various real domains and tasks in a zero-shot manner.
The optimal operation problem of electric vehicle aggregator (EVA) is considered. An EVA can participate in energy and regulation markets with its current and upcoming EVs, thus reducing its total cost of purchasing energy to fulfill EVs' charging requirements. A model predictive control (MPC) based optimization is developed to consider the future arrival of EVs as well as energy and regulation prices. The index of conditional value-at-risk (CVaR) is used to model the risk-averseness of an EVA. Simulations on a 2000-EV test system validate the effectiveness of our work in achieving a lucrative revenue while satisfying the charging requests from EV owners.
Autonomous racing represents a uniquely challenging control environment where agents must act while on the limits of a vehicle's capability in order to set competitive lap times. This places the agent on a knife's edge, with a very small margin between success and loss of control. Pushing towards this limit leads to a practical tension: we want agents to explore the limitations of vehicle control to maximise speed, but inadvertently going past that limit and losing control can cause irreparable damage to the vehicle itself. We provide a model predictive control (MPC) baseline that is able to, in a single lap, safely adapt to an unseen racetrack and achieve competitive lap times. Our approaches efficacy is demonstrated in simulation using the Learn To Race Challenge's environment and metrics.
We present a case study applying learning-based distributionally robust model predictive control to highway motion planning under stochastic uncertainty of the lane change behavior of surrounding road users. The dynamics of road users are modelled using Markov jump systems, in which the switching variable describes the desired lane of the vehicle under consideration and the continuous state describes the pose and velocity of the vehicles. We assume the switching probabilities of the underlying Markov chain to be unknown. As the vehicle is observed and thus, samples from the Markov chain are drawn, the transition probabilities are estimated along with an ambiguity set which accounts for misestimations of these probabilities. Correspondingly, a distributionally robust optimal control problem is formulated over a scenario tree, and solved in receding horizon. As a result, a motion planning procedure is obtained which through observation of the target vehicle gradually becomes less conservative while avoiding overconfidence in estimates obtained from small sample sizes. We present an extensive numerical case study, comparing the effects of several different design aspects on the controller performance and safety.
We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity.
Distributed model predictive control (DMPC) is often used to tackle path planning for unmanned aerial vehicle (UAV) swarms. However, it requires considerable computations on-board the UAV, leading to increased weight and power consumption. In this work, we propose to offload path planning computations to multiple ground-based computation units. As simultaneously communicating and recomputing all trajectories is not feasible for a large swarm with tight timing requirements, we develop a novel event-triggered DMPC that selects a subset of most relevant UAV trajectories to be replanned. The resulting architecture reduces UAV weight and power consumption, while the active redundancy provides robustness against computation unit failures. Moreover, the DMPC guarantees feasible and collision-free trajectories for UAVs with linear dynamics. In simulations, we demonstrate that our method can reliably plan trajectories, while saving 60% of network traffic and required computational power. Hardware-in-the-loop experiments show that it is suitable to control real quadcopter swarms.
Nonlinear model predictive control has been widely adopted to manipulate bilinear systems with dynamics that include products of the inputs and the states. These systems are ubiquitous in chemical processes, mechanical systems, and quantum physics, to name a few. Running a bilinear MPC controller in real time requires solving a non-convex optimization problem within a limited sampling time. This paper proposes a novel parallel proximal-point Lagrangian based bilinear MPC solver via an interlacing horizon-splitting scheme. The resulting algorithm converts the non-convex MPC control problem into a set of parallelizable small-scale multi-parametric quadratic programs (mpQPs) and an equality-constrained linear-quadratic regulator problem. As a result, the solutions of mpQPs can be pre-computed offline to enable efficient online computation. The proposed algorithm is validated on a simulation of an HVAC system control. It is deployed on a TI LaunchPad XL F28379D microcontroller to execute speed control on a field-controlled DC motor, where the MPC updates at 10 ms and solves the problem in 1.764 ms on average and at most 2.088 ms.
This paper proposes a Robust Safe Control Architecture (RSCA) for safe-decision making. The system to be controlled is a vehicle in the presence of bounded disturbances. The RSCA consists of two parts: a Supervisor MPC and a Controller MPC. Both the Supervisor and the Controller are tube MPCs (TMPCs). The Supervisor MPC provides a safety certificate for an operating controller and a backup control input in every step. After an unsafe action by the operating controller is predicted, the Controller MPC takes over the system. In this paper, a method for the computation of a terminal set is proposed, which is robust against changes in road curvature and forces the vehicle to reach a safe reference. Moreover, two important proofs are provided in this paper. First, it is shown that the backup control input is safe to be applied to the system to lead the vehicle to a safe state. Next, the recursive feasibility of the RSCA is proven. By simulating some obstacle avoidance scenarios, the effectiveness of the proposed RSCA is confirmed.
Traditional biological and pharmaceutical manufacturing plants are controlled by human workers or pre-defined thresholds. Modernized factories have advanced process control algorithms such as model predictive control (MPC). However, there is little exploration of applying deep reinforcement learning to control manufacturing plants. One of the reasons is the lack of high fidelity simulations and standard APIs for benchmarking. To bridge this gap, we develop an easy-to-use library that includes five high-fidelity simulation environments: BeerFMTEnv, ReactorEnv, AtropineEnv, PenSimEnv and mAbEnv, which cover a wide range of manufacturing processes. We build these environments on published dynamics models. Furthermore, we benchmark online and offline, model-based and model-free reinforcement learning algorithms for comparisons of follow-up research.
We show that the explicit realization of data-driven predictive control (DPC) for linear deterministic systems is more tractable than previously thought. To this end, we compare the optimal control problems (OCP) corresponding to deterministic DPC and classical model predictive control (MPC), specify its close relation, and systematically eliminate ambiguity inherent in DPC. As a central result, we find that the explicit solutions to these types of DPC and MPC are of exactly the same complexity. We illustrate our results with two numerical examples highlighting features of our approach.
Smart home appliances can time-shift and curtail their power demand to assist demand side management or allow operation with limited power, as in an off-grid application. This paper proposes a scheduling process to start appliances with time-varying deterministic load profiles. Self-triggered model predictive control is used to limit the household net power demand below a given threshold. Meanwhile, deterministic load profiles are more difficult to schedule compared to variable charging or thermal loads because system failure will occur once power demand is not satisfied. The proposed scheme formulates the decision of the load shifting time as a continuous optimization problem, and an inhomogeneous time grid system is introduced to handle the optimization of different appliances and their consensus at this resolution. The efficacy of the proposed scheme is studied by numerical comparison with a mixed-integer MPC controller and by a case study of three home appliances and an interruptible washing machine.