Deep-learning-based techniques have been widely adopted for autonomous driving software stacks for mass production in recent years, focusing primarily on perception modules, with some work extending this method to prediction modules. However, the downstream planning and control modules are still designed with hefty handcrafted rules, dominated by optimization-based methods such as quadratic programming or model predictive control. This results in a performance bottleneck for autonomous driving systems in that corner cases simply cannot be solved by enumerating hand-crafted rules. We present a deep-learning-based approach that brings prediction, decision, and planning modules together with the attempt to overcome the rule-based methods' deficiency in real-world applications of autonomous driving, especially for urban scenes. The DNN model we proposed is solely trained with 10 hours of human driver data, and it supports all mass-production ADAS features available on the market to date. This method is deployed onto a Jiyue test car with no modification to its factory-ready sensor set and compute platform. the feasibility, usability, and commercial potential are demonstrated in this article.
Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods.
We propose a novel adaptive learning-based model predictive control (MPC) scheme for interconnected systems which can be decomposed into several smaller dynamically coupled subsystems with uncertain coupling. The proposed scheme is mainly divided into two main online phases; a learning phase and an adaptation phase. Set membership identification is used in the learning phase to learn an uncertainty set that contains the coupling strength using online data. In the adaptation phase, rigid tube-based robust MPC is used to compute the optimal predicted states and inputs. Besides computing the optimal trajectories, the MPC ingredients are adapted in the adaptation phase taking the learnt uncertainty set into account. These MPC ingredients include the prestabilizing controller, the rigid tube, the tightened constraints and the terminal ingredients. The recursive feasibility of the proposed scheme as well as the stability of the corresponding closed-loop system are discussed. The developed scheme is compared in simulations to existing schemes including robust, adaptive and learning-based MPC.
In Part-I, we presented an optimal day-ahead scheduling scheme for dispatching active distribution networks accounting for the flexibility provided by electric vehicle charging stations (EVCSs) and other controllable resources such as battery energy storage systems (BESSs). Part-II presents the intra-day control layer for tracking the dispatch plan computed from the day-ahead scheduling stage. The control problem is formulated as model predictive control (MPC) with an objective to track the dispatch plan setpoint every 5 minutes, while actuated every 30 seconds. MPC accounts for the uncertainty of the power injections from stochastic resources (such as demand and generation from photovoltaic - PV plants) by short-term forecasts. MPC also accounts for the grid's operational constraints (i.e., the limits on the nodal voltages and the line power-flows) by a linearized optimal power flow (LOPF) model based on the power-flow sensitivity coefficients, and for the operational constraints of the controllable resources (i.e., BESSs and EVCSs). The proposed framework is experimentally validated on a real-life ADN at the EPFL's Distributed Electrical Systems Laboratory and is composed of a medium voltage (MV) bus connected to three low voltage distribution networks. It hosts two controllable EVCSs (172 kWp and 32 F~kWp), multiple PV plants (aggregated generation of 42~kWp), uncontrollable demand from office buildings (20 kWp), and two controllable BESSs (150kW/300kWh and 25kW/25kWh).
This paper proposes a grid-aware scheduling and control framework for Electric Vehicle Charging Stations (EVCSs) for dispatching the operation of an active power distribution network. The framework consists of two stages. In the first stage, we determine an optimal day-ahead power schedule at the grid connection point (GCP), referred to as the dispatch plan. Then, in the second stage, a real-time model predictive control is proposed to track the day-ahead dispatch plan using flexibility from EVCSs. The dispatch plan accounts for the uncertainties of vehicles connected to the EVCS along with other uncontrollable power injections, by day-ahead predicted scenarios. We propose using a Gaussian-Mixture-Model (GMM) for the forecasting of EVCS demand using the historical dataset on arrival, departure times, EV battery capacity, State-of-Charge (SoC) targets, etc. The framework ensures that the grid is operated within its voltage and branches power-flow operational bounds, modeled by a linearized optimal power-flow model, maintaining the tractability of the problem formulation. The scheme is numerically and experimentally validated on a real-life distribution network at the EPFL connected to two EVCSs, two batteries, three photovoltaic plants, and multiple heterogeneous loads. The day-ahead and real-time stages are described in Part-I and Part-II papers respectively.
In this paper, we consider the problem of reference tracking in uncertain nonlinear systems. A neural State-Space Model (NSSM) is used to approximate the nonlinear system, where a deep encoder network learns the nonlinearity from data, and a state-space component captures the temporal relationship. This transforms the nonlinear system into a linear system in a latent space, enabling the application of model predictive control (MPC) to determine effective control actions. Our objective is to design the optimal controller using limited data from the \textit{target system} (the system of interest). To this end, we employ an implicit model-agnostic meta-learning (iMAML) framework that leverages information from \textit{source systems} (systems that share similarities with the target system) to expedite training in the target system and enhance its control performance. The framework consists of two phases: the (offine) meta-training phase learns a aggregated NSSM using data from source systems, and the (online) meta-inference phase quickly adapts this aggregated model to the target system using only a few data points and few online training iterations, based on local loss function gradients. The iMAML algorithm exploits the implicit function theorem to exactly compute the gradient during training, without relying on the entire optimization path. By focusing solely on the optimal solution, rather than the path, we can meta-train with less storage complexity and fewer approximations than other contemporary meta-learning algorithms. We demonstrate through numerical examples that our proposed method can yield accurate predictive models by adaptation, resulting in a downstream MPC that outperforms several baselines.
Model predictive control (MPC) for linear systems with quadratic costs and linear constraints is shown to admit an exact representation as an implicit neural network. A method to "unravel" the implicit neural network of MPC into an explicit one is also introduced. As well as building links between model-based and data-driven control, these results emphasize the capability of implicit neural networks for representing solutions of optimisation problems, as such problems are themselves implicitly defined functions.
Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix structure. In this case, a common approach is to transform the problem into standard vector form using the vectorization (vec) operator and the Kronecker product, known as vec-permutation. However, the use of the Kronecker product introduces extraneous zero terms in the regressor, resulting in unnecessary additional computational and space requirements. This work derives matrix BLS and RLS formulations which, under mild assumptions, minimize the same cost as the vec-permutation approach. This new approach requires less computational complexity and space complexity than vec-permutation in both BLS and RLS identification. It is also shown that persistent excitation guarantees convergence to the true matrix parameters. This method can used to improve computation time in the online identification of multiple-input, multiple-output systems for indirect adaptive model predictive control.
Satisfying safety constraints is a priority concern when solving optimal control problems (OCPs). Due to the existence of infeasibility phenomenon, where a constraint-satisfying solution cannot be found, it is necessary to identify a feasible region before implementing a policy. Existing feasibility theories built for model predictive control (MPC) only consider the feasibility of optimal policy. However, reinforcement learning (RL), as another important control method, solves the optimal policy in an iterative manner, which comes with a series of non-optimal intermediate policies. Feasibility analysis of these non-optimal policies is also necessary for iteratively improving constraint satisfaction; but that is not available under existing MPC feasibility theories. This paper proposes a feasibility theory that applies to both MPC and RL by filling in the missing part of feasibility analysis for an arbitrary policy. The basis of our theory is to decouple policy solving and implementation into two temporal domains: virtual-time domain and real-time domain. This allows us to separately define initial and endless, state and policy feasibility, and their corresponding feasible regions. Based on these definitions, we analyze the containment relationships between different feasible regions, which enables us to describe the feasible region of an arbitrary policy. We further provide virtual-time constraint design rules along with a practical design tool called feasibility function that helps to achieve the maximum feasible region. We review most of existing constraint formulations and point out that they are essentially applications of feasibility functions in different forms. We demonstrate our feasibility theory by visualizing different feasible regions under both MPC and RL policies in an emergency braking control task.
This paper presents a robust MPC scheme for linear systems subject to time-varying, uncertain constraints that arise from uncertain environments. The predicted input sequence is parameterized over future environment states to guarantee constraint satisfaction despite an imprecise environment prediction and unknown evolution of the future constraints. We provide theoretical guarantees for recursive feasibility and asymptotic convergence. Finally, a brief simulation example showcases our results.
Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support heating and cooling of buildings. This way, the use of classical fossil fuel-based heating, ventilation, and air conditioning can be significantly reduced. Exploiting the benefits of ATES beyond "seasonal" heating in winter and cooling in summer as well as meeting legislative restrictions requires sophisticated control. We propose a tailored model predictive control (MPC) scheme for the sustainable operation of ATES systems, which mainly builds on a novel model and objective function. The new approach leads to a mixed-integer quadratic program. Its performance is evaluated on real data from an ATES system in Belgium.
In this work, we propose a cascaded scheme of linear Model prediction Control (MPC) based on Control Barrier Functions (CBF) with Dynamic Feedback Linearization (DFL) for Vertical Take-off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs). CBF is a tool that allows enforcement of forward invariance of a set using Lyapunov-like functions to ensure safety. The First control synthesis that employed CBF was based on Quadratic Program (QP) that modifies the existing controller to satisfy the safety requirements. However, the CBF-QP-based controllers leading to longer detours and undesirable transient performance. Recent contributions utilize the framework of MPC benefiting from the prediction capabilities and constraints imposed on the state and control inputs. Due to the intrinsic nonlinearities of the dynamics of robotics systems, all the existing MPC-CBF solutions rely on nonlinear MPC formulations or operate on less accurate linear models. In contrast, our novel solution unlocks the benefits of linear MPC-CBF while considering the full underactuated dynamics without any linear approximations. The cascaded scheme converts the problem of safe VTOL-UAV navigation to a Quadratic Constraint Quadratic Programming (QCQP) problem solved efficiently by off-the-shelf solvers. The closed-loop stability and recursive feasibility is proved along with numerical simulations showing the effective and robust solutions. Keywords: Unmanned Aerial Vehicles, Vertical Take-off and Landing, Model Predictive Control, MPC, Nonlinearity, Dynamic Feedback Linearization, Optimal Control.
This paper presents a Model Predictive Control (MPC) scheme for flight scheduling and energy management of electric aviation networks, where electric aircraft transport passengers between electrified airports equipped with sustainable energy sources and battery storage, with the goal of minimizing grid dependency. Specifically, we first model the aircraft flight and charge scheduling problem jointly with the airport energy management problem, explicitly accounting for local weather forecasts. Second, we frame the minimum-grid-energy operational problem as a mixed-integer linear program and solve it in a receding horizon fashion, where the route assignment and charging decisions of each aircraft can be dynamically reassigned to mitigate disruptions. We showcase the proposed MPC scheme on real-world data taken from conventional flights and weather conditions in the Dutch Leeward Antilles. Our results show that MPC can effectively guarantee operation of the network by efficiently re-assigning flights and rescheduling aircraft charging, whilst maximizing the efficiency of the on-site energy systems.
This paper develops a correct-by-design controller for an autonomous vehicle interacting with opponent vehicles with unknown intentions. We define an intention-aware control problem incorporating epistemic uncertainties of the opponent vehicles and model their intentions as discrete-valued random variables. Then, we focus on a control objective specified as belief-space temporal logic specifications. From this stochastic control problem, we derive a sound deterministic control problem using stochastic expansion and solve it using shrinking-horizon model predictive control. The solved intention-aware controller allows a vehicle to adjust its behaviors according to its opponents' intentions. It ensures provable safety by restricting the probabilistic risk under a desired level. We show with experimental studies that the proposed method ensures strict limitation of risk probabilities, validating its efficacy in autonomous driving cases. This work provides a novel solution for the risk-aware control of interactive vehicles with formal safety guarantees.
The accuracy of the underlying model predictions is crucial for the success of model predictive control (MPC) applications. If the model is unable to accurately analyze the dynamics of the controlled system, the performance and stability guarantees provided by MPC may not be achieved. Learning-based MPC can learn models from data, improving the applicability and reliability of MPC. This study develops a nonlinear sparse variational Bayesian learning based MPC (NSVB-MPC) for nonlinear systems, where the model is learned by the developed NSVB method. Variational inference is used by NSVB-MPC to assess the predictive accuracy and make the necessary corrections to quantify system uncertainty. The suggested approach ensures input-to-state (ISS) and the feasibility of recursive constraints in accordance with the concept of an invariant terminal region. Finally, a PEMFC temperature control model experiment confirms the effectiveness of the NSVB-MPC method.
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization.
With the increasing presence of autonomous vehicles (AVs) on public roads, developing robust control strategies to navigate the uncertainty of human-driven vehicles (HVs) is crucial. This paper introduces an advanced method for modeling HV behavior, combining a first-principles model with Gaussian process (GP) learning to enhance velocity prediction accuracy and provide a measurable uncertainty. We validated this innovative HV model using real-world data from field experiments and applied it to develop a GP-enhanced model predictive control (GP-MPC) strategy. This strategy aims to improve safety in mixed vehicle platoons by integrating uncertainty assessment into distance constraints. Comparative simulation studies with a conventional model predictive control (MPC) approach demonstrated that our GP-MPC strategy ensures more reliable safe distancing and fosters efficient vehicular dynamics, achieving notably higher speeds within the platoon. By incorporating a sparse GP technique in HV modeling and adopting a dynamic GP prediction within the MPC framework, we significantly reduced the computation time of GP-MPC, marking it only 4.6% higher than that of the conventional MPC. This represents a substantial improvement, making the process about 100 times faster than our preliminary work without these approximations. Our findings underscore the effectiveness of learning-based HV modeling in enhancing both safety and operational efficiency in mixed-traffic environments, paving the way for more harmonious AV-HV interactions.
As the occurrence of extreme weather events is increasing so are the outages caused by them. During such unplanned outages, a house needs to be provided with an energy supply to maintain habitable conditions by maintaining thermal comfort and servicing at least critical loads. An energy system consisting of rooftop photovoltaic (PV) panels along with battery storage is an excellent carbon-free choice to provide energy resiliency to houses against extreme weather-related outages. However, to provide habitable conditions this energy system has to provide not only for the non-air-conditioning (non-AC) load demand but also for the turning on of the AC system which has a considerably higher startup power requirement as compared to its rated power. Hence, an intelligent automated decision-making controller is needed which can manage the trade-off between competing requirements. In this paper, we propose such an intelligent controller based on Model Predictive Control (MPC). We compare its performance with a Baseline controller which is unintelligent, and a Rule-Based controller which has some intelligence, based on three resiliency metrics that we have developed. We perform extensive simulations for numerous scenarios involving different energy system sizes and AC startup power requirements. Every simulation is one week long and is carried out for a single-family detached house located in Florida in the aftermath of Hurricane Irma in 2017. The simulation results show that the MPC controller performs better than the other controllers in the more energy-constrained scenarios (smaller PV-battery size, larger AC startup power requirement) in providing both thermal comfort and servicing non-AC loads in a balanced manner.
Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional stability requirements that may vary depending on the specific use case or environmental context. In this work, we address this problem by augmenting predictive safety filters with stability guarantees, ranging from bounded convergence to uniform asymptotic stability. The proposed framework extends well-known stability results from model predictive control (MPC) theory while supporting commonly used design techniques. As a result, straightforward extensions to dynamic trajectory tracking problems can be easily adapted, as outlined in this article. The practicality of the framework is demonstrated using an automotive advanced driver assistance scenario, involving a reference trajectory stabilization problem.
Biaxial motion control systems are used extensively in manufacturing and printing industries. To improve throughput and reduce machine cost, lightweight materials are being proposed in structural components but may result in higher flexibility in the machine links. This flexibility is often position dependent and compromises precision of the end effector of the machine. To address the need for improved contouring accuracy in industrial machines with position-dependent structural flexibility, this paper introduces a novel contouring error-bounded control algorithm for biaxial switched linear systems. The proposed algorithm utilizes model predictive control to guarantee the satisfaction of state, input, and contouring error constraints for any admissible mode switching. In this paper, the switching signal remains unknown to the controller, although information about the minimum time the system is expected to stay in a specific mode is considered to be available. The proposed algorithm has the property of recursive feasibility and ensures the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated by applying it to a high-fidelity simulation of a dual-drive industrial laser machine. The results show that the contouring error is successfully bounded within the given tolerance.