A Task Decomposition method for iterative learning Model Predictive Control (TDMPC) for linear time-varying systems is presented. We consider the availability of state-input trajectories which solve an original task T1, and design a feasible MPC policy for a new task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we formally define the task decomposition problem, and provide a feasibility proof for the resulting policy. The proposed algorithm reduces the computational burden for linear time-varying systems with piecewise convex constraints. Simulation results demonstrate the improved efficiency of the proposed method on a robotic path-planning task.
A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed…
Rollout approaches are an effective tool to address the problem of co-designing the transmission schedule and the corresponding input values, when the controller is connected to the plant via a resource-constrained communication network. These approaches typically employ an MPC, activated at multiples of the period length of a base transmission schedule. Using multi-step invariant terminal regions and a prediction horizon longer than the base period, stability can be ensured. This strategy, however, suffers from intrinsic shortcomings, such as a high computational complexity and low robustness…
University of California at Berkeley（加州大学伯克利分校）；California Institute of Technology（加州理工学院）
We present a Model Predictive Control (MPC) strategy for unknown input-affine nonlinear dynamical systems. A non-parametric method is used to estimate the nonlinear dynamics from observed data. The estimated nonlinear dynamics are then linearized over time varying regions of the state space to construct an Affine Time Varying (ATV) model. Error bounds arising from the estimation and linearization procedure are computed by using sampling techniques. The ATV model and the uncertainty sets are used to design a robust Model Predictive Control (MPC) problem which guarantees safety for the unknown s…
Adaptive Data-Driven Min-Max MPC for Linear Time-Varying Systems
University of Stuttgart（斯图加特大学）；Institute for Systems Theory and Automatic Control, University of Stuttgart（斯图加特大学系统理论与自动控制研究所）；Center for Integrated Quantum Science and Technology (IQST), University of Stuttgart（斯图加特大学集成量子科学与技术中心）
This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds, and a time varying offset that we wish to identify. The time varying offset uncertainty is assumed unknown point-wise in time. Its domain, called the Feasible Parameter Set, and its maximum rate of change are known to the control designer. As new data becomes available, we refine the Feasible Parameter S…
T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics
JHU Department of Applied Mathematics and Statistics, Johns Hopkins University, MD, USA（约翰霍普金斯大学应用数学与统计学系）；CMU Department of Electrical and Computer Engineering, Carnegie Mellon University, PA, USA（卡内基梅隆大学电气与计算机工程系）
Georgia Institute of Technology（佐治亚理工学院）；Massachusetts Institute of Technology（麻省理工学院）
Model Predictive Path Integral (MPPI) control is a type of sampling-based model predictive control that simulates thousands of trajectories and uses these trajectories to synthesize optimal controls on-the-fly. In practice, however, MPPI encounters problems limiting its application. For instance, it has been observed that MPPI tends to make poor decisions if unmodeled dynamics or environmental disturbances exist, preventing its use in safety-critical applications. Moreover, the multi-threaded simulations used by MPPI require significant onboard computational resources, making the algorithm ina…
In this paper, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implemen…
National Research Council of Italy（意大利国家研究委员会）；Universidad de Sevilla（塞维利亚大学）
In recent years, the increasing interest in Stochastic model predictive control (SMPC) schemes has highlighted the limitation arising from their inherent computational demand, which has restricted their applicability to slow-dynamics and high-performing systems. To reduce the computational burden, in this paper we extend the probabilistic scaling approach to obtain low-complexity inner approximation of chance-constrained sets. This approach provides probabilistic guarantees at a lower computational cost than other schemes for which the sample complexity depends on the design space dimension. T…
Department of Electrical and Computer Engineering（电气与计算机工程系）；Department of Computer Science and Engineering（计算机科学与工程系）；Engineering, Michigan State University, East Lansing, MI 48824 USA（工程，密歇根州立大学，东兰辛，MI 48824 USA）
Computationally efficient Gauss-Newton reinforcement learning for model predictive control
Chair of Process Automation Systems, TU Dortmund University（多特蒙德工业大学过程自动化系统教席）；Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU)（挪威科技大学工程控制论系）
In this paper, we propose a learning-based Model Predictive Control (MPC) approach for the polytopic Linear Parameter-Varying (LPV) systems with inexact scheduling parameters (as exogenous signals with inexact bounds), where the Linear Time Invariant (LTI) models (vertices) captured by combinations of the scheduling parameters becomes wrong. We first propose to adopt a Moving Horizon Estimation (MHE) scheme to simultaneously estimate the convex combination vector and unmeasured states based on the observations and model matching error. To tackle the wrong LTI models used in both the MPC and MH…
We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-appr…
Model predictive control (MPC) schemes are commonly designed with fixed, i.e., time-invariant, horizon length and cost functions. If no stabilizing terminal ingredients are used, stability can be guaranteed via a sufficiently long horizon. A suboptimality index can be derived that gives bounds on the performance of the MPC law over an infinite-horizon (IH). While for time-invariant schemes such index can be computed offline, less attention has been paid to time-varying strategies with adapting cost function which can be found, e.g., in learning-based optimal control. This work addresses the pe…
The high thermal efficiency and reliability of the compression-ignition engine makes it the first choice for many applications. For this to continue, a reduction of the pollutant emissions is needed. One solution is the use of machine learning (ML) and model predictive control (MPC) to minimize emissions and fuel consumption, without adding substantial computational cost to the engine controller. ML is developed in this paper for both modeling engine performance and emissions and for imitating the behaviour of an Linear Parameter Varying (LPV) MPC. Using a support vector machine-based linear p…
We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-lo…
In this paper, we present the use of Model Predictive Control (MPC) based on Reinforcement Learning (RL) to find the optimal policy for a multi-agent battery storage system. A time-varying prediction of the power price and production-demand uncertainty are considered. We focus on optimizing an economic objective cost while avoiding very low or very high state of charge, which can damage the battery. We consider the bounded power provided by the main grid and the constraints on the power input and state of each agent. A parametrized MPC-scheme is used as a function approximator for the determin…
In this paper, we propose a novel framework for approximating the explicit MPC policy for linear parameter-varying systems using supervised learning. Our learning scheme guarantees feasibility and near-optimality of the approximated MPC policy with high probability. Furthermore, in contrast to most existing approaches that only learn the MPC policy, we also learn the "dual policy", which enables us to keep a check on the approximated MPC's optimality online during the control process. If the check deems the control input from the approximated MPC policy safe and near-optimal, then it is applie…
The control of constrained systems using model predictive control (MPC) becomes more challenging when full state information is not available and when the nominal system model and measurements are corrupted by noise. Since these conditions are often seen in practical scenarios, techniques such as robust output feedback MPC have been developed to address them. However, existing approaches to robust output feedback MPC are challenged by increased complexity of the online optimization problem, increased computational requirements for controller synthesis, or both. In this work we present a simple…
Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the oil flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two Quadratic Program…
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 f…
Cross-coupled iterative learning control (ILC) can achieve high performance for manufacturing applications in which tracking a contour is essential for the quality of a product. The aim of this paper is to develop a framework for norm-optimal cross-coupled ILC that enables the use of exact contour errors that are calculated offline, and iteration- and time-varying weights. Conditions for the monotonic convergence of this iteration-varying ILC algorithm are developed. In addition, a resource-efficient implementation is proposed in which the ILC update law is reframed as a linear quadratic track…
Stony Brook University（石溪大学）；University of London, Royal Holloway（伦敦大学皇家霍洛威学院）
Even though model predictive control (MPC) is currently the main algorithm for insulin control in the artificial pancreas (AP), it usually requires complex online optimizations, which are infeasible for resource-constrained medical devices. MPC also typically relies on state estimation, an error-prone process. In this paper, we introduce a novel approach to AP control that uses Imitation Learning to synthesize neural-network insulin policies from MPC-computed demonstrations. Such policies are computationally efficient and, by instrumenting MPC at training time with full state information, they…
Norwegian University of Technology, NTNU（挪威科技大学（NTNU））；IMT School for Advanced Studies Lucca（卢卡IMT高等研究院）
Model Predictive Control has been recently proposed as policy approximation for Reinforcement Learning, offering a path towards safe and explainable Reinforcement Learning. This approach has been investigated for Q-learning and actor-critic methods, both in the context of nominal Economic MPC and Robust (N)MPC, showing very promising results. In that context, actor-critic methods seem to be the most reliable approach. Many applications include a mixture of continuous and integer inputs, for which the classical actor-critic methods need to be adapted. In this paper, we present a policy approxim…
