Solving the explicit Model Predictive Control (MPC) problem requires enumerating all critical regions and their associated feedback laws, a task that scales exponentially with the system dimension and the prediction horizon, as well. When the problem's constraints are boxes or zonotopes, the feasible domain admits a compact constrained-zonotope representation. Building on this insight, we exploit the geometric properties of the equivalent constrained-zonotope reformulation to accelerate the computation of the explicit solution. Specifically, we formulate the multi-parametric problem in the lifted generator space and solve it using second-order optimality conditions, employ low-rank matrix updates to reduce computation time, and introduce an analytic enumeration of candidate active sets that yields the explicit solution in tree form.
In this paper, we present an effective online tube-based model predictive control (T-MPC) solution for autonomous driving that aims at improving the computational load while ensuring robust stability and performance in fast and disturbed scenarios. We focus on reformulating the non-linear original problem into a pseudo-linear problem by transforming the non-linear vehicle equations to be expressed in a Linear Parameter Varying (LPV) form. An scheme composed by a nominal controller and a corrective local controller is propossed. First, the local controller is designed as a polytopic LPV-H$_{\in…
We propose a method to perform set-based state estimation of an unknown dynamical linear system using a data-driven set propagation function. Our method comes with set-containment guarantees, making it applicable to safety-critical systems. The method consists of two phases: (1) an offline learning phase where we collect noisy input-output data to determine a function to propagate the state-set ahead in time; and (2) an online estimation phase consisting of a time update and a measurement update. It is assumed that known finite sets bound measurement noise and disturbances, but we assume no kn…
We present a novel tube-based data-driven predictive control method for linear systems affected by a bounded addictive disturbance. Our method leverages recent results in the reachability analysis of unknown linear systems to formulate and solve a robust tube-based predictive control problem. More precisely, our approach consists in deriving, from the collected data, a zonotope that includes the true state error set. We show how to guarantee the stability of the resulting error zonotope, which can be exploited to increase the computational efficiency of existing zonotopic data-driven MPC formu…
This paper proposes novel set-theoretic approaches for state estimation in bounded-error discrete-time nonlinear systems, subject to nonlinear observations/constraints. By transforming the polytopic sets that are characterized as zonotope bundles (ZB) and/or constrained zonotopes (CZ), from the state space to the space of the generators of ZB/CZ, we leverage a recent result on the remainder-form mixed-monotone decomposition functions to compute the propagated set, i.e., a ZB/CZ that is guaranteed to enclose the set of the state trajectories of the considered system. Further, by applying the re…
Robust Model Predictive Control Design for Autonomous Vehicles with Perception-based Observers
Department of Mechanical Engineering, Michigan State University（机械工程系，密歇根州立大学）；Department of Electrical and Computer Engineering, Michigan State University（电气与计算机工程系，密歇根州立大学）
NTNU（挪威科技大学）；IMT School for Advanced Studies Lucca（卢卡IMT高等研究院）
The combination of learning methods with Model Predictive Control (MPC) has attracted a significant amount of attention in the recent literature. The hope of this combination is to reduce the reliance of MPC schemes on accurate models, and to tap into the fast developing machine learning and reinforcement learning tools to exploit the growing amount of data available for many systems. In particular, the combination of reinforcement learning and MPC has been proposed as a viable and theoretically justified approach to introduce explainable, safe and stable policies in reinforcement learning. Ho…
Model Predictive Control (MPC) schemes have proven their efficiency in controlling high degree-of-freedom (DoF) complex robotic systems. However, they come at a high computational cost and an update rate of about tens of hertz. This relatively slow update rate hinders the possibility of stable haptic teleoperation of such systems since the slow feedback loops can cause instabilities and loss of transparency to the operator. This work presents a novel framework for transparent teleoperation of MPC-controlled complex robotic systems. In particular, we employ a feedback MPC approach and exploit i…
We present a learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that…
We present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input-output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parametrization provided by the Fundamental Lemma of Willems et al. We use new input-output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) opt…
This paper investigates the rendezvous problem for the autonomous cooperative landing of an unmanned aerial vehicle (UAV) on an unmanned surface vehicle (USV). Such heterogeneous agents, with nonlinear dynamics, are dynamically decoupled but share a common cooperative rendezvous task. The underlying control scheme is based on distributed Model Predictive Control (MPC). The main contribution is a rendezvous algorithm with an online update rule of the rendezvous location. The algorithm only requires the agents to exchange information when they can not guarantee to rendezvous. Hence, the exchange…
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution of such block-sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank-one factorization updates of the preconditioner result in a per-iteration computational complexity of $\mathcal{O}(N m^2)$, where $m$ denotes the number of state and control variables and $N$ the number of control intervals. Three dif…
Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the…
Tight performance specifications in combination with operational constraints make model predictive control (MPC) the method of choice in various industries. As the performance of an MPC controller depends on a sufficiently accurate objective and prediction model of the process, a significant effort in the MPC design procedure is dedicated to modeling and identification. Driven by the increasing amount of available system data and advances in the field of machine learning, data-driven MPC techniques have been developed to facilitate the MPC controller design. While these methods are able to lev…
An autonomous adaptive MPC architecture is presented for control of heating, ventilation and air condition (HVAC) systems to maintain indoor temperature while reducing energy use. Although equipment use and occupant changes with time, existing MPC methods are not capable of automatically relearning models and computing control decisions reliably for extended periods without intervention from a human expert. We seek to address this weakness. Two major features are embedded in the proposed architecture to enable autonomy: (i) a system identification algorithm from our prior work that periodicall…
We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show…
Certifiable Explicit Model Predictive Control for Spacecraft Rendezvous under Bounded Disturbances
NOVA University of Lisbon（诺瓦大学）；Center for Technology and Systems (CTS)（技术与系统中心）；Institute for Systems and Robotics, Instituto Superior Técnico, University of Lisbon（里斯本大学高等技术学院系统与机器人研究所）
Cooperative driving, enabled by communication between automated vehicle systems, is expected to significantly contribute to transportation safety and efficiency. Cooperative Adaptive Cruise Control (CACC) and platooning are two of the main cooperative driving applications that are currently under study. These applications offer significant improvements over current advanced driver assistant systems such as adaptive cruise control (ACC). The primary motivation of CACC and Platooning is to reduce traffic congestion and improve traffic flow, traffic throughput, and highway capacity. These applica…
A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to mo…
In control applications there is often a compromise that needs to be made with regards to the complexity and performance of the controller and the computational resources that are available. For instance, the typical hardware platform in embedded control applications is a microcontroller with limited memory and processing power, and for battery powered applications the control system can account for a significant portion of the energy consumption. We propose a controller architecture in which the computational cost is explicitly optimized along with the control objective. This is achieved by a…
Sampling-based Model Predictive Control Using Trust Regions
Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology（智能传感器执行器系统实验室，人机学与机器人研究所，卡尔斯鲁厄理工学院）
Cost-Matching Model Predictive Control for Efficient Reinforcement Learning in Humanoid Locomotion
New York University Abu Dhabi (NYUAD)（纽约大学阿布扎比分校）；Georgia Institute of Technology（佐治亚理工学院）；Norwegian University of Science and Technology (NTNU)（挪威科技大学）
Michigan State University（密歇根州立大学）；Utah State University（犹他州立大学）
This paper presents a sample-efficient data-driven method to design model predictive control (MPC) for cable-actuated soft robotics using Bayesian optimization. Instead of modeling the complex dynamics of the soft robots, the proposed approach uses Bayesian optimization to search the best-guessed low-dimensional prediction model and its associated controller to minimize the objective function of closed-loop responses. The prediction model is updated by Bayesian optimization from the closed-loop input-output data in each iteration. A linear MPC is then designed based on the updated prediction m…
