An MPC/hybrid system approach to traction control

doi:10.1109/TCST.2005.860527

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An MPC/hybrid system approach to traction control

Journal Article•DOI•

An MPC/hybrid system approach to traction control

Francesco Borrelli¹, Alberto Bemporad¹, Michael Glenn Fodor², Davor Hrovat²•Institutions (2)

ETH Zurich¹, Ford Motor Company²

24 Apr 2006-IEEE Transactions on Control Systems and Technology (IEEE)-Vol. 14, Iss: 3, pp 541-552

TL;DR: Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques.

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Abstract: This paper describes a hybrid model and a model predictive control (MPC) strategy for solving a traction control problem. The problem is tackled in a systematic way from modeling to control synthesis and implementation. The model is described first in the Hybrid Systems Description Language to obtain a mixed-logical dynamical (MLD) hybrid model of the open-loop system. For the resulting MLD model, we design a receding horizon finite-time optimal controller. The resulting optimal controller is converted to its equivalent piecewise affine form by employing multiparametric programming techniques, and finally experimentally tested on a car prototype. Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques.

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Journal Article•DOI•

Predictive Active Steering Control for Autonomous Vehicle Systems

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Paolo Falcone¹, Francesco Borrelli¹, Jahan Asgari², Hongtei Eric Tseng², Davor Hrovat² - Show less +1 more•Institutions (2)

University of Sannio¹, Ford Motor Company²

30 Apr 2007-IEEE Transactions on Control Systems and Technology

TL;DR: The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m/s on icy roads, and two approaches with different computational complexities are presented.

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Abstract: In this paper, a model predictive control (MPC) approach for controlling an active front steering system in an autonomous vehicle is presented. At each time step, a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We present two approaches with different computational complexities. In the first approach, we formulate the MPC problem by using a nonlinear vehicle model. The second approach is based on successive online linearization of the vehicle model. Discussions on computational complexity and performance of the two schemes are presented. The effectiveness of the proposed MPC formulation is demonstrated by simulation and experimental tests up to 21 m/s on icy roads

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1,184 citations

Cites background or methods from "An MPC/hybrid system approach to tr..."

...The approach used in [6] can be used for the online estimation of ....
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...The main concept of MPC is to use a model of the plant to predict the future evolution of the system [6], [14], [17], [26], [27]....
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Book•

Predictive Control for Linear and Hybrid Systems

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Francesco Borrelli¹, Alberto Bemporad², Manfred Morari³•Institutions (3)

University of California, Berkeley¹, IMT Institute for Advanced Studies Lucca², ETH Zurich³

27 Jul 2017

TL;DR: Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

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Abstract: Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

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1,142 citations

Cites background from "An MPC/hybrid system approach to tr..."

...Hybrid systems arise in a large number of application areas and are attracting increasing attention in both academic theory-oriented circles as well as in industry, for instance in the automotive industry [16, 157, 62, 125, 74, 214]....
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Journal Article•DOI•

Model predictive control: Review of the three decades of development

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Jay H. Lee¹•Institutions (1)

KAIST¹

04 Jun 2011-International Journal of Control Automation and Systems

TL;DR: Model predictive control (MPC) has been studied extensively in the last three decades as mentioned in this paper, and the main focus has been on the development of fast MPC, a term chosen to collectively describe the various efforts to bring orders-of-magnitude improvement in the efficiency of the on-line computation so that the technology can be applied to systems requiring very fast sampling rates.

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Abstract: Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial / commercial activities on model predictive control (MPC). This article reviews major developments and achievements during the three decades and attempts to put a perspective on them. The first decade is characterized by the fast-growing industrial adoption of the technology, primarily in the refining and petrochemical sectors, which sparked much interest and also confusion among the academicians. The second decade saw a number of significant advances in understanding the MPC from a control theoretician’s viewpoint, which included state-space interpretations / formulations and stability proofs. These theoretical triumphs contributed to the makings of the second generation of commercial software, which was significantly enhanced in generality and rigor. The third decade’s main focus has been on the development of “fast MPC,” a term chosen to collectively describe the various efforts to bring orders-of-magnitude improvement in the efficiency of the on-line computation so that the technology can be applied to systems requiring very fast sampling rates. Throughout the three decades of the development, theory and practice supported each other quite effectively, a primary reason for the fast and steady rise of the technology.

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550 citations

Additional excerpts

...The reported applications include vehicle traction control [ 58 ], suspension [59], direct injection stratified charge engines [60], ducted fan in a thrust-vectored flight control experiment [61], automotive powertrains [62,63], magnetically actuated mass spring damper system [64], power converters [65,66], multicore thermal management [67], and so on....
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Journal Article•DOI•

Perception, Planning, Control, and Coordination for Autonomous Vehicles

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Scott Pendleton, Hans Andersen, Xinxin Du, Xiaotong Shen, Malika Meghjani, You Hong Eng, Daniela Rus, Marcelo H. Ang - Show less +4 more

17 Feb 2017

TL;DR: In this paper, the authors provide a general overview of the recent developments in the realm of autonomous vehicle software systems, and discuss the fundamental components of the software, as well as recent developments of each area.

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Abstract: Autonomous vehicles are expected to play a key role in the future of urban transportation systems, as they offer potential for additional safety, increased productivity, greater accessibility, better road efﬁciency, and positive impact on the environment. Research in autonomous systems has seen dramatic advances in recent years, due to the increases in available computing power and reduced cost in sensing and computing technologies, resulting in maturing technological readiness level of fully autonomous vehicles. The objective of this paper is to provide a general overview of the recent developments in the realm of autonomous vehicle software systems. Fundamental components of autonomous vehicle software are reviewed, and recent developments in each area are discussed.

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434 citations

Cites background from "An MPC/hybrid system approach to tr..."

...MPC has already been applied in several automotive control applications, including traction control [265], braking and steering [266,267], lane keeping [268] etc....
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Journal Article•DOI•

Identification of hybrid systems - A tutorial

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Simone Paoletti¹, A.L. Juloski², Giancarlo Ferrari-Trecate³, René Vidal⁴•Institutions (4)

University of Siena¹, Eindhoven University of Technology², University of Pavia³, Johns Hopkins University⁴

01 Jan 2007-European Journal of Control

TL;DR: In this paper, the identification of hybrid models with a hybrid structure is discussed, and the main features of the selected procedures are presented, and possible interactions to still enhance their effectiveness are suggested.

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339 citations

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References

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Open Access

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Journal Article•DOI•

Survey Constrained model predictive control: Stability and optimality

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David Q. Mayne¹, James B. Rawlings², Christopher V. Rao², P. O. M. Scokaert³•Institutions (3)

Imperial College London¹, University of Wisconsin-Madison², Centre national d'études des télécommunications³

01 Jun 2000-Automatica

TL;DR: This review focuses on model predictive control of constrained systems, both linear and nonlinear, and distill from an extensive literature essential principles that ensure stability to present a concise characterization of most of the model predictive controllers that have been proposed in the literature.

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8,064 citations

"An MPC/hybrid system approach to tr..." refers methods in this paper

...The main idea of MPC is to use the model of the plant to predict the future evolution of the system [23]....
[...]

Journal Article•DOI•

The explicit linear quadratic regulator for constrained systems

[...]

Alberto Bemporad, Manfred Morari, Vivek Dua¹, Efstratios N. Pistikopoulos¹•Institutions (1)

Imperial College London¹

01 Jan 2002-Automatica

TL;DR: A technique to compute the explicit state-feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints is presented, and it is shown that this closed form solution is piecewise linear and continuous.

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3,187 citations

"An MPC/hybrid system approach to tr..." refers background in this paper

...As in general the complexity of the final piecewise affine controller increases dramatically with the number of constraints in (11) (see [10] for the case of linear systems), tuning amounts to finding the smallest , which leads to a satisfactory closedloop behavior....
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Journal Article•DOI•

Control of systems integrating logic, dynamics, and constraints

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Alberto Bemporad¹, Manfred Morari¹•Institutions (1)

École Polytechnique Fédérale de Lausanne¹

01 Mar 1999-Automatica

TL;DR: A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules.

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2,980 citations

"An MPC/hybrid system approach to tr..." refers background or methods in this paper

...Mixed logic dynamical (MLD) systems [9] allow specifying the evolution of continuous variables through linear dynamic equations, of binary variables through propositional logic statements and automata, and the mutual interaction between the two....
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...By collecting the equalities and inequalities derived from the representation of the hybrid system, we obtain the MLD system [9]...
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...In this paper, we describe how the hybrid framework [9] and the optimization-based control strategy [12] can be successfully applied for solving the traction control problem in a systematic way....
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...The key idea of the approach consists of embedding the logic part in the state equations by transforming Boolean variables into 0–1 integers, and by expressing the relations as mixed-integer linear inequalities [9], [14], [24], [30]....
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...Recently, we proposed a new framework for modeling hybrid systems [9] and an algorithm to synthesize piecewise linear (indeed, piecewise affine) optimal controllers for such systems [11], [12]....
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Journal Article•DOI•

A clustering technique for the identification of piecewise affine systems

[...]

Giancarlo Ferrari-Trecate¹, Marco Muselli, Diego Liberati², Manfred Morari¹•Institutions (2)

École Polytechnique Fédérale de Lausanne¹, Polytechnic University of Milan²

01 Feb 2003-Automatica

TL;DR: An algorithm is provided that exploits the combined use of clustering, linear identification, and pattern recognition techniques to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures.

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612 citations

"An MPC/hybrid system approach to tr..." refers methods in this paper

...1) The frictional torque is approximated as a piecewise affine function of the slip and of the road coefficient of friction by using the approach described in [16]....
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...Such a model is based on a simplified model and a set of parameters provided by Ford Research Laboratories, and involves piecewise linearization techniques of the nonlinear torque function that are based on hybrid system identification tools [16]....
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...The algorithm proposed in [16] generates a polyhedral partition of the -space and the corresponding affine approximation of the torque in each region....
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Journal Article•DOI•

Slip-based tire-road friction estimation

[...]

Fredrik Gustafsson¹•Institutions (1)

Linköping University¹

01 Jun 1997-Automatica

TL;DR: An approach to estimate the tire-road friction using only the wheel slip, that is, the relative difference in wheel velocities, is presented and an adaptive estimator is presented for a model linear in parameters, designed to work for periods of poor excitation, errors in variables, simultaneous slow and fast parameter drifts and abrupt changes.

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545 citations