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Stability Conditions for Linear Time-Varying Model Predictive Control in Autonomous Driving
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-6802-7520
KTH, School of Technology and Health (STH), Medical Engineering, Medical Imaging. KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems. KTH, School of Engineering Sciences (SCI), Applied Physics, Biomedical and X-ray Physics.ORCID iD: 0000-0002-3672-5316
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, Superseded Departments (pre-2005), Signals, Sensors and Systems. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.ORCID iD: 0000-0002-1927-1690
2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

This paper presents stability conditions when designing a linear time-varying model predictive controller for lateral control of an autonomous vehicle. Stability is proved via Lyapunov techniques by adding a terminal state constraint and a terminal cost. We detail how to compute the terminal state and the terminal cost for the linear time-varying case, and interpret the obtained results in the light of an autonomous driving application. To determine the stability conditions, the concept of multi-model description is used, where the linear time-varying model is separated into a finite number of time- invariant models that depend on a single parameter. The terminal set is the maximum positive invariant set of the multi- model description and the terminal cost is the result of a min-max optimization that determines the worst time-invariant model if used as a prediction model. In fact, in the autonomous driving case, we show that the min-max approach is a convex optimization problem. The stability conditions are computed offline, maintain the convexity of the optimization, and do not affect the execution time of the controller. In simulation, we demonstrate the stabilizing effectiveness of the proposed conditions through an illustrative example of path following with a heavy-duty vehicle. 

Place, publisher, year, edition, pages
2017.
Keyword [en]
Autonomous Driving, Model Predictive Control, Stability
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-220576OAI: oai:DiVA.org:kth-220576DiVA: diva2:1169480
Conference
IEEE Conference on Decision and Control
Available from: 2017-12-27 Created: 2017-12-27 Last updated: 2017-12-27

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Lima, Pedro F.Mårtensson, JonasWahlberg, Bo

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Automatic ControlACCESS Linnaeus CentreMedical ImagingSignals, Sensors and SystemsBiomedical and X-ray PhysicsOptimization and Systems TheoryCentre for Autonomous Systems, CAS
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