Robust tubes in nonlinear model predictive control

Cannon, Mark; Buerger, Johannes; Kouvaritakis, B.; Raković, Sas̆a V.

doi:10.3182/20100901-3-it-2016.00202

Cited by 12 publications

(12 citation statements)

References 10 publications

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“…Tube-based approaches for nonlinear discrete-time systems have been considered in other works. [19][20][21][22][23] Farina and Scattolini 24 have addressed the linear continuous-time case. In the works of Wang et al 25 and Sun et al, 26 regarding the computation of the offline feedback controller, the discrepancy between the nominal nonlinear system with the corresponding linear system has been considered.…”

Section: Discussionmentioning

confidence: 99%

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Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

Νίκου

Dimarogonas

2019

Intl J Robust & Nonlinear

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Summary This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.

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Section: Discussionmentioning

confidence: 99%

“…Tube‐based approaches for nonlinear discrete‐time systems have been considered in other works . Farina and Scattolini have addressed the linear continuous‐time case.…”

Section: Introductionmentioning

confidence: 99%

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

Νίκου

Dimarogonas

2019

Intl J Robust & Nonlinear

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“…Accordingly, one of the current main research thrusts in Model Predictive Control (MPC) is to find techniques that can robustly address uncertainty [1,2,3]. Techniques for handling uncertainty within the MPC framework fall broadly into three categories: (1) min-max formulations, where the performance indices to be minimized are computed with respect to the worst possible disturbance realization [4,5,1], (2) tube-based formulations, where classical (uncertainty-unaware) MPC is modified to use tightened constraints and augmented with a tracking ancillary controller to maintain the system within an invariant tube around the nominal MPC trajectory [6,7,8], and (3) stochastic formulations, where risk-neutral expected values of performance indices (and possibly constraints) are considered [9,10,11,12,13] (see also the recent reviews [1,3]). The main drawback of the min-max approach is that the control law may be too conservative, since the performance index is being optimized under the worst-case disturbance realizations (which may have an arbitrarily small probability of occurring).…”

Section: Introductionmentioning

confidence: 99%

A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms

Singh

Chow

Majumdar

et al. 2019

IEEE Trans. Automat. Contr.

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In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the cumulative cost as the objective function to be minimized. This framework is axiomatically justified in terms of time-consistency of risk assessments, is amenable to dynamic optimization, and is unifying in the sense that it captures a full range of risk preferences from risk-neutral (i.e., expectation) to worst case. Within this framework, we propose and analyze an online risk-sensitive MPC algorithm that is provably stabilizing. Furthermore, by exploiting the dual representation of time-consistent, dynamic risk measures, we cast the computation of the MPC control law as a convex optimization problem amenable to real-time implementation. Simulation results are presented and discussed.

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“…Tube MPC uses an uncertainty prediction in form of a tube and has been extended to nonlinear predictive control for example in [18], [19]. Nonlinear, robust predictive control approaches for discrete time MPC using the computation of reachable sets are investigated in [20] using Lipschitz continuity and in [21] utilizing interval analysis.…”

Section: Introductionmentioning

confidence: 99%

Discrete-time robust model predictive control for continuous-time nonlinear systems

Kögel¹,

Findeisen²

2015

2015 American Control Conference (ACC)

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We consider robust predictive control of continuous-time, constrained, nonlinear systems by means of a discrete-time control scheme. The key idea is to discretize the system first and to explicitly bound the arising discretization error. Taking this error into account a robustly stabilizing predictive controller is proposed that guarantees constraint satisfaction at the sampling instances and via a simple modification also continuous constraint satisfaction. The results are illustrated by an example.

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Robust tubes in nonlinear model predictive control

Cited by 12 publications

References 10 publications

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

A Framework for Time-Consistent, Risk-Sensitive Model Predictive Control: Theory and Algorithms

Discrete-time robust model predictive control for continuous-time nonlinear systems

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