Stochastic Tubes in Model Predictive Control With Probabilistic Constraints

Cannon, Mark; Kouvaritakis, B.; Raković, Sas̆a V.; Cheng, Qifeng

doi:10.1109/tac.2010.2086553

Cited by 219 publications

(192 citation statements)

References 19 publications

Supporting

Mentioning

190

Contrasting

Order By: Relevance

“…Recent work [83,84] proposed SMPC algorithms that use probabilistic information on additive disturbances in order to minimize the expected value of a predicted cost subject to hard and soft (probabilistic) constraints. Stochastic tubes were used to provide a recursive guarantee of feasibility and thus ensure closed loop stability and constraint satisfaction.…”

Section: Earlier Workmentioning

confidence: 99%

Discrete-Time Model Predictive Control

Li¹,

Xia²,

Fu³

et al. 2012

Advances in Discrete Time Systems

View full text Add to dashboard Cite

Section: Earlier Workmentioning

confidence: 99%

Discrete-Time Model Predictive Control

Li¹,

Xia²,

Fu³

et al. 2012

Advances in Discrete Time Systems

View full text Add to dashboard Cite

“…The first class consists of stochastic tube approaches [5,6,7] that use stochastic tubes with fixed or variable cross sections to replace chance constraints with linear constraints on the nominal state predictions and to construct terminal sets for guaranteeing recursive feasibility. These approaches use a prestabilizing feedback controller to ensure closed-loop stability.…”

Section: Introductionmentioning

confidence: 99%

Stochastic model predictive control with joint chance constraints

Paulson

Buehler

Braatz

et al. 2017

International Journal of Control

105

View full text Add to dashboard Cite

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states.A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.

show abstract

“…The occurrence of probabilistic constraints mainly arises from two reasons: one is that random uncertainty may have infinitely support such that constraints will be impossible to be obeyed with a probability of 100%, and the other is that probabilistic constraints can lead to considerably better performance when the corresponding deterministic constraints are over conservative. There are several interesting progresses on the research of the theory of SMPC recently (Cannon et al 2011;Oldewurtel et al 2013;Calafiore and Fagiano 2013;Kouvaritakis et al 2010;Cannon et al 2012), which readers can refer to.…”

Section: Introduction Of Smpcmentioning

confidence: 99%

Modelling of coal trade process for the logistics enterprise and its optimisation with stochastic predictive control

Cheng

Ning

Xia

et al. 2015

International Journal of Production Research

Self Cite

View full text Add to dashboard Cite

In the paper, a typical coal trade process is described and modelled, where one logistics enterprise with blending equipments lies in the core and two types of common contracts are elucidated to define constraints. A mixed-integer model is built and featured by addressing contract violation, blending operation, real time price information and arbitrarily distributed stochastic demands. To deal with the stochastic demands, probabilistic constraints are formed. Accordingly, stochastic model predictive control (SM-PC) strategy with both receding horizon and decreasing horizon formulations is developed to handle the probabilistic constraints and exploit the value of newest price information. By solving a series of mixed-integer linear programs, optimal coal trade decisions for the logistics enterprise can be obtained, including procurement decision, selling decision and operational decision of the blending equipments. Thorough simulation experiments are carried out and compared under three different strategies, which interpret the effectiveness of the proposed strategy.

show abstract

Stochastic Tubes in Model Predictive Control With Probabilistic Constraints

Cited by 219 publications

References 19 publications

Discrete-Time Model Predictive Control

Discrete-Time Model Predictive Control

Stochastic model predictive control with joint chance constraints

Modelling of coal trade process for the logistics enterprise and its optimisation with stochastic predictive control

Contact Info

Product

Resources

About