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Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

2016 IEEE Control Systems  
Stochastic Model Predictive Control M odel predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems [1], [2].  ...  The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control  ...  MPC of stochastic linear systems has been investigated in a series of articles [50] - [53] . A discrete-time system subject to unbounded disturbances with bounded variance is considered in [50] .  ... 
doi:10.1109/mcs.2016.2602087 fatcat:k62qjtmbbzh4tcprcjufparf64

Recursively Feasible Stochastic Model Predictive Control using Indirect Feedback [article]

Lukas Hewing, Kim P. Wabersich, Melanie N. Zeilinger
2019 arXiv   pre-print
We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences.  ...  Chance constraints are treated in analogy to robust MPC using the concept of probabilistic reachable sets for constraint tightening.  ...  ACKNOWLEDGMENTS The authors would like to thank A. Bollinger, C. Gaehler, J. Lygeros, and R. Smith for providing the building control simulation model.  ... 
arXiv:1812.06860v2 fatcat:cnkvysb73ngmzmzfebiqbii67u

Stochastic and Robust MPC for Bipedal Locomotion: A Comparative Study on Robustness and Performance [article]

Ahmad Gazar, Majid Khadiv, Andrea Del Prete, Ludovic Righetti
2020 arXiv   pre-print
Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots.  ...  In this letter, we propose for the first time to use linear stochastic MPC (SMPC) to account for uncertainties in bipedal walking.  ...  Stochastic (OCP) formulation and control objectives Consider the following discrete-LTI prediction model subject to additive stochastic disturbance w t : x t+i+1|t = Ax t+i|t + Bu t+i|t + w t+i , (15a)  ... 
arXiv:2005.07555v2 fatcat:x3vxbzysgrc7tdnbtom7itzcty

A tractable approximation of chance constrained stochastic MPC based on affine disturbance feedback

Frauke Oldewurtel, Colin N. Jones, Manfred Morari
2008 2008 47th IEEE Conference on Decision and Control  
This paper deals with model predictive control of uncertain linear discrete-time systems with polytopic constraints on the input and chance constraints on the states.  ...  We show that in the presence of chance constraints and stochastic disturbances, this closed-loop formulation can be used together with a tractable approximation of the chance constraints to further increase  ...  INTRODUCTION This paper deals with solving a model predictive control (MPC) problem for the class of discrete-time linear systems subject to stochastic disturbances.  ... 
doi:10.1109/cdc.2008.4738806 dblp:conf/cdc/OldewurtelJM08 fatcat:24jdkoinhzf55hfll4rlpsyezy

Stochastic Model Predictive Control using Initial State Optimization [article]

Henning Schlüter, Frank Allgöwer
2022 arXiv   pre-print
Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use constraint tightening based on probabilistic reachable sets to design the  ...  We show that the stabilizing control scheme can guarantee constraint satisfaction in closed loop, assuming unimodal disturbances.  ...  For linear time-invariant systems with general additive stochastic disturbances, we have shown that standard guarantees can still be obtained.  ... 
arXiv:2203.01844v2 fatcat:v352kvcqyfdb5goemp6rduqwjm

Learning Stochastic Parametric Differentiable Predictive Control Policies [article]

Ján Drgoňa, Sayak Mukherjee, Aaron Tuor, Mahantesh Halappanavar, Draguna Vrabie
2022 arXiv   pre-print
linear systems subject to nonlinear chance constraints.  ...  The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods  ...  In particular, we consider the linear quadcopter model 1 with x k ∈ R 12 , and u k ∈ R 4 , subject to additive uncertainties ω k ∈ R 12 ∼ N (0, 0.02 2 ).  ... 
arXiv:2203.01447v2 fatcat:mysvqaloqbdhleaw5xluvyzvhi

Discrete-Time Model Predictive Control [chapter]

Li Dai, Yuanqing Xia, Mengyin Fu, Magdi S.
2012 Advances in Discrete Time Systems  
Linear Model Predictive Control MPC has become an attractive feedback strategy, especially for linear processes. "y now, linear MPC theory is quite mature.  ...  More than years after model predictive control MPC or receding horizon control RHC appeared in industry as an effective tool to deal with multivariable constrained control problems, a theoretical basis  ...  With respect to other results on networked control, in [ ], stability and disturbance attenuation issues for a class of linear networked control systems subject to data losses mod-Advances in Discrete  ... 
doi:10.5772/51122 fatcat:5ucjd5ecprcrtdtcihz2bw6lkq

A Probabilistic Particle-Control Approximation of Chance-Constrained Stochastic Predictive Control

Lars Blackmore, Masahiro Ono, Askar Bektassov, Brian C. Williams
2010 IEEE Transactions on robotics  
In this paper, we present a novel method for chance-constrained predictive stochastic control of dynamic systems.  ...  This uncertainty arises due to uncertain state estimation, disturbances, and modeling errors, as well as stochastic mode transitions such as component failures.  ...  This scenario approach can be applied to chance-constrained predictive control problems with non-Gaussian noise and linear system dynamics.  ... 
doi:10.1109/tro.2010.2044948 fatcat:qjjnhug7i5hn7makakx2dx64lq

Data-Driven Distributed Stochastic Model Predictive Control with Closed-Loop Chance Constraint Satisfaction [article]

Simon Muntwiler, Kim P. Wabersich, Lukas Hewing, Melanie N. Zeilinger
2020 arXiv   pre-print
In this work, we propose a distributed stochastic model predictive control (DSMPC) scheme for dynamically coupled linear discrete-time systems subject to unbounded additive disturbances that are potentially  ...  Distributed model predictive control methods for uncertain systems often suffer from considerable conservatism and can tolerate only small uncertainties, due to the use of robust formulations that are  ...  In model predictive control (MPC), resulting uncertainties are often modeled through additive disturbances acting on the system.  ... 
arXiv:2004.02907v1 fatcat:ib4aerw4ujdqhnkjqblbxy4btm

A probabilistic validation approach for penalty function design in Stochastic Model Predictive Control

Martina Mammarella, Teodoro Alamo, Sergio Lucia, Fabrizio Dabbene
2020 IFAC-PapersOnLine  
In this paper, we consider a stochastic Model Predictive Control able to account for effects of additive stochastic disturbance with unbounded support, and requiring no restrictive assumption on either  ...  This is due to the fact that the sample complexity for both probabilistic design problems depends on the prediction horizon in a logarithmic way, unlike scenario-based approaches which exhibit linear dependence  ...  CONCLUSIONS stochastic model predictive controller able to account for the effects of additive stochastic disturbances is presented in this paper.  ... 
doi:10.1016/j.ifacol.2020.12.362 fatcat:t4hsaz2l4fe3fmpsixag6ehfy4

An improved constraint-tightening approach for Stochastic MPC

Matthias Lorenzen, Frank Allgower, Fabrizio Dabbene, Roberto Tempo
2015 2015 American Control Conference (ACC)  
The online computational complexity of the resulting Model Predictive Control (MPC) algorithm is similar to that of a nominal MPC with terminal region.  ...  The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing  ...  Ongoing work includes relaxing the assumption of identically and independently distributed disturbance to e.g.  ... 
doi:10.1109/acc.2015.7170855 dblp:conf/amcc/LorenzenADT15 fatcat:lmctny3kzncxvh3oxtjclaesry

Stochastic Model Predictive Control for Linear Systems Using Probabilistic Reachable Sets

Lukas Hewing, Melanie N. Zeilinger
2018 2018 IEEE Conference on Decision and Control (CDC)  
In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints  ...  Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.  ...  INTRODUCTION Robust model predictive control (MPC) methods are wellestablished for dealing with bounded disturbances in a principled way [1] .  ... 
doi:10.1109/cdc.2018.8619554 dblp:conf/cdc/HewingZ18 fatcat:b6agji6znvghjkkms6vdr7anpi

Stochastic Model Predictive Control for Building HVAC Systems: Complexity and Conservatism

Yudong Ma, Jadranko Matusko, Francesco Borrelli
2015 IEEE Transactions on Control Systems Technology  
This paper presents a stochastic model predictive control (SMPC) approach to building heating, ventilation, and air conditioning (HVAC) systems.  ...  Index Terms-Building energy system, nonlinear system, stochastic model predictive control (SMPC).  ...  The authors would like to thank the anonymous reviewers for their helpful comments on the original version of the manuscript.  ... 
doi:10.1109/tcst.2014.2313736 fatcat:md2ny5mkg5bsvm4s2sixard2fm

Stochastic model predictive control with joint chance constraints

Joel A. Paulson, Edward A. Buehler, Richard D. Braatz, Ali Mesbah
2017 International Journal of Control  
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  ...  Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization.  ...  AFigure 2 : 2 tractable convex optimization program is derived to solve receding-horizon stochastic model predictive control of linear systems with (possibly) unbounded stochastic disturbances.  ... 
doi:10.1080/00207179.2017.1323351 fatcat:6twj4dibffaqxcrjnrbtnzz7gu

Stochastic Model Predictive Control Using Simplified Affine Disturbance Feedback for Chance-Constrained Systems

Jingyu Zhang, Toshiyuki Ohtsuka
2020 IEEE Control Systems Letters  
This letter covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and chance constraints on their state and control input.  ...  We propose a simplified control parameterization under the framework of affine disturbance feedback, and we show that our method is equivalent to parameterization over the family of state feedback policies  ...  Content may change prior to final publication. Citation information: DOI 10.1109/LCSYS.2020.3042085, IEEE Control Systems Letters  ... 
doi:10.1109/lcsys.2020.3042085 fatcat:sxvivjcrjzdq3mt2x74ufwprae
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