Explicit use of probabilistic distributions in linear predictive control

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

doi:10.1016/j.automatica.2010.06.034

Cited by 173 publications

(136 citation statements)

References 9 publications

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“…Unlike the approaches of [5], [13], which assume the additive disturbance lies in a compact set, the disturbance ω k is not assumed to be bounded and its distribution may have infinite support. It is assumed that the system state is measured directly and available to the controller at each sample instant.…”

Section: Problem Descriptionmentioning

confidence: 99%

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

Yan

Goulart

Cannon

2018

2018 European Control Conference (ECC)

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This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law to minimise a quadratic cost function subject to a chance constraint. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and ignoring violation probabilities in the far future, this form of constraint enables the feasibility of the online optimisation to be guaranteed without an assumption of boundedness of the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility based on knowledge of a suboptimal solution. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition.

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Section: Problem Descriptionmentioning

confidence: 99%

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

Yan

Goulart

Cannon

2018

2018 European Control Conference (ECC)

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“…Theorem 2. Consider the scalar system (55) with cost function (16) and constraints (17), (18)- (20). Then, POMPC on horizon N yields the same control input as traditional (average) MPC on horizon N and SOMPC on horizon N.…”

Section: Pompc and Sompc Are Equivalent To Average Mpc For A Scalar Smentioning

confidence: 99%

“…Examples of stochastic MPC can be found in related works. [18][19][20][21][22][23] . In-depth discussions of the topic can be found in the works of Mayne 2 and Mesbah.…”

Section: Introductionmentioning

confidence: 99%

Stochastic model predictive control: Insights and performance comparisons for linear systems

Serón

Goodwin

Carrasco

2018

Intl J Robust & Nonlinear

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In this paper, we define several instances of model predictive control (MPC) for linear systems, including both deterministic and stochastic formulations.We show by explicit computation of the associated control laws that, under certain conditions, different formulations lead to identical results. This paper provides insights into the performance of stochastic MPC. Amongst other things, it shows that stochastic MPC and traditional MPC can give identical results in special cases. In cases where the solutions are different, we show that the explicit formulation of the problem can give insight into the performance gap.KEYWORDS linear systems, model predictive control, stochastic predictive control 5038

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“…In the sequel, we will design the MPC algorithm based on the autonomous system descriptions (15) to (17). Inspired by Kouvaritakis et al, 20 to guarantee constraint (16), we give the following lemma. Lemma 3.…”

Section: Predictive Control Law Designmentioning

confidence: 99%

“…As pointed out by Kouvaritakis et al, 20 finite support assumption of random disturbance is more general in real applications compared with the one of infinite support. For the case of infinite support, probabilistically constrained MPC designs have also been addressed.…”

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confidence: 99%

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Lǚ

2017

Intl J Robust & Nonlinear

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Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode-dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady-state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed-loop long-run average cost is not more than that of the unconstrained closed-loop system with static feedback.Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results. KEYWORDSlong-run average cost, Markovian jump linear systems, maximal admissible sets, optimal control, probabilistic constraints, stochastic model predictive control INTRODUCTIONMarkovian jump linear systems (MJLSs), as an important class of stochastic hybrid systems, are usually used to model dynamics, whose structures are subject to random abrupt changes. These changes are usually common in economic systems, aircraft control systems, solar thermal central receivers, etc. 1 Extensive applications of MJLSs make their research a hot research topic in past decades. [1][2][3][4][5][6][7][8] In real applications, due to physical limitations and/or safety and performance requirements, constraints are very common. For dealing with constraints, model predictive control (MPC) is a powerful tool. Thus, MPC for MJLSs has been attracting more and more attention. [3][4][5][9][10][11][12][13][14] 5002

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Explicit use of probabilistic distributions in linear predictive control

Cited by 173 publications

References 9 publications

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

Stochastic model predictive control: Insights and performance comparisons for linear systems

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

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