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Stabilizing model predictive control of stochastic constrained linear systems

Bernardini, Daniele and Bemporad, Alberto Stabilizing model predictive control of stochastic constrained linear systems. IEEE Transactions on Automatic Control , 57 (6). 1468 -1480 . ISSN 0018-9286 (2012)

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This paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop performance while enforcing constraints. Conditions for stochastic convergence and robust constraints fulfillment of the closed-loop system are enforced by solving linear matrix inequality problems off line. Performance is optimized on line using multi-stage stochastic optimization based on enumeration of scenarios, that amounts to solving a quadratic program subject to either quadratic or linear constraints. In the latter case, an explicit form is computable to ease the implementation of the proposed SMPC law. The approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution. The effectiveness of the proposed SMPC formulation is shown on a numerical example and compared to traditional MPC schemes.

Item Type: Article
Identification Number: 10.1109/TAC.2011.2176429
Projects: This work was partially supported by the European project E-PRICE: Pricebased Control of Electrical Power Systems, FP7-IST contract no. 249096.
Uncontrolled Keywords: Model predictive control , constrained linear systems , stochastic control
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 09 Jan 2012 14:07
Last Modified: 01 Jul 2014 13:34
URI: http://eprints.imtlucca.it/id/eprint/1051

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