2017
DOI: 10.1080/00207179.2017.1323351
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Stochastic model predictive control with joint chance constraints

Abstract: 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 guara… Show more

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Cited by 110 publications
(94 citation statements)
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“…An algorithm is then presented for solving two convex optimization problems iteratively to determine the best feedback gain and optimal risk allocation. Simulation studies show that optimizing the risk allocation in [55] can lead to improved control performance as compared to an MPC algorithm with fixed risk allocation.…”
Section: Approaches Based On Affine Parameterization Of the Control Pmentioning
confidence: 99%
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“…An algorithm is then presented for solving two convex optimization problems iteratively to determine the best feedback gain and optimal risk allocation. Simulation studies show that optimizing the risk allocation in [55] can lead to improved control performance as compared to an MPC algorithm with fixed risk allocation.…”
Section: Approaches Based On Affine Parameterization Of the Control Pmentioning
confidence: 99%
“…The main shortcomings of the SMPC algorithm presented in [73] are 1) an inability to consider saturation functions in the control policy to enable handling hard input bounds (as in [52]), 2) the conservatism associated with the Chebyshev-Cantelli inequality used for chance constraint approximation, and 3) nonconvexity of the algorithm. Using a problem setup similar to that in [52] and [73], an SMPC approach is presented in [55] that can handle joint state chance constraints and hard input constraints under closed-loop prediction in the presence of arbitrary (possibly unbounded) additive disturbances. The SMPC approach uses risk allocation [83], [84] in combination with the Cantelli-Chebyshev inequality to obtain computationally tractable surrogates for the joint state-chance constraints when the first two moments of the arbitrary disturbance distributions are known.…”
Section: Approaches Based On Affine Parameterization Of the Control Pmentioning
confidence: 99%
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