On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach |
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Affiliation: | 2. Research Center for Automatic Control of Nancy (CRAN), Université de Lorraine, IUT de Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France\n |
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Abstract: | In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system. |
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Keywords: | Jump linear systems Stochastic model predictive control Probabilistic state constraints Linear state-feedback Second moment stability |
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