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Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets

Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets,10.1016/j.automatica.2006.05.003,Automatica,J. M. Bravo

Robust MPC of constrained discrete-time nonlinear systems based on approximated reachable sets   (Citations: 5)
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A robust MPC for constrained nonlinear systems with uncertainties is presented. Outer bounds of the reachable sets of the system are used to predict the evolution of the system under uncertainty. A method that uses zonotopes to represent the approximated reachable sets is proposed. The closed-loop system is ultimately bounded thanks to a contractive constraint that drives the system to a robust invariant set.
Journal: Automatica , vol. 42, no. 10, pp. 1745-1751, 2006
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    • ...Outer bounds on the evolution of the states in nonlinear dynamical systems subject to disturbances and uncertain initial conditions can play an important role in many control problems including the analysis of batch and semibatch processes [1], [2], model invalidation and parameter estimation [3], [4], [5], fault diagnosis and isolation [6], [7], robust model predictive control [8], [9], [10], [11], [12], [13], and safety analysis of plant ...

    Masako Kishidaet al. Efficient polynomial-time outer bounds on state trajectories for uncer...

    • ...In the last years, the modern control theory has begun to use Set Theory in many applications [1], [4], [5], [10], [11]; because Set Theory has the advantage of allowing the inclusion of state restrictions and control action restrictions in a natural way...

    César A. Gómezet al. An approach to stability and controllability analysis in batch process...

    • ...sequence of reachable sets) based approach [7, 28, 32, 5, 44, 55, 43] has been considered...
    • ...In the case of cost functions based on nominal predictions [7, 47, 28, 32, 5, 44, 55, 43], ISS is proved subject to continuity of some ingredients...
    • ...Recently, this idea has emerged again as a tool for robust constraint satisfaction [7, 28, 32, 5, 15] or for design robust predictive controllers for linear [24, 44] and for nonlinear systems [54, 55, 43]...
    • ...This procedure is assumed to be computationally tractable and uses a specialized algorithm or property to calculate a compact set of a certain class (as for instance, balls, boxes, intervals, zonotopes, polytopes) which is an outer bound of the exact range [32, 5, 1, 54]...
    • ...In [5] the procedure used is based on zonotope inclusion and an extension of the mean value theorem, and returns a zonotope (i.e...
    • ...The idea consists in replacing the constraints on the sequence of predicted trajectory with the constraints on the sequence of predicted reachable sets derived from the current state [32, 5]. In [44], the authors propose a tube with an invariant set as constant section and centered in a nominal predicted trajectory which initial state is considered as decision variable...

    D. Limonet al. Input-to-State Stability: A Unifying Framework for Robust Model Predic...

    • ...where β is a parameter contained in (0, 1) and � A� B denotes a measure of the maximum distance between sets A and B. Clearly, if A ⊆ B, then this measure is zero. The proposed stabilizing constraint is [5]...

    D. Limonet al. Interval Arithmetic in Robust Nonlinear MPC

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