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Developments in Model-Based Optimization and Control pp 277–300Cite as

An Optimization-Based Framework for Impulsive Control Systems

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 464))

Abstract

This chapter concerns a discrete-time sampling state feedback control optimizing framework for dynamic impulsive systems. This class of control systems differs from the conventional ones in that the control space is enlarged to contain measures and, thus, the associated trajectories are merely of bounded variation. In other words, it may well exhibit jumps. We adopt the most recent impulsive control solution concept that pertains to important classes of engineering systems and, in this context, present impulsive control theory results on invariance, stability , and sampled data trajectories having in mind the optimization-based framework that relies on an MPC-like scheme. The stability of the proposed MPC scheme is addressed.

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Notes

  1. 1.

    This problem can be solved by using direct methods or indirect methods which take advantage of necessary conditions of optimality, possibly, in the form of a maximum principle such as the ones proved in [9, 10].

  2. 2.

    Here, we consider a mathematical abstraction of a scheme whose physical realization may involve sampling “during” the “atomic activities” at a frequency several orders of magnitude higher than the one when the trajectory is evolving continuously.

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Acknowledgments

All the authors gratefully acknowledge the support of FCT under the projects “Advanced control of a fleet of heterogeneous autonomous vehicles” (PESSOA program), PTDC/EEI-AUT/1450/2012 and “Incentivo/EEI/UI0147/2014.” The first three authors also acknowledge the support of FCT under the projects PEst-OE/EEI/UI0147/2014, and the R&D unit SYSTEC—UID/EEA/00147/2013.

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Authors and Affiliations

  1. LSTS—Laboratory of Underwater Systems and Technologies, SYSTEC—Research Center for Systems and Technologies, ISR—Institute for Systems and Robotics, Faculty of Engineering, Porto University (FEUP), 4200-465, Porto, Portugal

    Fernando Lobo Pereira & António Pedro Aguiar

  2. SYSTEC—Research Center for Systems and Technologies, ISR—Institute for Systems and Robotics, Faculty of Engineering, Porto University (FEUP), 4200-465, Porto, Portugal

    Fernando A. C. C. Fontes

  3. LSTS—Laboratory of Underwater Systems and Technologies, Faculty of Engineering, Porto University (FEUP), 4200-465, Porto, Portugal

    João Borges de Sousa

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  1. Fernando Lobo Pereira
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  2. Fernando A. C. C. Fontes
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  3. António Pedro Aguiar
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  4. João Borges de Sousa
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Correspondence to Fernando Lobo Pereira .

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Editors and Affiliations

  1. Laboratory of Signals and Systems, CentraleSupélec-CNRS-Université Paris-Sud, Université Paris-Saclay, Gif sur Yvette, France

    Sorin Olaru

  2. Department of Industrial Automation, Univ. of Chem.Tech. and Metallurgy Department of Industrial Automation, Sofia, Bulgaria

    Alexandra Grancharova

  3. Faculty of Engineering, Porto University Faculty of Engineering, Porto, Portugal

    Fernando Lobo Pereira

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Lobo Pereira, F., Fontes, F.A.C.C., Pedro Aguiar, A., Borges de Sousa, J. (2015). An Optimization-Based Framework for Impulsive Control Systems. In: Olaru, S., Grancharova, A., Lobo Pereira, F. (eds) Developments in Model-Based Optimization and Control. Lecture Notes in Control and Information Sciences, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-26687-9_13

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  • DOI: https://doi.org/10.1007/978-3-319-26687-9_13

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