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Sampled–Data Model Predictive Control Using Adaptive Time–Mesh Refinement Algorithms

Part of the Lecture Notes in Electrical Engineering book series (LNEE,volume 402)

Abstract

We address sampled–data nonlinear Model Predictive Control (MPC) schemes, in particular we address methods to efficiently and accurately solve the underlying continuous-time optimal control problems (OCP). In nonlinear OCPs, the number of discretization points is a major factor affecting the computational time. Also, the location of these points is a major factor affecting the accuracy of the solutions. We propose the use of an algorithm that iteratively finds the adequate time–mesh to satisfy some pre–defined error estimate on the obtained trajectories. The proposed adaptive time–mesh refinement algorithm provides local mesh resolution considering a time–dependent stopping criterion, enabling an higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. The results show the advantage of the proposed adaptive mesh strategy, which leads to results obtained approximately as fast as the ones given by a coarse equidistant–spaced mesh and as accurate as the ones given by a fine equidistant–spaced mesh.

Keywords

  • Predictive control
  • Nonlinear systems
  • Optimal control
  • Real–time optimization
  • Continuous–time systems
  • Adaptive algorithms
  • Time–mesh refinement
  • Sampled-data systems

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Acknowledgments

Research carried out while the 2nd author was a visiting scholar at Texas A&M University, College Station, USA. The support from Texas A&M and FEDER/COMPETE2020-POCI/FCT funds through grants POCI-01-0145-FEDER-006933 - SYSTEC and PTDC/EEI-AUT/2933/2014 is acknowledged.

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Correspondence to Luís Tiago Paiva .

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Paiva, L.T., Fontes, F.A.C.C. (2017). Sampled–Data Model Predictive Control Using Adaptive Time–Mesh Refinement Algorithms. In: Garrido, P., Soares, F., Moreira, A. (eds) CONTROLO 2016. Lecture Notes in Electrical Engineering, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-319-43671-5_13

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  • DOI: https://doi.org/10.1007/978-3-319-43671-5_13

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