Imperial College London
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ProfessorThomasParisini

Faculty of Engineering, Department of Electrical and Electronic Engineering

Chair in Industrial Control, Head of Group for CAP
 
 
 
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Contact

 

+44 (0)20 7594 6240t.parisini Website

 
 
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Location

 

1114Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inbook{Zoppoli:2020:10.1007/978-3-030-29693-3_6,
author = {Zoppoli, R and Sanguineti, M and Gnecco, G and Parisini, T},
booktitle = {Communications and Control Engineering},
doi = {10.1007/978-3-030-29693-3_6},
pages = {255--298},
title = {Deterministic optimal control over a finite Horizon},
url = {http://dx.doi.org/10.1007/978-3-030-29693-3_6},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - CHAP
AB  - This chapter addresses discrete-time deterministic problems, where optimal controls have to be generated at a finite number of decision stages. No random variables influence either the dynamic system or the cost function. Then, there is no necessity of estimating the state vector. Such optimization problems are stated for their intrinsic practical importance and to describe the basic concepts of dynamic programming. As the problems are formulated under very general assumptions, their optimal solutions cannot be found in an analytical form. Therefore, we resort to an approximation consisting of the discretization of the state space into suitable grids at each decision stage. The discretization by regular grids is the simplest approach (and the one most widely used until some time ago). However, unless a small dimension of the state space is considered, this approach leads to an exponential growth of the number of samples, and thus to the curse of dimensionality. Therefore, the discretization by deterministic sequences of samples is addressed, which spread the samples in the most uniform way. Specifically, low-discrepancy sequences are considered, like quasi-Monte Carlo sequences. We also point out that the optimization problem can even be viewed as a nonlinear programming problem solvable by gradient-based descent techniques.
AU  - Zoppoli,R
AU  - Sanguineti,M
AU  - Gnecco,G
AU  - Parisini,T
DO  - 10.1007/978-3-030-29693-3_6
EP  - 298
PY  - 2020///
SP  - 255
TI  - Deterministic optimal control over a finite Horizon
T1  - Communications and Control Engineering
UR  - http://dx.doi.org/10.1007/978-3-030-29693-3_6
ER  -
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