Capítols de llibre
http://hdl.handle.net/2117/6474
2024-03-28T09:54:22ZOn the numerical stability of discretised optimal control problems
http://hdl.handle.net/2117/399249
On the numerical stability of discretised optimal control problems
Bijalwan, Ashutosh; Muñoz Romero, José
Optimal Control Problems (OCP) consist in optimising an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation is discretised in time. In particular, we analyse a OCP with a quadratic functional and linear ODE, discretised with Mid-point and implicit Euler. We show that the numerical stability and the presence of numerical oscillations depends not only on the time-step size, but also on the parameters of the objective functional, which measures the amount of control input. Finally, we also show with an illustrative example that these results also carry over non-linear optimal control problems.
2024-01-12T11:02:06ZBijalwan, AshutoshMuñoz Romero, JoséOptimal Control Problems (OCP) consist in optimising an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation is discretised in time. In particular, we analyse a OCP with a quadratic functional and linear ODE, discretised with Mid-point and implicit Euler. We show that the numerical stability and the presence of numerical oscillations depends not only on the time-step size, but also on the parameters of the objective functional, which measures the amount of control input. Finally, we also show with an illustrative example that these results also carry over non-linear optimal control problems.Differential equations
http://hdl.handle.net/2117/366031
Differential equations
Zlotnik, Sergio; Soler Villanueva, Jaume
The Encyclopedia of Mathematical Geosciences is a complete and authoritative reference work. It provides concise explanation on each term that is related to Mathematical Geosciences. Over 300 international scientists, each expert in their specialties, have written over 300 separate articles on different topics of mathematical geosciences including contributions on Artificial Intelligence, Big Data, Compositional Data Analysis, Geomathematics, Geostatistics, Mathematical Morphology, Mathematical Petrology, Multifractals, Multiple Point Statistics and Stochastic Process Modeling. Each topic incorporates cross-referencing to related articles, and also has its own reference list to lead the reader to essential articles within the published literature. The entries are arranged alphabetically, for easy access, and the subject and author indices are comprehensive and extensive.
2022-04-19T09:14:21ZZlotnik, SergioSoler Villanueva, JaumeThe Encyclopedia of Mathematical Geosciences is a complete and authoritative reference work. It provides concise explanation on each term that is related to Mathematical Geosciences. Over 300 international scientists, each expert in their specialties, have written over 300 separate articles on different topics of mathematical geosciences including contributions on Artificial Intelligence, Big Data, Compositional Data Analysis, Geomathematics, Geostatistics, Mathematical Morphology, Mathematical Petrology, Multifractals, Multiple Point Statistics and Stochastic Process Modeling. Each topic incorporates cross-referencing to related articles, and also has its own reference list to lead the reader to essential articles within the published literature. The entries are arranged alphabetically, for easy access, and the subject and author indices are comprehensive and extensive.Numbers: Natural numbers, principle of induction and complex numbers
http://hdl.handle.net/2117/363373
Numbers: Natural numbers, principle of induction and complex numbers
Pozo Montero, Francesc; Parés Mariné, Núria; Vidal Seguí, Yolanda; García López, Alfonsa; Lapedriza Garcia, Àgata
2022-03-03T12:00:36ZPozo Montero, FrancescParés Mariné, NúriaVidal Seguí, YolandaGarcía López, AlfonsaLapedriza Garcia, ÀgataSucesiones y series de números reales
http://hdl.handle.net/2117/354239
Sucesiones y series de números reales
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T13:12:03ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaIntegración: El problema del área
http://hdl.handle.net/2117/354237
Integración: El problema del área
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T13:10:19ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaDerivación: El problema de la tangente
http://hdl.handle.net/2117/354236
Derivación: El problema de la tangente
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T13:08:20ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaLímites de funciones y continuidad
http://hdl.handle.net/2117/354230
Límites de funciones y continuidad
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T12:56:19ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaFunciones reales de variable real. Introducción al cálculo
http://hdl.handle.net/2117/354227
Funciones reales de variable real. Introducción al cálculo
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T12:51:40ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaSuccessions i sèries de nombres reals
http://hdl.handle.net/2117/354221
Successions i sèries de nombres reals
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T12:47:56ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, NúriaIntegració. El problema de l'àrea
http://hdl.handle.net/2117/354219
Integració. El problema de l'àrea
Pozo Montero, Francesc; Ripoll Missé, Jordi; Parés Mariné, Núria
2021-10-21T12:46:15ZPozo Montero, FrancescRipoll Missé, JordiParés Mariné, Núria