Search results for "Optimal control"
showing 10 items of 209 documents
Geometric optimal control : homotopic methods and applications
2012
This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different r…
Development and pilot-scale validation of a fuzzy-logic control system for optimization of methane production in fixed-bed reactors
2018
International audience; The objective of this study was to develop an advanced control system for optimizing the performance of fixed-bed anaerobic reactors. The controller aimed at maximizing the bio-methane production whilst controlling the volatile fatty acids content in the effluent. For this purpose, a fuzzy-logic controller was developed, tuned and validated in an anaerobic fixed-bed reactor at pilot scale (350 L) treating raw winery wastewater. The results showed that the controller was able to adequately optimize the process performance, maximizing the methane production in terms of methane flow rate, resulting in an average methane yield of about 0.29 LCH4 g−1 COD. On the other han…
Collision Avoidance Trajectory for an Ekranoplan.
2009
The risk of collision is one of the crucial aspects for the applications of Ekranoplans in civil transportation. In fact, the extremely low flight altitude of these aircraft increases dramatically the chances of interference between their flight path and the multitude of obstacles populating the surrounding area. In this work we consider the optimal collision avoidance problem between a cruising Ekranoplan and a steady obstacle located on its flight path. First we solve the optimal control problem imposing that the collision avoidance maneuver lies on the longitudinal plane identified by the initial cruising conditions. In the second part of this work we state the three-dimensional version …
Second order optimality conditions with applications
2007
International audience; The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assump- tions, the tra jectory ceases to be optimal at such a point. An implementation of this algorithm, called cotcot, is available online and based on recent devel- opments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.
Second order optimality conditions in optimal control with applications
2006
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point. An implementation of this algorithm, called \texttt{cotcot}, is available online and based on recent developments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.
Estabilización de modelos económicos dinámicos con control óptimo en tiempo continuo
1990
En esta Tesis de Licenciatura se lleva a cabo el estudio de un problema determinado de optimización dinámica y sus aplicaciones en el campo de la Ciencia Económica. Un problema de optimización consiste, fundamentalmente, en la búsqueda de un extremo de una función o un funcional objetivo que proporcione un máximo o un mínimo para esa función. Cuando se habla de optimización dinámica hay que incorporar el factor tiempo al problema, en todas y cada una de las diferentes variables que intervienen, lo que afectará a los modelos matemáticos que se empleen para representar el comportamiento y las relaciones existentes entre dichas variables. También afecta al funcional objetivo a optimizar. Así, …
Predictive control of convex polyhedron LPV systems with Markov jumping parameters
2012
The problem of receding horizon predictive control of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of linear parameter varying system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficients matrices for the time variable system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic convex polyhedron linear parameter varying systems, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon…
LPV model identification for gain scheduling control: An application to rotating stall and surge control problem
2006
Abstract We approach the problem of identifying a nonlinear plant by parameterizing its dynamics as a linear parameter varying (LPV) model. The system under consideration is the Moore–Greitzer model which captures surge and stall phenomena in compressors. The control task is formulated as a problem of output regulation at various set points (stable and unstable) of the system under inputs and states constraints. We assume that inputs, outputs and scheduling parameters are measurable. It is worth pointing out that the adopted technique allows for identification of an LPV model's coefficients without the requirements of slow variations amongst set points. An example of combined identification…
Optimal control in models with conductive‐radiative heat transfer
2003
In this paper an optimal control problem for the elliptic boundary value problem with nonlocal boundary conditions is considered. It is shown that the weak solutions of the boundary value problem depend smoothly on the control parameter and that the cost functional of the optimal control problem is Frechet differentiable with respect to the control parameter. Optimalus valdymas modeliuose su laidžiu-radioaktyviu šilumos pernešimu Santrauka Darbe nagrinejamas nelokalaus kraštinio uždavinio optimalaus valdymo uždavinys. Parodyta, kad silpnasis kraštinio uždavinio sprendinys tolydžiai priklauso nuo valdomojo parametro, taigi, optimalaus valdymo tikslo funkcija yra diferencijuojama Freše prasme…
Optimal Heating of an Indoor Swimming Pool
2020
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given…