scholarly journals General LQG Homing Problems in One Dimension

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Mario Lefebvre ◽  
Foued Zitouni
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Diffusion Processes ◽  
Approximate Solutions ◽  
One Dimension ◽  
Control Problems ◽  
One Dimensional ◽  
Controlled Processes ◽  
Dimensional Diffusion ◽  
The One

Optimal control problems for one-dimensional diffusion processes in the interval (d1,d2) are considered. The aim is either to maximize or to minimize the time spent by the controlled processes in (d1,d2). Exact solutions are obtained when the processes are symmetrical with respect to d∗∈(d1,d2). Approximate solutions are derived in the asymmetrical case. The one-barrier cases are also treated. Examples are presented.

scholarly journals Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Foued Zitouni ◽  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Dimensional Problem ◽  
Matrix Riccati Equation ◽  
One Dimensional ◽  
The Matrix ◽  
The One

The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.

scholarly journals Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Francesco Topputo ◽  
Franco Bernelli-Zazzera
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Approximate Solutions ◽  
Nonlinear Optimal Control ◽  
The State ◽  
Control Problems ◽  
Linear Quadratic ◽  
Approximating Sequence

A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as “approximating sequence of Riccati equations.” Sample problems in astrodynamics are treated to show the effectiveness of the method, whose limitations are also discussed.

scholarly journals Constants within Error Estimates for Legendre-Galerkin Spectral Approximations of Control-Constrained Optimal Control Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jianwei Zhou
Keyword(s):  
Optimal Control ◽  
Error Estimate ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
One Dimensional ◽  
Error Indicator ◽  
Spectral Approximations ◽  
Explicit Formulae

Explicit formulae of constants within the aposteriorierror estimate for optimal control problems are investigated with Legendre-Galerkin spectral methods. The constrained set is put on the control variable. For simpleness, one-dimensional bounded domain is taken. Meanwhile, the corresponding aposteriorierror indicator is established with explicit constants.

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