Optimal Control Problem for Linear System Based on Adaptive Dynamics Programming and Gradient Descent Method

2021 ◽  
Author(s):  
Yanzhi Wu ◽  
Lu Liu
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Gradient Descent ◽  
Adaptive Dynamics ◽  
Descent Method ◽  
Gradient Descent Method

scholarly journals Mean-field optimal control for biological pattern formation

2021 ◽  
Author(s):  
Martin Burger ◽  
Lisa Maria Kreusser ◽  
Claudia Totzeck
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Mean Field ◽  
Wasserstein Distance ◽  
Descent Method ◽  
Gradient Descent Method ◽  
First Order ◽  
First Order Optimality Conditions

We propose a mean-field optimal control problem for the parameter identification of a  given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The first-order optimality conditions corresponding to the optimal control problem are derived using a Lagrangian approach on the mean-field level. Based on these conditions we propose a gradient descent method to identify relevant parameters such as angle of rotation  and force scaling which may be spatially inhomogeneous. We discretize the first-order optimality conditions in order to employ the algorithm on the particle level.  Moreover, we prove a rate for the convergence of the controls as the number of particles used for the discretization tends to infinity. Numerical results for the spatially homogeneous case demonstrate the feasibility of the approach.

scholarly journals Optimal control of mixing in Stokes fluid flows

2007 ◽  
Vol 580 ◽  
pp. 261-281 ◽  
Author(s):  
GEORGE MATHEW ◽  
IGOR MEZIĆ ◽  
SYMEON GRIVOPOULOS ◽  
UMESH VAIDYA ◽  
LINDA PETZOLD
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fluid Flows ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Optimal Controls ◽  
Microfluidic Mixing ◽  
Space Norm ◽  
Stokes Fluid

Motivated by the problem of microfluidic mixing, optimal control of advective mixing in Stokes fluid flows is considered. The velocity field is assumed to be induced by a finite set of spatially distributed force fields that can be modulated arbitrarily with time, and a passive material is advected by the flow. To quantify the degree of mixedness of a density field, we use a Sobolev space norm of negative index. We frame a finite-time optimal control problem for which we aim to find the modulation that achieves the best mixing for a fixed value of the action (the time integral of the kinetic energy of the fluid body) per unit mass. We derive the first-order necessary conditions for optimality that can be expressed as a two-point boundary value problem (TPBVP) and discuss some elementary properties that the optimal controls must satisfy. A conjugate gradient descent method is used to solve the optimal control problem and we present numerical results for two problems involving arrays of vortices. A comparison of the mixing performance shows that optimal aperiodic inputs give better results than sinusoidal inputs with the same energy.

scholarly journals On an Optimal Control Problem for a Linear System With Variable Structure

2016 ◽  
Author(s):  
Р.О. Масталиев
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variable Structure

В задаче оптимального управления с переменной линейной структурой, описываемой линейным разностным и интегро-дифференциальным уравнениями типа Вольтерра, получено необходимое и достаточное условие оптимальности в форме принципа максимума Понтрягина. В случае выпуклости функционала критерия качества получено достаточное условие оптимальности.

scholarly journals Solving Optimal Control Linear Systems by Using New Third kind Chebyshev Wavelets Operational Matrix of Derivative

2014 ◽  
Vol 11 (2) ◽  
pp. 229-234
Author(s):  
Baghdad Science Journal
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Operational Matrix ◽  
Control Problems ◽  
State Variables ◽  
Algebraic Equations ◽  
Chebyshev Wavelets

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

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