scholarly journals SYARAT CUKUP UNTUK OPTIMALITAS MASALAH KONTROL KUADRATIK LINIER

2013 ◽  
Vol 2 (2) ◽  
pp. 63
Author(s):  
Suci Fratama Sari
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Riccati Equation ◽  
Existence And Uniqueness ◽  
Algebraic Riccati Equation ◽  
Lqr Problem ◽  
Existence Of Optimal Control

The LQR problem is an optimal control problem which is now used in variouselds of science. The optimal control is given by u(t) = 􀀀Kx(t), where K = R􀀀1(PB)Tand P is a unique positive semidenite solution of Algebraic Riccati Equation (ARE).The existence of optimal control u(t) depends on the existence matrix P. In this paper,the sucient conditions which ensures the existence and uniqueness of the optimal con-trol u(t) will be determined. Moreover, some examples as an illustration of the LQRproblem will be given.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

scholarly journals PENYELESAIAN MASALAH KONTROL KUADRATIK LINIER YANG MEMUAT FAKTOR DISKON

2013 ◽  
Vol 2 (1) ◽  
pp. 65
Author(s):  
Mezi Fauziatul Husna
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discount Factor ◽  
Sufficient Condition ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Change Of Variables ◽  
Existence Of Optimal Control ◽  
Linear Quadratic Control Problem

The linear quadratic control problem is an optimal control problem whichhas been used in various fields. In this paper, we will study the solving of linear quadraticcontrol problem that contains a discount factor. By using the change of variables technique, some sufficient condition for the existence of optimal control is determined. Someexamples are also presented.

scholarly journals Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Xueping Zhu ◽  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Horizon ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic delay evolution equation in Hilbert spaces. The existence and uniqueness of the optimal control are obtained by means of associated infinite horizon backward stochastic differential equations without assuming the Gâteaux differentiability of the drift coefficient and the diffusion coefficient. An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.

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