Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems

2000 ◽  
Vol 45 (4) ◽  
pp. 790-794 ◽  
Author(s):  
C. Coumarbatch ◽  
Z. Gajic
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Optimal Control Problems ◽  
Algebraic Riccati Equation ◽  
Control Problems

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.

A New Approach to the Solution of Linear Optimal Control Problems

1969 ◽  
Vol 91 (2) ◽  
pp. 149-154 ◽  
Author(s):  
W. J. Rugh ◽  
G. J. Murphy
Keyword(s):  
Optimal Control ◽  
Riccati Equation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Phase Variable ◽  
Linear Optimal Control ◽  
Matrix Riccati Equation ◽  
Terminal Time ◽  
Forcing Functions ◽  
Linear Optimal Control Problems

A simplified approach to the solution of linear optimal control problems with quadratic performance indexes is described in this paper. The phase-variable canonical form is used to develop a new type of optimal system equivalence. This concept leads to a substantial simplification of the matrix Riccati equation. The simplified matrix Riccati equation is of the same form for any problem of a given order, say, n, and contains only n nonzero forcing functions. That is, it always corresponds to a set of constant-coefficient scalar differential equations; in various nth-order problems the n nonzero forcing functions and the terminal conditions simply assume different forms. In a very strong sense, this simplified matrix Riccati equation is the simplest possible Riccati equation arising from optimization problems. The method is developed for general time-varying systems with finite terminal time. It is developed also for the important special case of time-invariant systems with infinite terminal time.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Sign in / Sign up

Export Citation Format

Share Document