Optimal control of stochastic processes

Cybernetics ◽  
1973 ◽  
Vol 6 (2) ◽  
pp. 84-97
Author(s):  
Yu. M. Ermol'ev
Keyword(s):  
Optimal Control ◽  
Stochastic Processes

scholarly journals OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES

2010 ◽  
Vol 15 (4) ◽  
pp. 393-407 ◽  
Author(s):  
Mario Annunziato ◽  
Alfio Borzì
Keyword(s):  
Optimal Control ◽  
Stochastic Processes ◽  
Probability Density ◽  
Control Strategy ◽  
Time Windows ◽  
Probability Density Functions ◽  
Density Functions ◽  
Optimal Control Strategy ◽  
Control Laws ◽  
Fokker Planck

A Fokker‐Planck framework for the formulation of an optimal control strategy of stochastic processes is presented. Within this strategy, the control objectives are defined based on the probability density functions of the stochastic processes. The optimal control is obtained as the minimizer of the objective under the constraint given by the Fokker‐Planck model. Representative stochastic processes are considered with different control laws and with the purpose of attaining a final target configuration or tracking a desired trajectory. In this latter case, a receding‐horizon algorithm over a sequence of time windows is implemented.

scholarly journals Optimal control of ultimately bounded stochastic processes

1974 ◽  
Vol 53 ◽  
pp. 157-170
Author(s):  
Yoshio Miyahara
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Markov Process ◽  
Stochastic Differential Equation ◽  
Stochastic Processes ◽  
Wiener Process ◽  
Admissible Control ◽  
Standard Wiener Process ◽  
The Cost

We shall consider the optimal control for a system governed by a stochastic differential equationwhere u(t, x) is an admissible control and W(t) is a standard Wiener process. By an optimal control we mean a control which minimizes the cost and in addition makes the corresponding Markov process stable.

Improving the state estimation for optimal control of stochastic processes subject to multiplicative noise

Automatica ◽  
2011 ◽  
Vol 47 (3) ◽  
pp. 591-596 ◽  
Author(s):  
F. Crevecoeur ◽  
R.J. Sepulchre ◽  
J.-L. Thonnard ◽  
P. Lefèvre
Keyword(s):  
Optimal Control ◽  
Stochastic Processes ◽  
State Estimation ◽  
Multiplicative Noise ◽  
The State

scholarly journals Pseudo Almost Automorphic Solutions for Stochastic Differential Equations Driven by Lévy Noise and Its Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1674
Author(s):  
Chao Tang ◽  
Rong Hou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Processes ◽  
Stochastic Differential Equations ◽  
Lévy Noise ◽  
Bounded Interval ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Levy Noise ◽  
Theoretical Results

As we know, the periodic functions are symmetric within a cycle time, and it is meaningful to generalize the periodicity into more general cases, such as almost periodicity or almost automorphy. In this work, we introduce the concept of Poisson Sγ2-pseudo almost automorphy (or Poisson generalized Stepanov-like pseudo almost automorphy) for stochastic processes, which are almost-symmetric within a suitable period, and establish some useful properties of such stochastic processes, including the composition theorems. In addition, we apply a Krasnoselskii–Schaefer type fixed point theorem to obtain the existence of pseudo almost automorphic solutions in distribution for some semilinear stochastic differential equations driven by Lévy noise under Sγ2-pseudo almost automorphic coefficients. In addition, then we establish optimal control results on the bounded interval. Finally, an example is provided to illustrate the theoretical results obtained in this paper.

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