Filtering method for linear and non-linear stochastic optimal control of partially observable systems

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5979-5992 ◽  
Author(s):  
A. Delavarkhalafi ◽  
A. Poursherafatan
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Heuristic Method ◽  
Control Factor ◽  
Filtering Method ◽  
Observable System ◽  
State Process ◽  
Non Linear ◽  
Partially Observable System ◽  
Partially Observable

This paper studies two linear methods for linear and non-linear stochastic optimal control of partially observable problem (SOCPP). At first, it introduces the general form of a SOCPP and states it as a functional matrix. A SOCPP has a payoff function which should be minimized. It also has two dynamic processes: state and observation. In this study, it is presented a deterministic method to find the control factor which has named feedback control and stated a modified complete proof of control optimality in a general SOCPP. After finding the optimal control factor, it should be substituted in the state process to make the partially observable system. Next, it introduces a linear filtering method to solve the related partially observable system with complete details. Finally, it is presented a heuristic method in discrete form for estimating non-linear SOCPPs and it is stated some examples to evaluate the performance of introducing methods.

scholarly journals Filtering method for linear and non-linear stochastic optimal control of partially observable systems II

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5089-5103 ◽  
Author(s):  
Ali Poursherafatan ◽  
Ali Delavarkhalafi
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Payoff Function ◽  
Estimation Methods ◽  
Control Factor ◽  
Diffusion Term ◽  
Filtering Method ◽  
Partially Observable Systems ◽  
Partially Observable System ◽  
Partially Observable

In this paper we studied stochastic optimal control problem based on partially observable systems (SOCPP) with a control factor on the diffusion term. A SOCPP has state and observation processes. This kind of problem has also a minimum payoff function. The payoff function should be minimized according to the partially observable systems consist of the state and observation processes. In this regard, the filtering method is used to evaluat this kind of problem and express full consideration of it. Finally, presented estimation methods are used to simulate the solution of a partially observable system corresponding to the control factor of this problem. These methods are numerically used to solve linear and nonlinear cases.

Nonlinear Stochastic Optimal Control of MDOF Partially Observable Linear Systems Excited by Combined Harmonic and Wide-Band Noises

2019 ◽  
Vol 19 (03) ◽  
pp. 1950019 ◽  
Author(s):  
R. C. Hu ◽  
X. F. Wang ◽  
X. D. Gu ◽  
R. H. Huan
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Control Problem ◽  
Linear Systems ◽  
Control Strategy ◽  
Stochastic Optimal Control ◽  
Wide Band ◽  
Dynamic Programming Principle ◽  
Stochastic Dynamic ◽  
Partially Observable

In this paper, nonlinear stochastic optimal control of multi-degree-of-freedom (MDOF) partially observable linear systems subjected to combined harmonic and wide-band random excitations is investigated. Based on the separation principle, the control problem of a partially observable system is converted into a completely observable one. The dynamic programming equation for the completely observable control problem is then set up based on the stochastic averaging method and stochastic dynamic programming principle, from which the nonlinear optimal control law is derived. To illustrate the feasibility and efficiency of the proposed control strategy, the responses of the uncontrolled and optimal controlled systems are respectively obtained by solving the associated Fokker–Planck–Kolmogorov (FPK) equation. Numerical results show the proposed control strategy can dramatically reduce the response of stochastic systems subjected to both harmonic and wide-band random excitations.

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