scholarly journals Optimization for Nonlinear Uncertain Switched Stochastic Systems with Initial State Difference in Batch Culture Process

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jinlong Yuan ◽  
Jun Xie ◽  
Honglei Xu ◽  
Enmin Feng ◽  
Zhilong Xiu
Keyword(s):  
Batch Culture ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Identification Problem ◽  
Complex Nature ◽  
Initial State ◽  
Approximation Techniques ◽  
System Parameters ◽  
Continuous State ◽  
State Difference

Based on the deterministic description of batch culture expressed in form of switched ordinary differential equations, we introduce a switched stochastic counterpart system with initial state difference together with uncertain switching instants and system parameters to model the process of glycerol biodissimilation to 1,3-propanediol (1,3-PD) induced byKlebsiella pneumoniae(K. pneumoniae). Important properties of the stochastic system are discussed. Our aim is to obtain the unified switched instants and system parameters under the condition of different initial states. To do this, we will formulate a system identification problem in which these uncertain switched instants and system parameters are regarded as decision variables to be chosen such that the relative error between experimental data and computational results is minimized. Such problem governed by the stochastic system is subject to continuous state inequality constraints and box constraints. By performing a time-scaling transformation as well as introducing the constraint transcription and local smoothing approximation techniques, we convert such problem into a sequence of approximation subproblems. Considering both the difficulty of finding analytical solutions and the complex nature of these subproblems, we develop a parallelized differential evolution (DE) algorithm to solve these approximation subproblems. From an extensive simulation, we show that the obtained optimal switched instants and system parameters are satisfactory with initial state difference.

scholarly journals Identification of linear stochastic systems based on partial information

1995 ◽  
Vol 8 (3) ◽  
pp. 249-260 ◽  
Author(s):  
N. U. Ahmed ◽  
S. M. Radaideh
Keyword(s):  
Stochastic Systems ◽  
Computational Algorithm ◽  
Partial Information ◽  
Identification Problem ◽  
Covariance Matrices ◽  
Unknown Parameters ◽  
System Parameters ◽  
Partially Observed ◽  
Linear Stochastic Systems ◽  
Deterministic Control

In this paper, we consider an identification problem for a system of partially observed linear stochastic differential equations. We present a result whereby one can determine all the system parameters including the covariance matrices of the noise processes. We formulate the original identification problem as a deterministic control problem and prove the equivalence of the two problems. The method of simulated annealing is used to develop a computational algorithm for identifying the unknown parameters from the available observation. The procedure is then illustrated by some examples.

scholarly journals PARAMETRIC IDENTIFICATION OF STOCHASTIC SYSTEM BY NON-GRADIENT RANDOM SEARCHING

2017 ◽  
Vol 16 (3) ◽  
pp. 256-261 ◽  
Author(s):  
A. A. Lobaty ◽  
V. Y. Stepanov
Keyword(s):  
Mathematical Model ◽  
Mathematical Simulation ◽  
Stochastic System ◽  
Stochastic Systems ◽  
A Priori ◽  
Quality Criteria ◽  
Identification Problem ◽  
Operational Capability ◽  
Identification Method ◽  
The Mathematical Model

At this moment we know a great variety of identification objects, tasks and methods and its significance is constantly increasing in various fields of science and technology.  The identification problem is dependent on a priori information about identification object, besides that  the existing approaches and methods of identification are determined by the form of mathematical models (deterministic, stochastic, frequency, temporal, spectral etc.). The paper considers a problem for determination of system parameters  (identification object) which is assigned by the stochastic mathematical model including random functions of time. It has been shown  that while making optimization of the stochastic systems subject to random actions deterministic methods can be applied only for a limited approximate optimization of the system by taking into account average random effects and fixed structure of the system. The paper proposes an algorithm for identification of  parameters in a mathematical model of  the stochastic system by non-gradient random searching. A specific  feature  of the algorithm is its applicability  practically to mathematic models of any type because the applied algorithm does not depend on linearization and differentiability of functions included in the mathematical model of the system. The proposed algorithm  ensures searching of  an extremum for the specified quality criteria in terms of external uncertainties and limitations while using random searching of parameters for a mathematical model of the system. The paper presents results of the investigations on operational capability of the considered identification method  while using mathematical simulation of hypothetical control system with a priori unknown parameter values of the mathematical model. The presented results of the mathematical simulation obviously demonstrate the operational capability of the proposed identification method.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

Application of the auxiliary performance index for automatic optimality control of discrete Kalman filter

2020 ◽  
pp. 77-87
Author(s):  
Иннокентий Васильевич Семушин ◽  
Юлия Владимировна Цыганова ◽  
Андрей Владимирович Цыганов
Keyword(s):  
Kalman Filter ◽  
Adaptive Filter ◽  
Stochastic System ◽  
Performance Index ◽  
Stochastic Systems ◽  
Joint Control ◽  
Vector Parameter ◽  
Optimal Value ◽  
Roundoff Errors ◽  
Dynamic Stochastic

Предложен новый метод автоматического контроля оптимальности дискретного фильтра Калмана, основанный на равенстве нулю градиента вспомогательного функционала качества (ВФК) по параметрам адаптивного дискретного фильтра. Для вычисления градиента ВФК применяется численно устойчивый к ошибкам машинного округления алгоритм модифицированной взвешенной ортогонализации Грама-Шмидта (MWGS-ортогонализации). Алгоритм реализован на языке Matlab. Результаты проведенных численных экспериментов подтверждают эффективность предложенного метода The paper proposes a new method for automatic control of the nominal operating mode of a dynamic stochastic system, based on a combination of two previously developed methods: the auxiliary performance index (API) method and the LD modification of an adaptive filter numerically robust to roundoff errors. The API method was previously developed to solve the problems of identification, adaptation, and control of stochastic systems with control and filtering. We suggest using the API not only as a tool for identifying the parameters of the stochastic system model from the measurement data but also for automatically monitoring the optimality of the adaptive filter, namely, the condition that the API gradient is close to zero should be satisfied (with the necessity and sufficiency) at the point corresponding to the optimal value of the vector parameter in the adaptive Kalman filter. The main result is the new eLD-KF-AC algorithm (extended LD Kalman-like adaptive filtering algorithm with automatic optimality control). The advantages of the obtained solution are as follows: 1) the choice of the adaptive filter structure in the form of an extended LD algorithm can significantly reduce the effect of machine roundoff errors on the calculation results when supplemented by the ability to calculate the sensitivity functions by the system vector parameter of the adaptive filter; 2) the application of the API method allows controlling the optimality of the adaptive filter by the condition that the API gradient is zero at the minimum point, which corresponds to the optimal value of the parameter in the adaptive filter; 3) the calculation of the API gradient in the adaptive extended LD filter does not require significant computational costs and such a control method can be carried out in real-time. The results of the work will be applied to solving problems of joint control and identification of parameters in the class of discrete-time linear stochastic systems represented by equations in the state-space form.

Comparing stochastic systems using regenerative simulation with common random numbers

1979 ◽  
Vol 11 (04) ◽  
pp. 804-819 ◽  
Author(s):  
Philip Heidelberger ◽  
Donald L. Iglehart
Keyword(s):  
Stochastic Models ◽  
Stochastic System ◽  
Variance Reduction ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Random Numbers ◽  
Numerical Examples ◽  
Common Random Numbers ◽  
Regenerative Simulation ◽  
Alternative Designs

Suppose two alternative designs for a stochastic system are to be compared. These two systems can be simulated independently or dependently. This paper presents a method for comparing two regenerative stochastic processes in a dependent fashion using common random numbers. A set of sufficient conditions is given that guarantees that the dependent simulations will produce a variance reduction over independent simulations. Numerical examples for a variety of simple stochastic models are included which illustrate the variance reduction achieved.

scholarly journals Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
FengJun Hu ◽  
Qian Zhang ◽  
Gang Wu
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Stochastic System ◽  
Stochastic Systems ◽  
System Control ◽  
Time Varying ◽  
Cubature Kalman Filter ◽  
Adaptive Correction ◽  
Kalman Filter Algorithm ◽  
Control Accuracy

Standard cubature Kalman filter (CKF) algorithm has some disadvantages in stochastic system control, such as low control accuracy and poor robustness. This paper proposes a stochastic system control method based on adaptive correction CKF algorithm. Firstly, a nonlinear time-varying discrete stochastic system model with stochastic disturbances is constructed. The control model is established by using the CKF algorithm, the covariance matrix of standard CKF is optimized by square root filter, the adaptive correction of error covariance matrix is realized by adding memory factor to the filter, and the disturbance factors in nonlinear time-varying discrete stochastic systems are eliminated by multistep feedback predictive control strategy, so as to improve the robustness of the algorithm. Simulation results show that the state estimation accuracy of the proposed adaptive cubature Kalman filter algorithm is better than that of the standard cubature Kalman filter algorithm, and the proposed adaptive correction CKF algorithm has good control accuracy and robustness in the UAV control test.

SCALING LAWS IN STOCHASTIC SYSTEMS WITH ANOMALOUS DIFFUSION

2002 ◽  
Vol 02 (04) ◽  
pp. L273-L278 ◽  
Author(s):  
DMITRII KHARCHENKO
Keyword(s):  
Phase Space ◽  
Anomalous Diffusion ◽  
Stochastic System ◽  
Hurst Exponent ◽  
Special Class ◽  
Scaling Laws ◽  
Stochastic Systems ◽  
Diffusion Processes ◽  
Anomalous Behaviour ◽  
Proposed Model

We consider the stochastic system with an anomalous diffusion. According to the obtained relations between characteristics of diffusion processes the special class of models which exhibit the anomalous behaviour is considered. It was shown that indexes of super- and subdiffusion are related to the Hürst exponent which defines the properties of the phase space inherent to the proposed model of stochastic system.

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