• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.592-597
• /
• 2003

In this paper, some differential geometric conditions for the observer using a recurrent neural network are provided in terms of a stochastic nonlinear system control. In the stochastic nonlinear system, it is necessary to make an additional condition for observation of stochastic nonlinear system, called perfect filtering condition. In addition, we provide a observer using a recurrent neural network for the observation of a stochastic nonlinear system with the proposed observation conditions. Computer simulation shows that the control performance of the stochastic nonlinear system with a observer using a recurrent neural network satisfying the proposed conditions is more efficient than the conventional observer as Kalman filter

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.38 no.9
• /
• pp.753-760
• /
• 1989

A method is suggested to design a stochastic observer which can be used as a state estimator for the optimal control of a one link flexible manipulator. This stochastic observer is derived from unifying the two concepts of reduced-state deterministic observer theory and optimal Kalman filtering theory. In estimating state variables for the optimal control, instead of using the two different state estimators for the deterministic system with noise free measurements and stochastic system with noise measurements, only one stochastic observer is designed which is to be used in both systems commonly. Through the simulation, it has been shown that the flexible system with the stochastic observer is similar in characteristics to the flexible system assuming that all states can be measured.

• Smart Structures and Systems
• /
• v.9 no.3
• /
• pp.231-251
• /
• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.156-161
• /
• 1994

In this paper, we consider an optimal control problem of a nonlinear stochastic system. Dynamic programming approach is employed for the formulation of a stochastic optimal control problem. As an optimality condition, dynamic programming equation so called the Bellman equation is obtained, which seldom yields an analytical solution, even very difficult to solve numerically. We obtain the numerical solution of the Bellman equation using an algorithm based on the finite difference approximation and the contraction mapping method. Optimal controls are constructed through the solution process of the Bellman equation. We also construct a test case in order to investigate the actual performance of the algorithm.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.440-444
• /
• 1998

In this paper, we consider numerical solution of a H-J-B (Hamilton-Jacobi-Bellman) equation of elliptic type arising from the stochastic control problem. For the numerical solution of the equation, we take an approach involving contraction mapping and finite difference approximation. We choose the It(equation omitted) type stochastic differential equation as the dynamic system concerned. The numerical method of solution is validated computationally by using the constructed test case. Map of optimal controls is obtained through the numerical solution process of the equation. We also show how the method applies by taking a simple example of nonlinear spacecraft control.

• Advances in aircraft and spacecraft science
• /
• v.7 no.5
• /
• pp.405-423
• /
• 2020

Non-linear energy sink (NES) is an emerging passive absorber able to mitigate the dynamic response of structures without any external energy supply, resonating with all the modes of the primary structure to control. However, its inherent non-linearities hinder its large-scale use and leads to complicated design procedures. For this purpose, an approximate design approach is herein proposed in a stochastic framework. Since loads are random in nature, the stochastic analysis of non-linear systems may be performed by means of computational intensive techniques such as Monte Carlo simulations (MCS). Alternatively, the Stochastic Linearisation (SL) technique has proven to be an effective tool to investigate the performance of different passive control systems under random loads. Since controlled systems are generally non-classically damped and most of SL algorithms operate recursively, the computational burden required is still large for those problems that make intensive use of SL technique, as optimal design procedures. Herein, a procedure to speed up the Stochastic Linearisation technique is proposed by avoiding or strongly reducing numerical evaluations of response statistics. The ability of the proposed procedure to effectively reduce the computational effort and to reliably design the NES is showed through an application on a well-known case study related to the vibrations mitigation of an aircraft wing.

• Smart Structures and Systems
• /
• v.19 no.1
• /
• pp.21-31
• /
• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Transactions on Control, Automation and Systems Engineering
• /
• v.4 no.3
• /
• pp.239-243
• /
• 2002

Multi-valued decision making for transitional stochastic events was newly derived based on conditional probability of knowledge database which included experts'knowledge and experience. The proposed multi-valued decision making was successfully adopted to the determination of the five levels of the vigilance of a subject during the EEG (electroencephalogram) recording; awake stage (stage W), and sleep stages (stage REM (rapid eye movement), stage 1, stage 2, stage $\sfrac{3}{4}$). Innovative feature of the proposed method is that the algorithm of decision making can be constructed only by use of the knowledge database, inspected by experts. The proposed multi-valued decision making with a mathematical background of the probability can also be applicable widely, in industries and in other medical fields for purposes of the multi-valued decision making.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.139-144
• /
• 1993

In this paper, a robust reduced order adaptive controller is proposed based on Internal Model Control(IMC) structure for stochastic linear stable systems. The concept of gain margin is utilized to make the adaptive IMC controller robust. We prove the stability of the proposed adaptive IMC system for stable plants under the assumption that upper bounds for system orders are known. Simulation results show that the proposed method has good performance and stability robustness.

• 제어로봇시스템학회:학술대회논문집
• /
• 1995.10a
• /
• pp.432-435
• /
• 1995

In this paper a new approach to obtain the solution of the linear-quadratic Gaussian control problem for singularly perturbed discrete-time stochastic systems is proposed. The alogorithm proposed is based on exploring the previous results that the exact solution of the global discrete algebraic Riccati equations is found in terms of the reduced-order pure-slow and pure-fast nonsymmetric continuous-time algebraic Riccati equations and, in addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.