• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.621-624
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• 2009

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

• Smart Structures and Systems
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• v.5 no.1
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• pp.69-79
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• 2009

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.3
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• pp.263-272
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• 2000

In this paper we give some geometric condition for a stochastic nonlinear system and we propose a control method for a stochastic nonlinear system using neural networks. Since a competitive learning neural networks has been developed based on the stochastcic approximation method it is regarded as a stochastic recursive filter algorithm. In addition we provide a filtering and control condition for a stochastic nonlinear system called the perfect filtering condition in a viewpoint of stochastic geometry. The stochastic nonlinear system satisfying the perfect filtering condition is decoupled with a deterministic part and purely semi martingale part. Hence the above system can be controlled by conventional control laws and various intelligent control laws. Computer simulation shows that the stochastic nonlinear system satisfying the perfect filtering condition is controllable and the proposed neural controller is more efficient than the conventional LQG controller and the canonical LQ-Neural controller.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.95.1-95
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• 2001

This paper is concerned with a novel S-stability (stochastic-stability) concept in linear time-invariant stochastic systems, where a stochastic mode in dynamics depends on both the external disturbance and the inner-parameter variations. This leads to an EAG (eigenstructure assignment gaussian) problem; that is, the problem of associating S-eigenvalues (stochastic-eigenvalues), S-eigenvectors (stochastic-eigenvectors), and their PDFs (probability density functions) with the stochastic information of the systems with the required stochastic specifications. These results explicitly characterize how S-eigenvalues, S-eigenvectors and their PDFs in the complex plane may impose S-stability on stochastic systems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.346-352
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• 1998

In this paper, we give some geometric condition for a stochastic nonlinear system and we propose a control method for a stochastic nonlinear system using neural networks. Since a competitive learning neural networks has been developed based on the stochastic approximation method, it is regarded as a stochastic recursive filter algorithm. In addition, we provide a filtering and control condition for a stochastic nonlinear system, called perfect filtering condition, in a viewpoint of stochastic geometry. The stochastic nonlinear system satisfying the perfect filtering condition is decoupled with a deterministic part and purely semi martingale part. Hence, the above system can be controlled by conventional control laws and various intelligent control laws. Computer simulation shows that the stochastic nonlinear system satisfying the perfect filtering condition is controllable. and the proposed neural controller is more efficient than the conventional LQG controller and the canoni al LQ-Neural controller.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.39-63
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• 2011

Referring to the formulation of physical stochastic optimal control of structures and the scheme of optimal polynomial control, a nonlinear stochastic optimal control strategy is developed for a class of structural systems with hysteretic behaviors in the present paper. This control strategy provides an amenable approach to the classical stochastic optimal control strategies, bypasses the dilemma involved in It$\hat{o}$-type stochastic differential equations and is applicable to the dynamical systems driven by practical non-stationary and non-white random excitations, such as earthquake ground motions, strong winds and sea waves. The newly developed generalized optimal control policy is integrated in the nonlinear stochastic optimal control scheme so as to logically distribute the controllers and design their parameters associated with control gains. For illustrative purposes, the stochastic optimal controls of two base-excited multi-degree-of-freedom structural systems with hysteretic behavior in Clough bilinear model and Bouc-Wen differential model, respectively, are investigated. Numerical results reveal that a linear control with the 1st-order controller suffices even for the hysteretic structural systems when a control criterion in exceedance probability performance function for designing the weighting matrices is employed. This is practically meaningful due to the nonlinear controllers which may be associated with dynamical instabilities being saved. It is also noted that using the generalized optimal control policy, the maximum control effectiveness with the few number of control devices can be achieved, allowing for a desirable structural performance. It is remarked, meanwhile, that the response process and energy-dissipation behavior of the hysteretic structures are controlled to a certain extent.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.513-522
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• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• International Journal of Control, Automation, and Systems
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• v.5 no.4
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• pp.355-363
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• 2007

The paper deals with the Kalman stochastic filtering problem for linear continuous-time systems with both instantaneous and time-delayed measurements. Different from the standard linear system, the system state is corrupted by multiplicative white noise, and the instantaneous measurement and the delayed measurement are also corrupted by multiplicative white noise. A new approach to the problem is presented by using projection formulation and reorganized innovation analysis. More importantly, the proposed approach in the paper can be applied to solve many complicated problems such as stochastic $H_{\infty}$ estimation, $H_{\infty}$ control stochastic system with preview and so on.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.11
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• pp.974-980
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• 2000

In this paper, we present a method that has flexibility of exact assignment of eigenstructure with the stochastic robustness for LTI(Linear-Time-Invariant) systems. The stochastic robustness of LTI systems is determined by the probability distributions of closed-loop eigenvalues. The probabilistic stability region is presented stochastically using the Monte Carlo evaluations. The proposed scheme is applied to designing a simple system and a flight control system with stochastic parameter variations to confirm the usefulness of the scheme.