Analysis and Design of Nonlinear Control Systems

Cheng, Daizhan; Hu, Xiaoming; Shen, Tielong

doi:10.1007/978-3-642-11550-9

Cited by 22 publications

(25 citation statements)

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“…This framework is proposed to avoid the high computational cost of direct Bayesian updating, of particular importance for real-time applications such as turbulent flow control [10,11]. The first step can involve any method for order reduction, including the k-means clustering method applied recently to the classification of dynamical and fluid mechanics systems [12].…”

Section: Nth-order Cyclesmentioning

confidence: 99%

Bayesian cyclic networks, mutual information and reduced-order Bayesian inference

Niven¹,

Noack

Cattafesta³

et al. 2016

AIP Conference Proceedings

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Abstract. We examine Bayesian cyclic networks, here defined as complete directed graphs in which the nodes, representing the domains of discrete or continuous variables, are connected by directed edges representing conditional probabilities between all pairs of variables. The prior probabilities associated with each domain are also included as probabilistic edges into each domain. Such networks provide a graphical representation of the inferential connections between variables, and substantially extend the standard definition of "Bayesian networks", usually defined as one-directional (acyclic) directed graphs. In a binary system, the proposed representation provides a graphical expression of Bayes' theorem. In higher-dimensional systems, further probabilistic relations can be recovered from the network cyclic properties and the joint probability of all variables. In particular, adopting a Markovian assumption leads to the theorem that the mutual information between any pair of variables on the network must be equivalent. Analysis of a hybrid Bayesian cyclic network of two continuous and two discrete variables -of the form of a commutative diagram -provides a framework for more computationally efficient reduced-order Bayesian inference, involving initial simplification by an order reduction process.

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“…The numerical method applied in nonlinear differential game began taking shape in the 1980s, and it has developed into the method which could deal with random response problems in nonlinear dynamics system so far. For non-linear mechanics with n degree of freedom, it could be expressed with differential mode [5][6][7]: …”

Section: Statistical Linear Theorymentioning

confidence: 99%

The research for mechanics stimulation method of nonlinear random vibration based on statistical linear theory

Guo-dong¹

2014

Frattura Ed Integrità Strutturale

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Earthquake disasters have brought great harm to people's life safety and economic property. Its effect on fabric mainly focus on random effects currently, the general pseudo excitation method could solve the inefficiency calculation problem of linear random earthquake. However it could not take the nonlinear problem factors into account for calculation. In this paper, we suggest that a nonlinear structural incentive method should be improved based on statistical linearity to calculate and solve absolute displacement value. Through the analysis and research for cases, we calculate the displacement, speed, random vibration spectrum of bridge's accelerated speed, as well as the influencing situation of axial force. The results indicate that such perfect incentive method could not only perform nonlinear structure analysis, but also to be very accurate and high effective. Such method could reasonably avoid the displacement decomposition and solution of the pseudostatic model，thus it will be widely applied in common software.

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“…Tin has no autocatalysis, which is different from nickel [18][19]. When there is only thiourea in electroless plating bath, nickel can continue depositing, but the deposition rate of tin will decrease gradually because the driving force of reaction attenuated gradually.…”

Section: Effect Of Sodium Hypophosphite On Deposition Ratementioning

confidence: 99%

Electroless Sn–Ni alloy plating with high Sn content free of activation pretreatment

Kong¹,

Shao

Wang³

et al. 2009

Journal of Alloys and Compounds

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“…However, the ARC design method is still subject to the same limitations of the Lyapunov-based control and the sliding mode control methods when dealing with nonlinear systems. Different from the above three methods, the key idea of the exact linearization via feedback method [11][12][13] is to construct a nonlinear state transform such that the nonlinear systems can be transformed to linear systems, design a robust controller using the existing linear theory, and then obtain the controller for the original nonlinear systems via nonlinear state inverse transform. It is noted that, the above method requires that the nominal nonlinear system can be exactly linearized, which is not the case for many systems.…”

Section: Introductionmentioning

confidence: 99%

A Piecewise Envelope Approach toH_∞Control of Nonlinear Systems

Liu

Zhou

et al. 2017

Asian Journal of Control

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This paper provides a computable approach for the H ∞ control synthesis of nonlinear systems using the piecewise envelope method. Firstly, the computation method of piecewise envelope is presented such that the required piecewise linear differential inclusions (PWLDIs) can be obtained by solving a linear optimization problem. Then, we propose the H ∞ control design method for PWLDIs using piecewise Lyapunov function theory, all the synthesis conditions are formulated as the feasibility of linear matrix inequalities, hence computationally tractable. Because of the inclusion relationship, the H ∞ controllers designed for PWLDIs are also effective for original nonlinear systems. The validity of the proposed approach is tested by application to control a wheeled mobile robot.

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“…A major thrust in developing algorithms is related to developing an optimal control algorithm which works for linear structures. An offshore structure is usually afflicted with nonlinearity and therefore, in order for these algorithms to show desired performance, the control algorithms should either be able to handle structural nonlinearity [6] or the existing algorithms can be used by linearization [7]. Recently, many advanced nonlinear regulation schemes such as recursive backstepping, sliding mode control, dynamic inversion, etc., are used to control of nonlinear systems [8,9] though their widespread usage is still limited as they are attempting to exploit the linear system theory.…”

Section: Introductionmentioning

confidence: 99%

A control algorithm for nonlinear offshore structural dynamical systems

Manikandan

Saha

2015

Proc. R. Soc. A.

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A reasonable knowledge about the response of nonlinear offshore structural systems under environmental loads is necessary but challenging. This is due to the coupling of internal forces along with external excitations. In this paper, a mathematical model of nonlinear offshore systems is studied with the intention of keeping the response close to the desired one. This is achieved using a novel sub-optimal control mechanism derived from nonlinear quadratic regulator (NQR) theory. Herein, two linearized functions of nonlinear motions—displacement and velocity—are introduced such that the parametrization of the state-dependent system matrices is obtained. By doing so, the system becomes conditioned only on the present state and therefore one needs to solve only an algebraic state-dependent Riccati problem. This results in a control law which may either be partial or full rank for the dynamical system depending on measurable states. The performance of the controller is compared with conventional NQR. The performance of the proposed control strategy is illustrated through a range of models of nonlinear offshore problems. The motions (generalized displacements and velocities) show that the proposed controller was not only able to restrict the undesirable behaviour but also provide means of shaping the transient performance.

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Analysis and Design of Nonlinear Control Systems

Cited by 22 publications

References 0 publications

Bayesian cyclic networks, mutual information and reduced-order Bayesian inference

The research for mechanics stimulation method of nonlinear random vibration based on statistical linear theory

Electroless Sn–Ni alloy plating with high Sn content free of activation pretreatment

A Piecewise Envelope Approach toH_∞Control of Nonlinear Systems

A control algorithm for nonlinear offshore structural dynamical systems

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Analysis and Design of Nonlinear Control Systems

Cited by 22 publications

References 0 publications

Bayesian cyclic networks, mutual information and reduced-order Bayesian inference

The research for mechanics stimulation method of nonlinear random vibration based on statistical linear theory

Electroless Sn–Ni alloy plating with high Sn content free of activation pretreatment

A Piecewise Envelope Approach toH∞Control of Nonlinear Systems

A control algorithm for nonlinear offshore structural dynamical systems

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A Piecewise Envelope Approach toH_∞Control of Nonlinear Systems