Covariance control for stochastic multivariable systems with hysteresis nonlinearity

Chang, Koan Yuh; Wang, Wen June; Chang, Wen Jer

doi:10.1080/00207729708929432

Cited by 23 publications

(8 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, k N s moments as (23) in which the PDF is characterized by the weights w α and abscissas x j α . This problem can be formulated as an nonlinear programming problem (NLP) where the objective function is described as (23). Equation (22) for the selected choice of k 1 , k 2 , .…”

Section: Parameters Optimization Via Nonlinear Programmingmentioning

confidence: 99%

See 1 more Smart Citation

A moment-based approach for nonlinear stochastic tracking control

Vedula

2011

Nonlinear Dyn

View full text Add to dashboard Cite

This paper describes a new stochastic control methodology for nonlinear affine systems subject to bounded parametric and functional uncertainties. The primary objective of this method is to control the statistical nature of the state of a nonlinear system to designed (attainable) statistical properties (e.g., moments). This methodology involves a constrained optimization problem for obtaining the undetermined control parameters, where the norm of the error between the desired and actual stationary moments of state responses is minimized subject to constraints on moments corresponding to a stationary distribution. To overcome the difficulties in solving the associated Fokker-Planck equation, generally experienced in nonlinear stochastic control and filtering problems, an approximation using the direct quadrature method of moments is proposed. In this approach, the state probability density function is expressed in terms of a finite collection of Dirac delta functions, and the partial differential equation can be converted to a set of ordinary differential equations. In addition to the above mentioned advantages, the state process can be nonGaussian. The effectiveness of the method is demonstrated in an example including robustness with respect to predefined uncertainties and able to achieve specified stationary moments of the state probability density function.

show abstract

Section: Parameters Optimization Via Nonlinear Programmingmentioning

confidence: 99%

“…A promising second category consists of approximation methods [21][22][23][24][25], through which the prespecified response mean and covariance in steady state can be achieved. For example, the Gaussian closure method investigated by Sun and Hsu [21] is one of such methods, in which the first and second-order moments are controlled.…”

Section: Introductionmentioning

confidence: 99%

A moment-based approach for nonlinear stochastic tracking control

Vedula

2011

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…The nonlinear control systems have gained more and more research attention, and lots of results have been published [1][2][3][4][5]. When analyzing and designing nonlinear dynamical systems, there are a wide range of nonlinear analysis tools, among which the most common and wildly used is linearization because of the powerful tools we know for linear systems.…”

Section: Introductionmentioning

confidence: 99%

“…When analyzing and designing nonlinear dynamical systems, there are a wide range of nonlinear analysis tools, among which the most common and wildly used is linearization because of the powerful tools we know for linear systems. On the other hand, due to the wide appearance of the stochastic phenomena in almost every aspect of our daily life, stochastic systems which have found successful applications in many branches of science and engineering practice have stirred quite a lot of research interests during the past few decades; see [1,2,6,7] and the references therein. Therefore, the control problems for nonlinear stochastic systems have been studied extensively so as to meet everincreasing demand toward systems with both nonlinearities and stochasticity.…”

Section: Introductionmentioning

confidence: 99%

“…However, the 2 / ∞ controllers minimize a linear quadratic performance index without guaranteeing the variance constraints with respect to individual system states. In order to deal with the individual state variance constrained control problem, the extending approach of covariance control theory [1,2,11,12] is investigated in this paper subject to passivity performance constraint.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

Chang

Huang²,

Chen³

2014

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

show abstract

Stochastic Control

Sun¹

2012

Global Analysis of Nonlinear Dynamics

View full text Add to dashboard Cite

Covariance control for stochastic multivariable systems with hysteresis nonlinearity

Cited by 23 publications

References 9 publications

A moment-based approach for nonlinear stochastic tracking control

A moment-based approach for nonlinear stochastic tracking control

Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

Stochastic Control

Contact Info

Product

Resources

About