An optimal control problem for a generalized vibration system in estimating instantaneously the optimal control forces

Huang, Cheng‐Hung

doi:10.1016/j.jfranklin.2003.04.001

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…Referring to Reference [5] for linear problems, the iterative process based on the conjugate gradient method will be used for the estimation of optimal control u i (t) by minimizing the function J h (u i ). Let n be the iteration times, and…”

Section: Updated Conjugate Gradient Methods For Minimizationmentioning

confidence: 99%

“…Therefore, by uniform Lipschitz continuity, and Carathéodory type existence theorem as in Reference [14], it is clear that the solution of ordinary differential equation is obtained. By taking the limit of approximate solution (5) to know that the solution of free (uncontrolled) system exist.…”

Section: Definition 11mentioning

confidence: 99%

“…The numerical approximations of optimal control for linear parabolic differential equations has been investigated in Reference [3]. Numerical experiments for ordinary differential equation with time-dependent control variable has been reported in Reference [5]. However, numerical approximation of optimal control for non-linear continuous control systems is hardly considered by their non-linearities and instability.…”

Section: Introductionmentioning

confidence: 99%

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Numerical approximation of optimal control for distributed diffusion Hopfield neural networks

Wang

2006

Numerical Meth Engineering

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SUMMARYThis work presents a numerical approximation of optimal control problems for non-linear distributed Hopfield Neural Network equations with diffusion term. For one spatial dimensional case, a semi-discrete numerical algorithm was constructed to find optimal control variable using finite element discretization, updated conjecture gradient iteration method. Furthermore, experiments demonstration will be implemented to show the effectiveness and stability through 3D graphics simulations.

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Section: Updated Conjugate Gradient Methods For Minimizationmentioning

confidence: 99%

Section: Definition 11mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical approximation of optimal control for distributed diffusion Hopfield neural networks

Wang

2006

Numerical Meth Engineering

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“…Various approaches have been proposed to solve disturbance rejection problems, such as ∞ control [1], adaptive control [2], internal model control [3], variable structure control (VSC) [4], and optimal control [5][6][7]. Optimal disturbance rejection appears in a variety of applications, vehicle engine [5], damped systems [6], and spacecraft attitude control [7], for instance.…”

Section: Introductionmentioning

confidence: 99%

Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

Lei

Wang

She

et al. 2013

Abstract and Applied Analysis

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The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.

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“…Inverse methods have also found their ways in optimization of quantities or geometries such as determining optimal thickness of insulation layer, optimizing shape of gas channel in fuel cell, and finding optimal control force in a vibration system [10,11]. However, reported applications of inverse methods in convective heat transfer problems were much less than those in inverse heat conduction problems.…”

Section: Introductionmentioning

confidence: 99%

Calculation of jet’s inlet temperature for plate temperature control in an impinging jet cooling problem

Chen

Salazar

2010

International Journal of Heat and Mass Transfer

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An optimal control problem for a generalized vibration system in estimating instantaneously the optimal control forces

Cited by 5 publications

References 13 publications

Numerical approximation of optimal control for distributed diffusion Hopfield neural networks

Numerical approximation of optimal control for distributed diffusion Hopfield neural networks

Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

Calculation of jet’s inlet temperature for plate temperature control in an impinging jet cooling problem

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