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The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using piezoelectric patches (voltages). The minimization of the performance index over these voltages is subject to the equation of motion governing the plate's structural vibration and a set of initial and boundary conditions. The solution method is a combination of modal space expansion and direct state parameterization. Modal space expansion will transform the optimal control of a distributed parameter system into the optimal control of a lumped parameter system. Using Legendre wavelets, the quadratic optimization problem is transformed into a mathematical programming problem, where the objective is to minimize a set of unknown coefficients to obtain the optimal trajectory and the optimal control. Numerical examples will be provided to illustrate the effectiveness and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The control of the uptake of growth factors in tissue engineering is mathematically modelled by a partial differential equation subject to boundary and initial conditions. The main objective is to regulate cellular processes for the growth or regeneration of a tissue within an assigned terminal time. The techniques of basis function expansion and direct state parameterization were employed to yield efficient computational methods for this problem. Using Legendre and Chebyshev wavelets, the optimal control of the lumped-parameter system was transformed into a system of algebraic equations. The computational efficiency and effectiveness of the proposed method are illustrated by numerical examples. [ABSTRACT FROM PUBLISHER]

The mathematical model of Oldham J. Phys. Chem. B 2000 , 104 , 4703 for rotating disc electrode in an unsupported system is discussed. This article presents a new analytical method for the calculation of concentration at a rotating disc electrode controlled by diffusion, convection, and migration. This model contains a steady-state nonlinear differential equation in a three-ion system under the assumption that all the ions have the same diffusivity. The homotopy perturbation method is employed to solve the nonlinear governing equation, where the ionic concentration and current are obtained analytically, in terms of charge numbers. The comparison between the analytical results of this study and previous studies confirms that the result of the proposed method is in stronger agreement with numerical simulations than other analytical methods.