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Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one.
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To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems.
Using the transformation technique, the transformed model can be derived.
First, the minimum delays equivalent system of the original system with multiple delays is derived based on the coordinate transformation technique, and then the corresponding Bellman equation and Q-function are presented, respectively.
The modal expansion method and a matrix transformation technique are used to solve the system equations to obtain the natural frequencies and modes of system.
With resorting to a matrix transformation technique to separate Lyapunov variables from system matrices, sufficient conditions are established in terms of linear matrix inequalities (LMIs).
It is suggested that an efficient gene expression system in the rice chloroplast has been established by chloroplast transformation technique.
The major problems of conventional techniques (e.g., Fourier Transformation Technique) are that they are (1) more appropriate in linear systems than nonlinear systems, and (2) stringently depend on state space functions.
The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear algebraic transformation technique.
A polynomial transformation technique is applied to obtain the mixed-rate model of the control system that is suitable for multirate adaptive control design.
It is shown that the point transformation technique is the most suitable to analyze the aeroelastic response of systems containing piecewise continuous restoring forces.
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