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Based on statistical thermodynamics principle or Michaelis-Menten kinetics equation, the models for biological systems contain linear fractional functions as reaction rates which are nonlinear in both parameters and states. Generally it is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration...
S-system models for biological systems are derived from the generalized mass action law and are typically a group of nonlinear differential equations. Estimation of parameters in these models from experimental measurements is thus a nonlinear problem. In principle, all algorithms for nonlinear optimization can be used to estimate parameters in molecular biological systems, for example, Gauss-Newton...
Derived from biochemical principles, molecular biological systems can be described by a group of differential equations. Generally these differential equations contain fractional functions plus polynomials (which we call improper fractional model) as reaction rates. As a result, molecular biological systems are nonlinear in both parameters and states. It is well known that it is challenging to estimate...
An iterative learning control problem for distributed parameter systems is discussed. Based on geometric analysis, a new iterative learning control algorithm is proposed, which is different from the present algorithms and has the form of nonlinear. Furthermore, complete convergence analysis is given to new algorithm by employing special norm.
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