A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems

Abstract

This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a quadratic functional, to compute the values of the unknown parameter vector. Numerical algorithm combining the method with appropriate fractional derivative approximation on graded mesh is applied to SIS and SEIR problems to illustrate the efficiency and accuracy. Tikhonov regularization is implemented to improve the convergence. Results from computations, both with noisy-free and noisy data, are provided and discussed. Simulations with real data are also performed.

Keywords

• coefficient inverse problems
• Caputo derivative
• nonlinear control ODE systems
• quasilinearization
• regularization
• SIR model