The Symbolic Description of Feedbacks in Nonlinear Control Problems with a Parameter Using Approximation Theory Methods

In this paper the algorithms for constructing parametric families of solutions for several classes of nonlinear dynamic problems on a finite time interval with a parameter on the basis of the state-dependent differential Riccati equation (SDDRE) approach and the Pade approximation (PA) are developed. Two-point Pade approximations of the differential Riccati equation solution are constructed using the pairs of local asymptotic approximations: for small and large values of the parameter and asymptotic approximations in the neighborhood of some fixed points. Pade approximations are applicable in a wider interval of parameter variation, then local asymptotic approximations. The proposed algorithms also use the approximation theory techniques, such as extrapolations and spline approximations and optimization. The possibility for increasing the accuracy of approximations and the improvement of the interpolation and extrapolation properties of two-point Spline Pade approximations (SPA) in comparison with local asymptotic approximations, SDDRE regulator is demonstrated on numerical experiments.