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 Padé approximation (PA) are developed. Two-point Padé 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. Padé 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 Padé approximations (SPA) in comparison with local asymptotic approximations, SDDRE regulator is demonstrated on numerical experiments.
DOI: 10.1007/978-3-031-56496-3_10
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Danik, Y., Dmitriev, M. (2024). The Symbolic Description of Feedbacks in Nonlinear Control Problems with a Parameter Using Approximation Theory Methods. In: Awrejcewicz, J. (eds) Perspectives in Dynamical Systems II — Numerical and Analytical Approaches. DSTA 2021. Springer Proceedings in Mathematics & Statistics, vol 454, pp. 121–135.