Symbolic Padé representation of stabilizing regulators for a class of nonlinear control systems with a parameter

Abstract

An approach for the construction of a parametric set of stabilizing controls for a class of pseudo-linear control systems with a parameter that varies on a certain interval of the positive semi-axis is described. The algorithm is based on a combination of the State-dependent Riccati equation approach (SDRE) for feedback control design, matrix Padé approximations and intellectual choice theory. Firstly, asymptotic expansions for the solutions of certain matrix algebraic state-dependent Riccati equations in the vicinity of the boundary points of the interval of the parameter variation are constructed. The obtained asymptotic expansions are matched into one symbolic construction using two-point diagonal Padé approximations and as a result a parametric set of solutions for the entire domain of parameter variation is obtained. The resulting controllers have the form of the Kalman regulators and can be used for systems with different control gains coefficients. The symbolic and parametric representation of the regulators allows to increase the efficiency of calculations and to propose algorithms for the intellectual selection of the parameters taking into account the changes in the characteristics of motion in real time.