Nonlinear static state feedback controller design to enlarge the domain of attraction for a class of nonlinear systems

Abstract

In this paper, the problem of computing state feedback controllers to enlarge the domain of attraction (DOA) in non-polynomial systems is considered. An optimization strategy based on a multidimensional gridding approach to estimate and to enlarge the guaranteed DOA of equilibrium points of nonpolynomial systems is developed. Our intention is to extend our approach for the estimation of the DOA for non-polynomial systems presented in [1] to controller design, which maximizes the estimated DOA induced by a given quadratic Lyapunov function (QLF). An inner and an outer approximation of the enlarged DOA and the corresponding state feedback controller can be calculated. Two illustrative examples with different state feedback controllers demonstrate the effectiveness of the presented method.

Control synthesis for non-polynomial systems: A domain of attraction perspective

“…In [12], the state space is recast into a higher dimensional one by introducing new variables to replace the non-polynomial terms of the original system. On the other hand, there are some effective approaches which investigate the DA of non-polynomial systems without polynomial approximation [14], [15]. In [14], the nonlinear systems is transformed to a linear system with state-dependent input saturation.…”

“…In this work, a novel approach is provided by using exact feedback linearization. In [15], based on the multidimensional gridding approach, a strategy is proposed for estimating the DA by employing Chebychev points and a fixed quadratic Lyapunov function. For non-polynomial systems, these explorations are useful for estimating the DA.…”