Data-Driven Polytopic Approximation of Non-Linear Systems Using Reduced Number of Vertices

We present a generic algorithm for estimating quasi-Linear Parameter Varying (qLPV) models using radial basis function (RBF) from state and output measurements of discrete autonomous systems. The proposed method guarantees a bounded approximation error across the entire training dataset and incorporates global stability constraints on the null equilibrium point when known. Extensions to continuous-time systems and systems with external inputs further enhance its versatility. The approach is illustrated on an FEM model of a soft pendulum, demonstrating its capability in capturing complex system dynamics. The algorithm reduces the number of vertices required in the polytopic representation, maintaining accuracy while minimizing computational complexity.