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We present a physics-informed machine learning (PIML) scheme for the feedbacklinearization of nonlinear discrete-time dynamical systems. The PIML finds thenonlinear transformation law, thus ensuring stability via pole placement, inone step. In order to facilitate convergence in the presence of steep gradientsin the nonlinear transformation law, we address a greedy-wise trainingprocedure. We assess the performance of the proposed PIML approach via abenchmark nonlinear discrete map for which the feedback linearizationtransformation law can be derived analytically; the example is characterized bysteep gradients, due to the presence of singularities, in the domain ofinterest. We show that the proposed PIML outperforms, in terms of numericalapproximation accuracy, the traditional numerical implementation, whichinvolves the construction--and the solution in terms of the coefficients of apower-series expansion--of a system of homological equations as well as theimplementation of the PIML in the entire domain, thus highlighting theimportance of continuation techniques in the training procedure of PIML.

Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning