Implicit Model Predictive Control for Discretized Brayton-Moser Equations

The dynamics of nonlinear RLC circuits including independent and controlled voltage or current sources can be described by the Brayton-Moser equations. The underlying geometric structure of Brayton-Moser equations can be written as an implicit dynamical system with respect to a noncanonical Dirac structure. In this study, the continuous-time Brayton-Moser equation is discretized as a discrete-time nonlinear implicit system. Model predictive control is a kind of optimal feedback control in which the control performance over a finite future is optimized and its performance index has a moving initial time and a moving terminal time. This study focuses on the model predictive control problem of discretized Brayton-Moser equations. The objective of this study is to propose a model predictive control method for a class of discrete-time nonlinear implicit systems. This paper provides a numerical solution method based on the so-called C/GMRES algorithm to solve the model predictive control problem.