Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method
It provides a simpler control synthesis method for nonlinear sampled switched systems, but the improvement is incremental over existing Runge-Kutta methods.
The paper proposes a symbolic control synthesis method for nonlinear sampled switched systems using Euler's method, achieving bounded error through suitable discretization. The method is implemented in Octave and compared favorably to a prior Runge-Kutta-based approach on literature examples.
In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed control. The benefit of this method is that the error introduced by symbolic modeling is bounded by choosing suitable time and space discretizations. The method is implemented in the interpreted language Octave. Several examples of the literature are performed and the results are compared with results obtained with a previous method based on the Runge-Kutta integration method.