Tuning PI controller in non-linear uncertain closed-loop systems with interval analysis

The tuning of a PI controller is usually done through simulation, except for few classes of problems, e.g., linear systems. With a new approach for validated integration allowing us to simulate dynamical systems with uncertain parameters, we are able to design guaranteed PI controllers. In practical, we propose a new method to identify the parameters of a PI controller for nonlinear plants with bounded uncertain parameters using tools from interval analysis and validated simulation. This work relies on interval computation and guaranteed numerical integration of ordinary differential equations based on Runge-Kutta methods. Our method is applied to the well-known cruise-control problem, under a simplified linear version and with the aerodynamic force taken into account leading to a non-linear formulation.