Polynomial chaos based approach for state limited robust control of systems with parametric uncertainty

The design of robust controllers for non-linear systems with parametric uncertainties is considered. Non linear controllers are developed using the Lyapunov Direct Stability Theorem. Special focus is placed on a design method using the Lyapunov direct method that places constrains the states of the system. Limits on the states are imposed by the use of log-barrier functions in the Lyapunov function.;In order to achieve robustness, an optimization problem is proposed which gives us the optimal gains of the nonlinear controller. The gains include the controller parameters as well as the values of the uncertain parameters used in the controller. The optimization problem is developed in the framework of Polynomial Chaos Expansion. The uncertain parameters of a system are considered as random variables with known probability distribution which results in a stochastic system. Polynomial Chaos expansions is used to propagate the distribution of the states of the system forward in time. This information is then used in the optimization problem to achieve robustness. The method is tested on the nonlinear spring system, the Van der Pol Oscillator and a 2-DOF helicopter system.