Backward Reachability Using Integral Quadratic Constraints for Uncertain Nonlinear Systems

A method is proposed to compute robust inner-approximations to the backward reachable set of nonlinear systems and to generate a robust control law that drives trajectories starting in these inner-approximations to a target set. The method merges dissipation inequalities and integral quadratic constraints (IQCs) with both hard and soft IQC factorizations, allowing for a variety of perturbations including parametric uncertainty, unmodeled dynamics, and uncertain time delays. Computational algorithms are developed using the generalized S-procedure and sum-of-squares techniques, and illustrated on a 6-state quadrotor with actuator uncertainties.