Robust control of input constrained nonlinear systems subject to unknown bounded disturbances based on convex optimization

This work studies the problem of controlling nonlinear, control affine systems which are subject to polytopic input constraints and are perturbed by unknown, bounded disturbances. The control problem is split into two interconnected parts. The first part is solved offline and corresponds to the characterization of the subset of the state space where stabilization under input constraints and disturbances is guaranteed to be possible. The second part refers to the calculation of control inputs, using state feedback, which stabilize the closed loop system for any initial condition in the set resulting from the offline calculations, under any effect of the disturbance. The proposed solutions are based on Lyapunov-based stabilization methods, which are fused with techniques from convex optimization. In particular, the solution to the first part is pursued by formulating and proving set containment relationships through Semidefinite Programming with sum of squares polynomials, while the feedback control laws are pointwisely equal to the minimizer of lightweight Quadratic Programming problems. Shifting the theoretical and computational burden towards the analysis enables the direct derivation and implementation of robust controllers with explicit stabilization guarantees.