Stabilization Of Input Constrained Nonlinear Systems With Imperfect State Feedback Using Sum-Of-Squares Programming

We study the problem of using imperfect state feedback to stabilize polynomial, control-affine systems which are subject to polytopic input constraints. The state feedback is assumed be subject to an additive, unknown, but bounded disturbance. An analysis framework based on Sum-of-Squares (SOS) programming is developed, in order to characterize the subset of the measurement space from where stabilization to a neighborhood of the origin with a Lyapunov-based, input constrained control law is guaranteed for the particular measurement assumptions. Subsequently, such a control law is developed based on the minimizer, at every (measured) state, of a low-dimension Quadratic Program (QP). The proposed control solution is designed in a way such that attempting to render the system stable from the perspective of a control law with knowledge of the imperfect measurement of the state implies the stabilization of the actual system. The stabilization guarantees provided by the SOS analysis part, combined with the efficiency of the QP-based control law make the proposed solution suitable for systems where embeddability, robustness to measurement disturbances and safety are important. Numerical simulations are used to illustrate the main contributions.