Data-Driven Input-to-State Stabilization of Polynomial Systems

For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator and process disturbances. We address this problem in a data-based setting when we cannot avail ourselves of the dynamics of the actual system but only of data generated by it under unknown bounded noise. For all dynamics consistent with data, we derive sum-of-squares programs to design an input-to-state stabilizing controller, an input to-state Lyapunov function, and the corresponding comparison functions. This numerical design for input-to-state stabilization seems to be relevant not only in the considered data-based setting but also in a model-based setting. Feasibility of the provided sum-of-squares programs is illustrated in anumerical example.