Data-driven H∞ control of constrained systems: an application to bilateral teleoperation system

A novel, identification-free, data-driven (DD) H∞ method is presented for discrete-time (DT) linear time-invariant (LTI) systems under physical limitations and norm-bounded disturbances. The presented approach does not demand information on system matrices or any measurements of disturbance affecting the system. The only information needed to develop a static state-feedback (SF) controller is the bounds on disturbances, states and control signals. It is assumed that only the disturbance input matrix and the performance matrices the user generally defines are known, and all others are entirely unknown. The proposed method relies on the closed-loop (CL) parametrization of the LTI system with control input and state measurements. The system states' disturbances are handled as affine uncertainties, later represented as Linear Fractional Transformation (LFT). For obtaining a less conservative controller, a full block S-procedure method (FBSPM) is used, which takes advantage of relaxations such as convex hull relaxation or Pólya relaxation for the inner approximation of the disturbance set with arbitrary precision. Numerical illustrations and extensive case studies on a bilateral teleoperation system indicate that the proposed design method allows us to obtain very effective controllers which never exceed the bounds of the state and input variables and are capable of reference and force tracking.