Discrete-time adaptive control of feedback linearizable nonlinear systems

For a class of multi-input multi-output (MIMO) discrete-time nonlinear systems, an adaptive controller or self tuning regulator (STR) which feedback linearizes the system is presented. The structure of the adaptive controller is derived using a filtered error notions and passivity approach. A uniform ultimate boundedness of the closed-loop system is given in the sense of Lyapunov. The notions of discrete-time passive STR a dissipative STR are defined and used with persistency of excitation condition to show the boundedness of STR parameter estimates. In addition, new online tuning algorithms for discrete-time systems are derived, which guarantee tracking as well as bounded STR parameters in nonideal situations so that persistency of excitation on the input signals (PE) is not needed. The notion of state strict passivity of STR is defined and used to show the input-output boundedness of the closed-loop system in the presence of additional unknown bounded disturbances.