On-line direct data driven controller design approach with automatic update for some of the tuning parameters

We consider a discrete, time invariant, nonlinear system with one input and nx states that can be represented by the following state equation: xt+1 = g(xt, ut) + et, (1) where t ∈ Z is the discrete time step, ut ∈ R is the control input, xt ∈ Rx is the vector of states and et ∈ Rx is the vector of disturbance signals that accounts for the contribution of both the measurement and process disturbances. We make the following two assumptions about the disturbance signal et and the nonlinear function g: Assumption 1 The disturbance et is bounded in magnitude: