3. Nonlinear Output Regulation
Society for Industrial and Applied Mathematics eBooks · 2004
3.1 Introduction Beginning with this chapter, we turn to the nonlinear output regulation problem, a nonlinear analog of the linear output regulation problem studied in Chapter 1. The typical scenario studied by the nonlinear output regulation problem is shown in Figure 3.1, where we have a nonlinear plant described by x˙ (t)=F(x(t),u(t),d(t)),x (0) = x0 ,y(t)=H(x(t),u(t),d(t)),t≥0, 3.1 where x (t) is the plant state, u (t) the plant input, y (t) the plant output, and d (t) the disturbance signal generated by an exogenous system described by d ˙ (t) = a1 (d (t) ) ,d (0) = d0 . 3.2 In addition, there is a reference input also generated by an exogenous system r ˙ (t) = a2 (r (t) ) ,r (0) = r0 . 3.3 The tracking error is defined by e(t)=y(t)−r(t). 3.4 To handle the nonlinear system described in (3.1), we need to go beyond the class of linear control laws described in Chapter 1 and resort to the class of nonlinear feedback control laws. A typical nonlinear feedback control law takes the following form: u(t)=k(z(t)), z ˙ (t) =g (z (t) ,e (t) ) , 3.5 where k and g are some nonlinear functions. This control law can be viewed as a nonlinear analog of the linear dynamic output feedback control law (1.49) described in Chapter 1.