Robust control: A note on the response of the control to changes in the “free” parameter

Robust Control: A Note on the Response of the Control to Changes in the ?Free? Parameter Conditional on the Character of Nature

“…In the other extreme, as the "free" parameter goes to infinity the response asymptotically approaches the certainty equivalence (CE) solution in both cases. Moreover, the response of the control to reductions in the "free" parameter is always more cautious in the benevolent case as opposed to the response in Gonzalez and Rodriguez (2003). Finally, nature switches from a malevolent character to a benevolent one as the "free" parameter moves from the right side onto the left side of the discontinuity observed in Gonzalez and Rodriguez (2003).…”

“…Gonzalez and Rodriguez (2003) found that the control variable (u k ) response is characterized by hyperbolic shapes as shown in Figure 2.…”

“…It is important to note that θ has a negative sign in the criterion function of the min-max problem posed in Gonzalez and Rodriguez (2003). In the next section, we show that it is precisely in the positive sign of θ in Equation (3.4) that: i) the policy maker's problem given by Equations (3.4)-(3.7) becomes an ordinary optimal control problem, and ii) this gives way to a benevolent "nature" -i.e.…”

“…Moreover, we show that the set up in Gonzalez and Rodriguez (2003) corresponds to a malevolent nature. The benevolent and malevolent cases are compared and contrasted.…”

“…Section 4 associates the benevolent case with a minimum and the malevolent case with a saddle point. Section 5 provides a numerical example to compare and contrast the benevolent case to the malevolent one in Gonzalez and Rodriguez (2003). Section 6 presents the concluding remarks.…”