A non-parametric Monte Carlo technique for controller verification
Assume an output variable \(y\), possibly a vector, is given in terms of certain monotone functions \(f_1,f_2,\dots, f_n\), thus \(y= F(f_1,\dots, f_n)\). For instance, \(y\) might be given as the solution of a system of differential equations whose parameters are the functions \(f_i\). If these are subject to uncertainties, then so is \(y\), possibly to a more complicated extent. Now assume each uncertainty function lies in a known envelope, that is, assume one knows lower and upper functions for which \(f^\ell_i(x)\leq f_i(x)\leq f^u_i(x)\), for all \(x\) in the domain of \(f_i\), for all \(i=1,\dots, n\). It is desired to find an envelope of behavior for \(y\). The proposed method for this is to repeatedly generate feasible monotone functions, \(\overline f_i\), \(i= 1,\dots, n\), randomly and evaluate \(y= F(\overline f_1,\dots, \overline f_n)\). An application of this idea is given for a chemical controller. Also, a method is given for generating the \(\overline f_i\) by a recursive subdivision of its domain.
scientific article; zbMATH DE number 1036535