Robust performance design of fixed structure controllers for systems with uncertain parameters

Abstract

In this paper we address the problem of designing robust controllers of given structure, depending on some free design parameters. The plant to be controlled is supposed to be a linear, time invariant, continuous time system, depending on a parameter vector, known only to belong to a bounded set. Assuming that a certain number of performance specifications are given (in the frequency domain), the design is carried on by constructing an inner and an outer approximation of the set of the robustly performing design parameters. We present a method based on Bernstein polynomial expansion, which can handle the quite general case of polynomial parametric perturbations.

Efficient solving of quantified inequality constraints over the real numbers

“…The example "circle" simply computes a description of the unit disc x 2 + y 2 ≤ 1, "silaghi" is a system of inequalities describing the geometry of a simple mechanical problem [Silaghi et al 2001], the example "anderson2" is a system of polynomial inequalities from control engineering [Anderson et al 1975;Abdallah et al 1996;Garloff and Graf 1999], the example "anderson2 proj" computes the projection of the former into two-dimensional space, the example "termination" proves the termination of a certain term-rewrite system [Collins and Hong 1991]. All examples starting with "robust" are taken from robust control [Dorato 2000;Fiorio et al 1993;Malan et al 1997;Dorato et al 1997;Jaulin and Walter 1996;Jaulin et al 2002] and laid out on a website [Ratschan 2001a]. …”

An efficient algorithm for a sharp approximation of universally quantified inequalities

“…Let us come back to Example 1. Evaluating (∂f /∂y)(x, y) = 10 − 2y = [8,10], (12) we prove that f is increasing w.r.t. y.…”

“…, ym) are vectors of intervals over continuous domains, and constraints ci are inequalities of the form fi(x, y) ≤ 0. In addition to the problems introduced in [2], this class of QCSPs can tackle the design of robust controllers, which has been addressed in numerous works [10,15,9,21,28,8].…”

Solving strict polynomial inequalities by Bernstein expansion

“…Then we can write an l-variate polynomial p in the form p(x) = X I2S a I x I ; x 2 R l ; (1) and refer to N as the degree of p and tô n = maxfn i : i = 1; : : : ; lg: (2) as the total degree of p. Also, we write I=N for (i 1 =n 1 ; : : : ; i l =n l ) and ? N I for ?…”