Input design using cylindrical algebraic decomposition

Abstract

Abstract-Experiment design for system identification has seen significant progress in the last decade. One contribution has been to derive convex relaxations of such problems. Consider that only a scalar function of the system parameters is of interest. A standard step in such a case is to first linearize this function with respect to the estimated parameters. The objective of this contribution is twofold: firstly, to examine if there are cases where the linearized approximation is inadequate, and secondly to explore how to improve upon this approximation. By way of examples we show that it is not difficult to construct examples where linearization is insufficient. Furthermore, we introduce the use of higher order approximations and we formally show that this leads to polynomial optimization problems under Gaussian assumptions. We propose the use of cylindrical algebraic decomposition as a method to obtain exact solutions for this type of problems. Numerical examples are provided.

Application set approximation in optimal input design for model predictive control

“…The method is general enough to be applied to other controller strategies and application areas where it is not possible to derive the application set explicitly. Specifically, the method can be extended to MPC for nonlinear plants, with more complicated noise structures, and the derivation of expressions for higher order derivatives of the cost function could be used, in principle, to obtain better approximations of the application set using techniques such as the one presented in [26].…”

“…The quality of the approximation not only depends on the application cost but also on the value of γ. For sufficiently large values of γ, E app gives an acceptable approximation while for smaller values, higher order terms of Taylor expansion may need to be considered [26]. However, calculation of the Hessian matrix is a challenging task.…”

A Novel Parametric Controller Design Method for Hopf Bifurcation System

“…Finally, region Q is found, which is surrounded by 3 2 L is part of the curves of g  (from point B to C ). Point A , B , and C are three specific points on 01 cc  plane, where A is the crossover point of conditions (20) and (23). From (20) and (23) Copyright ⓒ 2017 SERSC…”