Hifoo - A Matlab Package for Fixed-Order Controller Design and H Optimization

Abstract

H ∞ controller design for linear systems is a difficult, nonconvex and typically nonsmooth (nondifferentiable) optimization problem when the order of the controller is fixed to be less than that of the open-loop plant, a typical requirement in e.g. embedded aerospace control systems. In this paper we describe a new matlab package called hifoo, aimed at solving fixed-order stabilization and local optimization problems. It depends on a new hybrid algorithm for nonsmooth, nonconvex optimization based on several techniques, namely quasiNewton updating, bundling and gradient sampling. The user may request hifoo to optimize one of several objectives, including H ∞ norm, which requires either the Control System Toolbox for matlab or, for much better performance, the linorm function in the slicot package. No other external package is required, but the quadratic programming code quadprog from either mosek or the Optimization Toolbox for matlab is recommended. Numerical experiments on benchmark problem instances from the COMPl e ib database indicate that hifoo could be an efficient and reliable computer-aided control system design (CACSD) tool, with a potential for realistic industrial applications.

On computing the distance to stability for matrices using linear dissipative Hamiltonian systems

“…In [5], authors stabilize fixed order controllers using nonsmooth, nonconvex optimization. A MATLAB toolbox called HIFOO (H ∞ fixed order optimization) was designed to solve fixed order stabilization and local optimization problems [4]. In [7], authors stabilize transfer functions using a two step iterative procedure that guaranteed stable transfer function models from noisy data.…”

Control design in the time and frequency domain using nonsmooth techniques

“…See [10,8] for stabilization problems, [4,5,20,3,11] for H ∞ synthesis, and [3,6] for design with IQCs. These techniques are in our opinion a valuable addition to the designer's toolkit:…”

Fixed – Order and Structure H∞ Control With Model Based Feedforward for Elastic Web Winding Systems

“…The approach we follow to design a fixed-order linear controller ensuring closed-loop H ∞ performance is as follows: -first, the closed-loop system must be stabilized. The closed-loop system matrix is affine in the controller state-space matrices, see e.g.relation (3) in (Burke, et al, 2006). However, this matrix is nonsymmetric, hence the stabilization problem is nonconvex when formulated in the controller parameter space.…”

“…HANSO is at the core of another public-domain Matlab package called HIFOO (H ∞ Fixed Order Optimization) which is tailored at solving fixed-order controller design problems. See (Burke, et al, 2006) for a brief introduction to HIFOO 1.0, with some simple numerical examples. This software has been improved during 2006 to include fixed structure controller calculation: HIFOO 1.5 (Millstone, 2006 …”

“…However, recent progress in nonlinear variational analysis, tailored at solving H ∞ fixed-order control problems (Burke, et al, 2003) paved the way for the development of nonsmooth optimization algorithms based on quasi-Newton (BFGS), bundling and gradient sampling. A MATLAB software called HIFOO (H-Infinity FixedOrder Optimization) has been released in late 2005, see (Burke, et al, 2006), and uses local optimization techniques. This software has been used in this work for the reduced order and fixed structure controller calculation.…”