Structured H∞‐control of infinite‐dimensional systems

• Published in: International journal of robust and nonlinear control 2018-06, Vol.28 (9), p.3212-3238
• Main Authors: Apkarian, P., Noll, D.
• Format: Article
• Language: English
• Subjects: Approximation; Boundary control; Control systems; Controllers; Dimensional stability; Dimensional tolerances; frequency domain design; Frequency response; H-infinity control; H∞‐control; infinite‐dimensional systems; Mathematical analysis; Mathematics; Nyquist stability; Optimization and Control; Partial differential equations; performance certificate; stability certificate; Transfer functions
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4073

Summary We develop a novel frequency‐based H∞‐control method for a large class of infinite‐dimensional linear time‐invariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both state‐space or transfer function models and input/output frequency response data when only such are available. We aim for the design of practically useful H∞‐controllers of any convenient structure and size. We use a nonsmooth trust‐region bundle method to compute arbitrarily structured locally optimal H∞‐controllers for a frequency‐sampled approximation of the underlying infinite‐dimensional H∞‐problem in such a way that (i) exponential stability in closed loop is guaranteed and that (ii) the optimal H∞‐value of the approximation differs from the true infinite‐dimensional value only by a prior user‐specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite‐dimensional H∞‐synthesis problems, including distributed and boundary control of partial differential equations, control of dead‐time and delay systems, and using a rich testing set.