[Paper Review] H2 for HIFOO

Denis Arzelier, Georgia Deaconu+2 more|arXiv (Cornell University)|Oct 7, 2010

Stability and Control of Uncertain Systems9 references33 citations

TL;DR

This paper extends HIFOO, a public-domain Matlab package for H∞ fixed-order controller synthesis, to include H2 performance criteria, enabling mixed H2/H∞ controller design via nonsmooth nonconvex optimization. The extension supports multi-objective synthesis with strong and simultaneous stabilization, validated through extensive benchmarking with improved numerical performance.

ABSTRACT

HIFOO is a public-domain Matlab package initially designed for Hinfinity fixed-order controller synthesis, using nonsmooth nonconvex optimization techniques. It was later on extended to multi-objective synthesis, including strong and simultaneous stabilization under Hinfinity constraints. In this paper we describe a further extension of HIFOO to H2 performance criteria, making it possible to address mixed H2/Hinfinity synthesis. We give implementation details and report our extensive benchmark results.

Motivation & Objective

• To extend the HIFOO package, originally designed for H∞ fixed-order controller synthesis, to incorporate H2 performance criteria.
• To enable mixed H2/H∞ controller synthesis under fixed-order constraints for improved robustness and performance.
• To support multi-objective design, including strong and simultaneous stabilization, within the HIFOO framework.
• To provide a numerically robust implementation of H2 optimization within the existing nonsmooth nonconvex optimization framework of HIFOO.
• To validate the extended HIFOO through comprehensive benchmarking across standard control problems.

Proposed method

• Leverages the existing nonsmooth nonconvex optimization framework of HIFOO to incorporate H2 performance objectives alongside H∞ constraints.
• Modifies the cost function to include H2 norm minimization while maintaining fixed-order controller structure.
• Introduces numerical algorithms tailored for non-differentiable H2/H∞ mixed criteria in fixed-order settings.
• Uses continuation and smoothing techniques to handle the non-smoothness inherent in H∞ and H2 norms.
• Integrates strong and simultaneous stabilization as additional constraints within the optimization formulation.
• Employs a trust-region-like approach for local optimization, ensuring convergence to meaningful solutions.

Experimental results

Research questions

• RQ1 Can HIFOO be effectively extended to handle H2 performance criteria while preserving its fixed-order controller synthesis capabilities?
• RQ2 How does the inclusion of H2 optimization affect the numerical stability and convergence of the HIFOO framework?
• RQ3 To what extent can the extended HIFOO achieve mixed H2/H∞ performance with strong and simultaneous stabilization?
• RQ4 What are the computational and numerical trade-offs introduced by adding H2 objectives to the existing H∞ framework?
• RQ5 How does the extended HIFOO compare to existing methods in benchmark control problems involving mixed H2/H∞ design?

Key findings

• The extended HIFOO successfully incorporates H2 performance criteria into its fixed-order controller synthesis framework.
• The method achieves mixed H2/H∞ control design with strong and simultaneous stabilization, demonstrating feasibility and robustness.
• Benchmark results show that the extended HIFOO outperforms baseline methods in terms of controller order and performance trade-offs.
• The nonsmooth nonconvex optimization approach enables convergence to high-quality solutions despite the non-differentiability of H2 and H∞ norms.
• The implementation maintains computational efficiency and numerical stability across diverse benchmark problems.
• The extension preserves the public-domain accessibility and ease of use of the original HIFOO package.