# Optimization-based control design techniques and tools

## TL;DR

This paper discusses recent advances in structured output feedback controller synthesis, emphasizing optimization-based methods over traditional algebraic approaches, and highlights software tools for practical implementation.

## Contribution

It introduces a new paradigm in structured $H_0$-control synthesis based on optimization techniques, moving away from Riccati equations and matrix inequalities.

## Key findings

- Structured control synthesis is central in modern control engineering.
- Non-smooth optimization techniques are essential for computing structured control laws.
- Software tools facilitate practical application of these new control design methods.

## Abstract

Structured output feedback controller synthesis is an exciting recent concept in modern control design, which bridges between theory and practice in so far as it allows for the first time to apply sophisticated mathematical design paradigms like $H_\infty$- or $H_2$-control within control architectures preferred by practitioners. The new approach to structured $H_\infty$-control, developed by the authors during the past decade, is rooted in a change of paradigm in the synthesis algorithms. Structured design is no longer be based on solving algebraic Riccati equations or matrix inequalities. Instead, optimization-based design techniques are required. In this essay we indicate why structured controller synthesis is central in modern control engineering. We explain why non-smooth optimization techniques are needed to compute structured control laws, and we point to software tools which enable practitioners to use these new tools in high technology applications.