Pointwise in frequency performance weight optimization in μ-synthesis

A conceptually different approach to the μ-synthesis robust performance problem is proposed in this article. The optimization problem posed maximizes the performance weights with respect to a suitable cost function that captures the desired closed-loop performance. This maximization of performance weights is limited by the fact that there must exist some internally stabilizing controller that guarantees robust performance with respect to these maximized weights. Thus, performance weights and a controller that achieves an optimized level of robust performance are synthesized together by one algorithm in a systematic way. The designer is only required to specify the plant set and an optimization directionality. This directionality only appears in the cost function and reflects the desired closed-loop properties in particular frequency regions. It is pointed out that choosing this directionality is much easier than choosing the performance weights directly. Correspondingly, this approach greatly simplifies the often long and tedious process of designing 'good' performance weights directly and gives an indication of what is the achievable performance. A pointwise in frequency solution to the posed optimization problem is also developed in this article.