A general surrogate-based optimization algorithm for problems with computationally-expensive constraints with application to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mi>μ</mml:mi> </mml:math> -synthesis control

The design of robust and passive fault-tolerant controllers can be performed with several approaches, such as μ-synthesis. These control design tools can also include manually set weight functions for different control performance specifications. Although the literature already includes automatic tuning methods for such weights, these methods involve a nested optimization problem whose resolution is hindered by the presence of local minima and the evaluation of a computationally-expensive constraint. In this paper, we propose a novel surrogate-based global optimization algorithm to overcome the aforementioned limitations, also demonstrating its convergence. The effectiveness and efficiency of our proposal are compared against a local optimization method with multi-start and a global genetic algorithm, showing superior performance on both fronts. The engineering importance of the proposed algorithm is motivated by the design of passive fault-tolerant controllers that are robust to multiplicative faults, modeled as parametric uncertainties on the plant. In particular, we focus on the automatic tuning of the performance weight on the sensitivity function in the μ-synthesis control design procedure. Numerical results are provided to assess the susceptibility with respect to the order of the plant and the uncertainty level. The robustness properties of the designed controller are also evaluated on a simulated mechatronic system subject to a multiplicative fault.