Genetic algorithm approach to fixed-order mixed H2/H∞ optimal deconvolution filter designs

The mixed H₂/H_∞ optimal deconvolution filter is proposed to achieve the H₂ optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the H_∞ norm perspective. However, the conventional mixed H₂/H_∞ optimal design filters are very complicated and are not practical for industrial applications. For simplicity of implementation and conservation of operation time, the fixed-order mixed H₂/H_∞ optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective. In this study, to avoid the trap of local minima, a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed-order mixed H₂/H_∞ deconvolution filter. The convergence property of our design algorithm is also discussed. Finally, an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.