Multi-objective robust H₂/H_∞ deconvolution via evolutionary algorithms

The problem of mixed H₂/H_∞ robust deconvolution of linear discrete-time stationary processes is considered where the parameters of the process are partially known. Using the state space model of the system, the state space matrices are assumed to reside in a given polytope. A stationary deconvolver is obtained which achieves a preassigned input estimation level for all the matrices in the uncertainty polytope. The suggested synthesis technique for the deconvolution filters applies a recent parameter dependent Lyapunov approach to compute the H₂ and H _∞ norms of the transfer function matrix which relates the driving process and noise signals to the dynamically weighted error signal and a multi-objective evolutionary algorithm to find an estimate of the Pareto front which describes the trade-off between these two norms.