A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.
Evolutionary algorithms(EAs)were shown to be effective for complex constrained optimization problems.However,inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence regions.In this paper,we propose an iterative dynamic diversity evolutionary algorithm(IDDEA)with contractive subregions guiding exploitation through local extrema to the global optimum in suitable steps.In IDDEA,a novel optimum estimation strategy with multi-agents evolving diversely is suggested to e?ciently compute dominance trend and establish a subregion.In addition,a subregion converging iteration is designed to redistrict a smaller subregion in current subregion for next iteration,which is based on a special dominance estimation scheme.Meanwhile,an infimum penalty function is embedded into IDDEA to judge agents and penalize adaptively the unfeasible agents with the lowest fitness of feasible agents.Furthermore,several engineering design optimization problems taken from the specialized literature are successfully solved by the present algorithm with high reliable solutions.
