Subspace Identification of Bilinear Systems

Dr Huixin Chen (CUED)

In this paper, some asymptotically unbiased subspace algorithms for the identification of bilinear systems will be developed. Two three-block subspace algorithms will be developed for the deterministic system case and two four-block ones for the combined deterministic-stochastic system. The input signal to the system does not have to be white, which is a major advantage over an existing subspace method for bilinear systems.

All the identification algorithms give asymptotically unbiased estimates with general inputs, and the rate of reduction of bias can be estimated. Simulation results also show that the new algorithms converge much more rapidly (with sample size) than the existing method, and hence are more effective with small sample sizes. These advantages are achieved by a different arrangement of the input-output equations into `blocks', and projections onto different spaces than the ones used in the existing method. A further advantage of our algorithms is that the dimensions of the matrices involved are significantly smaller, so that the computational complexity is lower.

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