## Convergence of HLS estimation algorithms for multivariable ARX-like systems.(English)Zbl 1117.93332

Summary: A hierarchical least squares (HLS) algorithm is derived in details for identifying MIMO ARX-like systems based on the hierarchical identification principle. It is shown that the parameter estimation errors by the HLS algorithm consistently converge to zero for bounded noise variances by using the stochastic martingale theory. A numerical example is given.

### MSC:

 93C35 Multivariable systems, multidimensional control systems 93E11 Filtering in stochastic control theory 93E24 Least squares and related methods for stochastic control systems 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93E12 Identification in stochastic control theory
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### References:

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