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Automatica, Vol.74, 1-9, 2016
On the regional gradient observability of time fractional diffusion processes
This paper for the first time addresses the concepts of regional gradient observability for the Riemann-Liouville time fractional order diffusion system in an interested subregion of the whole domain without the knowledge of the initial vector and its gradient. The Riemann-Liouville time fractional order diffusion system which replaces the first order time derivative of normal diffusion system by a Riemann-Liouville time fractional order derivative of order alpha is an element of (0, 1] is used to well characterize those anomalous sub-diffusion processes. The characterizations of the strategic sensors when the system under consideration is regional gradient observability are explored. We then describe an approach leading to the reconstruction of the initial gradient in the considered subregion with zero residual gradient vector. At last, to illustrate the effectiveness of our results, we present several application examples where the sensors are zone, pointwise or filament ones. (C) 2016 Elsevier Ltd. All rights reserved.
Keywords:Regional gradient observability;Gradient reconstruction;Time fractional diffusion process;Strategic sensors