Backstepping in infinite dimensional for the time fractional order partial differential equations
Keywords:Boundary control, Backstepping, Stabilisation, Coordinate transformation, Fractional order PDE.
This paper focuses on the application of backstepping control scheme for the time fractional order partial differential equation (FPDE). The fractional derivative is presented by using Caputo fractional derivative. The design technique here can exhaust systems with an arbitrary finite number of open loop unstable eigenvalues and is not limited to a certain kind of boundary actuation. We show how the FPDE is converted into a Mittag-Leffler stability by designing invertible coordinate transformation. Numerical simulation is given to demonstrate the effectiveness of the proposed control scheme.
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