Global asymptotic stability of wavelet network adaptive control of a single-loop thermosyphon

Abstract

The governing equations for a single-loop thermosyphon are derived as modified Lorenz equations.  As the external heat increases, the flow patterns include heat conduction, steady convective flow, and chaotic time-dependent flow.  The control objective is to stabilize the system at its equilibrium when the flow is in its chaotic regime.  A measurable state variable is used for proportional single-state feedback to achieve the control objective.  A wavelet network is adopted to construct a wavelet controller when there are uncertainties in the system, such as uncertainties with system parameters, disturbances and inaccuracy of modeling. Global asymptotic stability of the state trajectory is established for the direct adaptive wavelet-control of the loop thermosyphon system.