Global Asymptotic Stability of Wavelet Network Adaptive Control of A Single-Loop Thermosyphon

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 equilib- rium 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 pa- rameters, 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.