Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  stabilize the unstable ldquoshock-likerdquo equilibrium profiles of the viscous Burgers equation using control at the boundaries. These equilibria are not stabilizable (even locally) using the standard ldquoradiation feedback boundary conditions.rdquo Using a nonlinear spatially-scaled transformation (that employs three ingredients, of which one is the Hopf-Cole nonlinear integral transformation) and linear backstepping,  design an explicit nonlinear full-state control law that achieves exponential stability, with a region of attraction for which  give an estimate. The region of attraction is not the entire state space since the Burgers PDE is known not to be globally controllable.
['Miroslav Krstic', 'Lionel Magnis', 'Rafael Vazquez']
I am writing a research paper on a idea Nonlinear Stabilization of Shock-Like Unstable Equilibria in the Viscous Burgers PDE
[{"from": "human", "value": "I am writing a research paper on a idea Nonlinear Stabilization of Shock-Like Unstable Equilibria in the Viscous Burgers PDE"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  stabilize the unstable ldquoshock-likerdquo equilibrium profiles of the viscous Burgers equation using control at the boundaries. These equilibria are not stabilizable (even locally) using the standard ldquoradiation feedback boundary conditions.rdquo Using a nonlinear spatially-scaled transformation (that employs three ingredients, of which one is the Hopf-Cole nonlinear integral transformation) and linear backstepping,  design an explicit nonlinear full-state control law that achieves exponential stability, with a region of attraction for which  give an estimate. The region of attraction is not the entire state space since the Burgers PDE is known not to be globally controllable."}]