Inverse Optimal Feedback Controllers for Partial Differential Equations with Convection and Counter-Convection

The authors develop inverse optimal feedback controllers for partial differential equations (PDEs) with quadratic convection, counter-convection, and diffusion, where the derivative of the control Lyapunov function (CLF) has a depressed cubic or quadratic dependence on the control input. The inverse optimal controllers minimize meaningful cost functionals that penalize the state and control.