It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a finite number of indicator functions of small subdomains. No constraint is imposed on the norm of the initial condition. Simulations are presented, which show the semiglobal stabilizing performance of the nonlinear feedback.
joint work with Michael Ulbrich
We consider distributionally robust optimization (DRO) for uncertain discretized PDE-constrained problems. To obtain a tractable and an accurate lower-level problem, we define ambiguity sets by moment constraints and approximate nonlinear functions using quadratic expansions w.r.t. parameters resulting in an approximate DRO problem. Its cost function is given as the sum of the value functions of a trust-region problem and an SDP. We construct smoothing functions and show global convergence of a homotopy method. Numerical results are presented using the adjoint approach to compute derivatives.