Averaged controllability of the random heat and Schrödinger equation

In this talk we will explore the notion of averaged controllability, focusing on the heat and Schrödinger equations

with a random diffusion. We will see necessary and sufficient conditions for the averaged null controllability of the heat equation. Moreover, we will obtain sufficient conditions for the averaged null controllability of the Schrödinger equation, and we will prove that on the Schrödinger equation we do not have averaged exact controllability if we just consider a $L^2$ setting. Finally, we will present many open problems regarding averaged controllability. 

References

Barcena-Petisco, Jon Asier; Et-tahri, Fouad. Averaged controllability of the random Schrödinger equation with diffusivity following absolutely continuous distributions. SIAM Journal on Control and Optimization, 2026, vol. 64, no 1, p. 387-408.

Barcena-Petisco, Jon Asier; Zuazua, Enrique. Averaged dynamics and control for heat equations with random diffusion. Systems & Control Letters, 2021, vol. 158, p. 105055