Mean-variance risk-averse optimal control of systems governed by PDEs with random parameter fields using quadratic approximations

Understand

We present a method for optimal control of systems governed by partial differential equations (PDEs) with uncertain parameter fields.

• We consider an objective function that involves the mean and variance of the control objective, leading to a risk-averse optimal control problem.
• To make the problem tractable, we invoke a quadratic Taylor series approximation of the control objective with respect to the uncertain parameter.
• This enables deriving explicit expressions for the mean and variance of the control objective in terms of its gradients and Hessians with respect to the uncertain parameter.