Optimization Landscape of Gradient Descent for Discrete-time Static Output Feedback

Understand

In this paper, we analyze the optimization landscape of gradient descent methods for static output feedback (SOF) control of discrete-time linear time-invariant systems with quadratic cost.

• The SOF setting can be quite common, for example, when there are unmodeled hidden states in the underlying process.
• We first establish several important properties of the SOF cost function, including coercivity, L-smoothness, and M-Lipschitz continuous Hessian.
• We then utilize these properties to show that the gradient descent is able to converge to a stationary point at a dimension-free rate.