Stephen Boyd

Title: Performance Bounds for Constrained Linear Stochastic Control

Abstract: We develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very useful as a comparison to the performance of suboptimal control policies, which we can evaluate using Monte Carlo simulation. Our method involves solving a semidefinite program (a linear optimization problem with linear matrix inequality constraints), a convex optimization problem which can be efficiently solved. Numerical experiments show that the lower bound obtained by our method is often close to the performance achieved by several widely-used suboptimal control policies, which shows that both are nearly optimal. As a by-product, our performance bound yields approximate value functions that can be used as control Lyapunov functions for suboptimal control policies. Joint work with Yang Wang.