H∞ Control for Continuous-time Systems with Multiple Input Delays: A Smoothing Estimation Approach

This paper is concerned with the finite horizon H_∞ full-information control for continuous-time systems with multiple input delays. The main contributions of the paper are two folds. First, parallel to the duality between the LQR of linear systems without delays and the optimal filtering, we establish a duality between the H_∞ full-information control of systems with multiple input delays and an H_∞ smoothing of a stochastic backward system without involving delays. The duality allows us to address the complicated multiple input delays problem via the standard projection and innovation analysis. Secondly, by defining a stochastic indefinite linear space and applying a re-organized innovation analysis, an explicit controller is constructed in terms of two standard Riccati differential equations