A Multiobjective LQR Synthesis Approach to Dual Control for Uncertain Plants

This letter proposes a dual control finite horizon LQR synthesis procedure for unknown systems characterized by mean and covariance estimates. The optimized policy comprises time-varying state-feedback and dithering components, and the control problem is framed as a multiobjective synthesis which seeks a balance between exploitation and exploration costs. It is shown that classic experiment design problems can be recast in this framework by replacing the exploitation cost with an information reward. Numerical examples demonstrate the different dual control trade-offs on plants with different properties.