We present an extended linear quadratic regulator (LQR) design for continuous-time linear time-invariant (LTI) systems in the
presence of exogenous inputs. We first propose a model-based solution with cost minimization guarantees for states and inputs
using dynamic programming (DP). The control law consists of a combination of the optimal state feedback and an additional
optimal term dependent on the exogenous inputs. The control gains for the two components are obtained by solving a set of
matrix differential equations. We provide these solutions for both finite horizons and steady-state cases. In the second part of
the paper, we formulate a reinforcement learning (RL) based algorithm which does not need any model information except the
input matrix, and can compute an approximate steady-state LQR gain using measurements of the states, the control inputs,
and the exogenous inputs. Both model-based and data-driven optimal control algorithms are tested with a numerical example
under different exogenous inputs showcasing the effectiveness of the designs.
Published: September 16, 2021
Citation
Mukherjee S., H. Bai, and A. Chakrabortty. 2021.Model-based and Model-free Designs for an Extended Continuous-time LQR with Exogenous Inputs.Systems and Control Letters 154.PNNL-SA-156098.doi:10.1016/j.sysconle.2021.104983