Approximate Solution of Linear-Quadratic Problem in Discrete-Time Multi-Delay Systems: Derivation and Quality Assessment

The paper addresses infinite-horizon linear-quadratic optimal control problem in discrete-time systems with multiple input-output delays. An extended state-space description is introduced which allows one to translate the original, complex problem into a standard solution framework. In order to circumvent the issues related to increased problem dimension in the extended state space, a modification of the solution procedure is proposed. The computational effort to determine the gains of thus obtained suboptimal controller is reduced to the undelayed system part. The proposed suboptimal strategy shows improved performance over the optimal one in certain classes of applications.