Robust Constrained Receding Horizon Control for Linear Time-Varying Systems with Delays

A robust infinite horizon receding horizon control (RHC) for linear time-varying systems with delays is synthesized. Known, constant, deterministic time delays are assumed to be present in both the state and input. The control input is subject to hard, symmetric constraints. Polytopic uncertainty, which is assumed to be obtained from e.g. input/output data at different operating points of a non-linear plant, is considered. At each time step, a robustly stabilizing, state-feedback control law is designed which minimizes a worst-case (infinite horizon) objective function. The numerically intractable minimax problem is relaxed to a series of linear matrix inequalities (LMIs) using widely known convex optimization techniques. Two examples are presented to illustrate the control design procedure. The first is a simple second order system for illustrative purposes whilst the second is an experimental heat transfer set-up. Potential extensions are discussed such as disturbance modelling, reference tracking, gain scheduling and Lyapunov-Krasovskii functionals which consider systems with variable time delay in both state and input.