Discrete time minimax tracking control with state and disturbance estimation II: Time-varying reference and disturbance signals

The paper characterizes the properties of discrete time minimax tracking control problem in the case of time varying references and disturbances. Hereunder, a multi step tracking control synthesis is suggested for linear time invariant (LTI) plants when the reference signal could be time dependent. Moreover, instead of directly rejecting the effect of the (time varying) disturbance signal, an intermediate estimation and centering step is proposed. This step eliminates the main part of the disturbance by its unbiased estimate. The solution combines the state and disturbance estimation with linear quadratic and optimal minimax tracking design. The resulted unified control solution is LQ optimal on infinite horizon with constant references and disturbances and sub-optimal on large horizons with time-varying references and disturbances. The paper clarify the effect of the time varying signals on the stability and performance criteria. The multi step procedure is illustrated via an ascending spiral trajectory tracking simulation of a quadrotor helicopter.