PROPERTIES OF A DISCRETE-TIME ENHANCED LINEAR-QUADRATIC CONTROLLER

This multi-input multi-output controller incorporates two features: optimal gains associated with known exogenous inputs; and penalties imposed both on squares of first backward differences in control actions and on control actions squared. Results are derived for both the time-varying finite-time problem and the time-invariant infinite-horizon problem. The optimal control is expressed in terms of feedback gains that weight the most recent control vector in addition to the current system state, and look-ahead gains that weight known exogenous inputs. For the infinite-horizon problem, results include: (1) conditions under which the optimal gains exist and stabilize the system; (2) time-invariant properties of the look-ahead gains and their characterization in terms of eigenvalues of the closed-loop system; (3) gains appropriate for constant exogenous inputs; (4) steady-state response conditions for constant exogenous inputs; and (5) conditions under which both linear combinations of states and of control variables are reduced to zero in the steady state.