  Time-distributed Optimization (TDO) is an approach for reducing the
computational burden of Model Predictive Control (MPC). When using TDO,
optimization iterations are distributed over time by maintaining a running
solution estimate and updating it at each sampling instant. In this paper, TDO
applied to input constrained linear MPC is studied in detail, and analytic
expressions for the system gains and a bound on the number of optimization
iterations per sampling instant required to guarantee closed-loop stability is
derived. Further, it is shown that the closed-loop stability of TDO-based MPC
can be guaranteed using multiple mechanisms including increasing the number of
solver iterations, preconditioning the optimal control problem, adjusting the
MPC cost matrices, and reducing the length of the receding horizon. These
results in a linear system setting also provide insights and guidelines that
could be more broadly applicable, e.g., to nonlinear MPC.
