  Time distributed optimization is an implementation strategy that can
significantly reduce the computational burden of model predictive control by
exploiting its robustness to incomplete optimization. When using this strategy,
optimization iterations are distributed over time by maintaining a running
solution estimate for the optimal control problem and updating it at each
sampling instant. The resulting controller can be viewed as a dynamic
compensator which is placed in closed-loop with the plant. This paper presents
a general systems theoretic analysis framework for time distributed
optimization. The coupled plant-optimizer system is analyzed using
input-to-state stability concepts and sufficient conditions for stability and
constraint satisfaction are derived. When applied to time distributed
sequential quadratic programming, the framework significantly extends the
existing theoretical analysis for the real-time iteration scheme. Numerical
simulations are presented that demonstrate the effectiveness of the scheme.
