Controllability and Observability Imply Exponential Decay of Sensitivity in Dynamic Optimization

We study a property of dynamic optimization (DO) problems (as those encountered in model predictive control and moving horizon estimation) that is known as exponential decay sensitivity (EDS). This indicates the solution at stage i against data perturbation j decays exponentially with |i-j|. Building upon our previous results, we show EDS holds under uniform boundedness Lagrangian Hessian, second order sufficiency condition (uSOSC), linear independence constraint qualification (uLICQ). Furthermore, prove uSOSC uLICQ can be obtained controllability observability. Hence, have observability imply EDS. These results provide insights into how perturbations propagate along enable development approximation schemes. illustrate developments numerical examples.