I've been reading some papers in economics (for example, this paper by Acemoglu et al.) that solve numerically for optimal control policies. Some mention that they're uncertain as to whether or not the optimal policy they've discovered is unique, but vary the initial value of the control variables to attempt to induce a shift in the optimal policy. They take such a lack of shift as an indication of uniqueness/validity.
I was wondering if there were a way to structure such a problem (maybe some conditions on the objective or the state equations?) so as to guarantee the existence of a unique optimal policy.
Thanks!