Strict dissipativity for discrete time discounted optimal control problems

<p style='text-indent:20px;'>The paradigm of discounting future costs is a common feature economic applications optimal control. In this paper, we provide several results for such discounted control aimed at replicating the now well-known in standard, undiscounted, setting whereby (strict) dissipativity, turnpike properties, and near-optimality closed-loop systems using model predictive are essentially equivalent. To that end, introduce notion strict dissipativity show implies various properties including existence available storage functions, required supply robustness equilibria. Additionally, discount factors sufficiently close to one demonstrate optimally controlled systems, derived from cost function, yield practically asymptotically stable Several examples provided throughout.</p>