In this paper, we investigate the convergence of a sequence of minimizing trajectories in infinite horizon optimization problems. The convergence is considered in the sense of ideals and their particular case called the statistical convergence. The optimality is defined as a total cost over the infinite horizon.

Infinite horizon optimization (IHO) problems present a number of challenges for their solution, most notably, the inclusion of an infinite data set. This hurdle is often circumvented by approximating its solution by solving increasingly longer finite horizon truncations of the original infinite horizon problem. In this paper, we adopt a novel transformation that reduces the infinite dimensional...

We give necessary and sufficient conditions for finite detection of an optimal initial decision for infinite horizon optimization under a broad set of assumptions and provide an algorithm that is guaranteed to solve every solvable problem under these assumptions. We illustrate the theory and algorithms developed with applications in production planning and equipment replacement.

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifyin...

This paper investigates the formulation of nonlinear model-predictive control problems with economic objectives on an infinite horizon. The proposed formulation guarantees nominal stability for closed-loop operation. Furthermore, a novel solution method of the infinite horizon method through a transformation of the independent time variable is employed. The closed-loop optimization with infinit...

We consider the optimization of nonquadratic measures of the transient response. We present a computational implementation of dynamic programming recursions to solve finite-horizon problems. In the limit, the finite-horizon performance converges to the infinite-horizon performance. We provide conditions based on finite-horizon computations which only assure that a receding horizon implementatio...