We consider an ergodic stochastic control problem for a class of one-dimensional Itô processes where the available control is an added bounded variation process. The corresponding infinite horizon discounted control problem is solved in [28]. Here, we show that, as the discount factor approaches zero, the optimal strategies derived in [28] “converge” to an optimal strategy for the ergodic contr...

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. In this note, we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapun...

We present a method that combines offline trajectory optimization and online Model Predictive Control (MPC), generating robust controllers for complex periodic behavior in domains with unilateral constraints (e.g., contact with the environment). MPC offers robust and adaptive control even in high-dimensional domains; however, the online optimization gets stuck in local minima when the domains h...

In this note the Infinite Horizon (IH) optimality property of Nonlinear Model Predictive Control (MPC) is analysed. In particular it is shown with a contra example that the conjecture that the IH cost of the closedloop system controlled with a stabilizing MPC controller is a monotonic decreasing function of the optimization horizon is fallacius.

Incorporating adaptive learning into macroeconomics requires assumptions about how agents incorporate their forecasts into their decision-making. We develop a theory of bounded rationality that we call finite-horizon learning. This approach generalizes the two existing benchmarks in the literature: Eulerequation learning, which assumes that consumption decisions are made to satisfy the one-step...

This paper introduces a new approach to reduce the computational load of nonlinear model based predictive controllers. The idea is based on dividing a long prediction horizon into only a few equidistant intervals with piecewise constant control signals. After solving a first dynamic optimization problem the prediction horizon is halved, keeping the second half of the solution fixed and doubling...

For a given initial state, a constrained infinite horizon linear quadratic optimal control problem can be reduced to a finite dimensional problem [12]. To find a conservative estimate of the size of the reduced problem, the existing algorithms require the on-line solutions of quadratic programs [10] or a linear program [2]. In this paper, we first show based on the Lyapunov theorem that the clo...

We consider a general deterministic infinite horizon optimization problem over discrete time with time-varying, i.e., non-stationary, data. Our formulation requires only that action spaces be compact, including both continuous and discrete controls. In the event that all total costs diverge, i.e., no least total cost optimum exists, we investigate the existence of efficient optima. (An infinite...

These notes are an attempt to give an overview of dynamic optimization and the solution methods used in solving dynamic optimization problems. Also, they are an attempt to highlight the connection between the different solution methods (finite horizon vs. infinite horizon or discrete vs. continuous time.) All through these notes I will use the consumption problem to illustrate solution methods ...

Many optimal portfolio problems, due to uncertainties with rare occurrences and the need to bypass so-called “end of the world effects” require considering an infinite time horizon. Among these in particular are insurer’s portfolios which may include catastrophic risks such as earthquakes, floods, etc. This paper sets up an approximation framework, and obtains bounds for a class of infinite hor...