Abstract
OPTCON is an algorithm for the optimal control of nonlinear stochastic systems which is particularly applicable to economic models. It delivers approximate numerical solutions to optimum control (dynamic optimization) problems with a quadratic objective function for nonlinear economic models with additive and multiplicative (parameter) uncertainties. The algorithm was first programmed in C# and then in MATLAB. It allows for deterministic and stochastic control, the latter with open loop (OPTCON1), passive learning (open-loop feedback, OPTCON2), and active learning (closed-loop, dual, or adaptive control, OPTCON3) information patterns. The mathematical aspects of the algorithm with open-loop feedback and closed-loop information patterns are presented in more detail in this paper.
Highlights
Optimal control of stochastic processes is a topic which occurs in many contexts of applied mathematics such as engineering, biology, chemistry, economics, and management science
We present the OPTCON algorithm for calculating numerically optimal control solutions to nonlinear dynamic stochastic optimization problems without and with learning
The present paper provides mathematical details for OPTCON3, which is the most sophisticated version of the OPTCON algorithm; in [18] we concentrate on computations aspects and applications of OPTCON3
Summary
Optimal control of stochastic processes is a topic which occurs in many contexts of applied mathematics such as engineering, biology, chemistry, economics, and management science. We present the OPTCON algorithm for calculating numerically (approximately) optimal control solutions to nonlinear dynamic stochastic optimization problems without and with learning. The OPTCON algorithm is applicable for stochastic control problems with the following properties: The model of the process is multivariable, formulated in discrete time, and described by a system of nonlinear difference equations with known functional form but additive noise and (possibly) unknown parameters. We consider optimal control problems with a quadratic objective function and a nonlinear multivariate discrete-time dynamic system under additive and parameter uncertainties. The OPTCON algorithm allows for the optimal control of the system (2) using a quadratic objective function To this end the modeler needs to define the following variables:. The equivalence between the quadratic tracking form and the general quadratic form is shown, for instance, in [23]
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