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Structure of solutions of nonautonomous optimal control problems in metric spaces

Zaslavski A. J.

Journal of Mathematics and Applications

2015

Vol. 38

151--169

We establish turnpike results for a nonautonomous discrete-time optimal control system describing a model of economic dynamics.

Structure of approximate solutions for a class of optimal control systems

Zaslavski A. J.

Journal of Mathematics and Applications

2011

Vol. 34

135--149

We study a turnpike property of approximate solutions of a discrete-time control system with a compact metric space of states which arises in economic dynamics. To have this property means that the approximate solutions of the optimal control problems are determined mainly by an objective function, and are essentially independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike property is stable under perturbations of an objective function.

An infinite horizon predictive control algorithm based on multivariable input-output models

Ławryńczuk M., Tatjewski P.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 2

167-180

In this paper an infinite horizon predictive control algorithm, for which closed loop stability is guaranteed, is developed in the framework of multivariable linear input-output models. The original infinite dimensional optimisation problem is transformed into a finite dimensional one with a penalty term. In the unconstrained case the stabilising control law, using a numerically reliable SVD decomposition, is derived as an analytical formula, calculated off-line. Considering constraints needs solving on-line a quadratic programming problem. Additionally, it is shown how free and forced responses can be calculated without the necessity of solving a matrix Diophantine equation.

Anoccupational measure solution to a singularly perturbed optimal control problem

Artstein Z.

Control and Cybernetics

2002

Vol. 31, no 3

623-642

Employing limit occupational measures, we provide an explicit solution to a singularly perturbed optimal control problem for which the order reduction method does not apply.