Abstract
In this article, optimal control problems for a class of time-delay nonlinear systems subject to mixed control–state constraints are studied. The delays in the systems are on the state and/or on the control input. The theory of optimal control based on measure theory, functional analysis and linear programming (LP) is extended in order to optimise a definite objective function, and to design an appropriate optimal control for the nonlinear time-delay systems. Using an embedding process, the problem is first transferred to a new optimal measure problem and then this new problem is replaced with one in which minimising a linear form over a subset of linear equalities is required. It is shown that this minimisation is global and the embedding procedure allows one to develop a computational method to find a solution using a finite-dimensional LP techniques. Numerical examples are also presented to illustrate the procedure of the design method.
Acknowledgements
The authors thank Sara Barati, Ferdowsi University of Mashhad, for her help in producing the simulation results.