An almost optimal control design method for nonlinear time-delay systems

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.