Optimal control of linear systems with delay

A real-time optimal control method is described for systems with delay in which the current optimal feedback values required for control on each interval are calculated in the control process. The formation of signals for a control process by applying optimal feedback synthesized preliminarily is called the optimal closed-loop control of the dynamical system. The optimal program is based on an iterative transformation of supports starting with an arbitrary one and ending with an optimal support. If the inequalities are unsatisfied, then the solution process halts and the pseudoprogram is the optimal program of the problem. The integration of the equation with delay is reduced to the integration of a collection of systems of ordinary differential equations (ODE). The dual method proposed for computing an optimal program underlies a real-time algorithm for the performance of an optimal controller, generating an optimal feedback implementation in each particular control process.