Shooting continuous Runge–Kuttamethod for delay optimal controlproblems

In this paper, we present an efficient method to solve linear time-delayoptimal control problems with a quadratic cost function. in this regard,first, by employing the pontryagin maximum principle to time-delay systems,the original problem is converted into a sequence of two-point boundaryvalue problems (tpbvps) that have both advance and delay terms.then, using the continuous runge–kutta (crk) method, the resultingsequences are recursively solved by the shooting method to obtain an optimalcontrol law. this obtained optimal control consists of a linear feedbackterm, which is obtained by solving a riccati matrix differential equation,and a forward term, which is an infinite sum of adjoint vectors, that canbe obtained by solving sequences of delay tpbvps by the shooting crkmethod. finally, numerical results and their comparison with other availableresults illustrate the high accuracy and efficiency of our proposedmethod.