Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong Hong A new computational method for a class of free terminal time optimal control problems. (English) Zbl 1211.49041 Pac. J. Optim. 7, No. 1, 63-81 (2011). Summary: We develop a numerical method for solving an optimal control problem whose terminal time is not fixed, but is instead determined by a state-dependent stopping criterion. The main idea of this method is to approximate the control by a piecewise constant function whose values and switching times are decision variables to be determined optimally. The optimal control problem then becomes an optimization problem with a finite number of decision variables. We develop a novel method for computing the gradient of the cost function in this approximate problem. On this basis, the approximate problem can be solved using any gradient-based optimization technique. We use this approach to solve an aeronautical control problem involving a gliding projectile. We also prove several important convergence results that justify our approximation scheme. Cited in 22 Documents MSC: 49M37 Numerical methods based on nonlinear programming 90C30 Nonlinear programming Keywords:nonlinear optimal control; control parameterization; gradient-based optimization; nonlinear programming PDFBibTeX XMLCite \textit{Q. Lin} et al., Pac. J. Optim. 7, No. 1, 63--81 (2011; Zbl 1211.49041)