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In this paper, we consider a class of optimal control problems governed by nonlinear time-delay switched systems, in which the system parameters and switching times between different subsystems are decision variables to be optimized. We propose a new computational approach to deal with the computational difficulties caused by variable switching times. The original time-delay switched system is firstly transformed into an equivalent switched system defined on a new time horizon where the switching times are fixed, but each of the subsystems contain a variable time-delay that depends on the durations of each sub-system in the original system. By deriving the analytical form for the variable time-delay in the new time horizon, we can solve the new time-delay switched system. Then, gradient-based optimization algorithm can be applied to solve the equivalent problem efficiently. Numerical results show that this new approach is effective. [ABSTRACT FROM AUTHOR]

This paper considers the three-dimensional path planning problem for horizontal oil wells. The decision variables in this problem are the curvature, tool-face angle and switching points for each turn segment in the path, and the optimization objective is to minimize the path length and target error. The optimal curvatures, tool-face angles and switching points can be readily determined using existing gradient-based dynamic optimization techniques. However, in a real drilling process, the actual curvatures and tool-face angles will inevitably deviate from the planned optimal values, thus causing an unexpected increase in the target error. This is a critical challenge that must be overcome for successful practical implementation. Accordingly, this paper introduces a sensitivity function that measures the rate of change in the target error with respect to the curvature and tool-face angle of each turn segment. Based on the sensitivity function, we propose a new optimization problem in which the switching points are adjusted to minimize target error sensitivity subject to continuous state inequality constraints arising from engineering specifications, and an additional constraint specifying the maximum allowable increase in the path length from the optimal value. Our main result shows that the sensitivity function can be evaluated by solving a set of auxiliary dynamic systems. By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms. Finally, the paper concludes with a numerical example involving a practical path planning problem for a Ci-16-Cp146 well. [ABSTRACT FROM AUTHOR]