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This paper considers an optimal train control problem with two challenging, non-standard constraints: a speed constraint that is piecewise-constant with respect to the train's position, and control constraints that are non-smooth functions of the train's speed. We formulate this problem as an optimal switching control problem in which the mode switching times are decision variables to be optimized, and the track gradient and speed limit in each mode are constant. Then, using control parameterization and time-scaling techniques, we approximate the switching control problem by a finite-dimensional optimization problem, which is still subject to the challenging speed limit constraint (imposed continuously during each mode) and the non-smooth control constraints. We show that the speed constraint can be transformed into a finite number of point constraints. We also show that the non-smooth control constraints can be approximated by a sequence of conventional (smooth) inequality constraints. The resulting approximate problem can be viewed as a nonlinear programming problem and solved using gradient-based optimization algorithms, where the gradients of the cost and constraint functions are computed via the sensitivity method. A case study using data for a real subway line shows that the proposed method yields a realistic optimal control profile without the undesirable control fluctuations that can occur with the pseudospectral method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the governing dynamic system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. We conclude the paper with four numerical examples. [Copyright &y& Elsevier]

This paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation. To solve the optimal boundary control problem, we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions, each of which depends on a set of decision parameters. Then, by using variational principles, we derive formulas for the gradient of the objective function (which measures pressure fluctuation) with respect to the decision parameters. Based on the gradient formulas obtained, we propose a gradient-based optimization method for solving the optimal boundary control problem. Numerical results demonstrate the capability of optimal boundary control to significantly reduce pressure fluctuation. [ABSTRACT FROM AUTHOR]