A symplectic Newton interior-point algorithm for constrained time-optimal control

This article proposes a symplectic Newton interior-point algorithm to solve constrained time-optimal control problems. In the context of time optimization, traditional indirect numerical methods typically treat the terminal time as a static parameter, and require solving multiple coupled equations, which significantly increases the problem’s dimensionality and computational complexity. In contrast, we derive necessary conditions for time optimality using the variational method and reduce the determination of the terminal time to a single condition via a time-domain transformation. Based on the optimality conditions, a discretized optimal control problem is constructed by applying symplectic discretization to the state and costate equations, where a perturbation interior-point method is adopted to handle the inequality constraints. To solve this resulting problem, a symplectic Newton interior-point algorithm is developed, where a global Newton step-size selection strategy is proposed by combining analytical solutions with an adaptive bisection method. This strategy preserves the non-negativity of slack variables and multipliers associated with inequality constraints while guaranteeing the global convergence of the algorithm. On this basis, theoretical analysis establishes the convergence properties of the proposed algorithm, while comparative numerical simulations verify its effectiveness, numerical stability, and practical applicability.