Numerical algorithms for constructing phase portraits in a plane nonlinear time-optimality problem. The program package SINTEZ (Q5955725)

The time-optimal control problem: \( T\to\min\), \(\dot{x} (t) = f(x(t)) + u(t)\), \(x(t) \in \mathbb{R}^n\), \(u(t) \in U \subset\mathbb{R}^n, x(0) = x_0\), \(x(T) = 0\) is considered, where \(f\colon \mathbb{R}^n \to \mathbb{R}^n\) is a smooth map, \(U\) is a ``smooth'' convex and compact subset of \(\mathbb{R}^n\) and the admissible controls are all continuous functions \(u(\cdot)\) with values in \(U\). The authors study a numerical approach based on the Pontryagin maximum principle and the corresponding numerical algorithms for the construction of extremal trajectories. A computer implementation for two-dimensional control systems and some numerical examples is given.