A gradient matching method for computing bang-bang time-optimal controls is described. A horizon-depending auxiliary functional, parameterized by the horizon weighting factor, is minimized for an appropriately chosen sequence of the parameter values. Every iteration of quasi-Newton search for optimal wwitching times and horizon is preceded by a possible generation of new switchings and followed by a reduction of coinciding ones. The generations results from an analysis of the gradient of the auxiliary functional w.r.t control. The algorithm normally converges to a local minimum in control space, and the auxiliary function decreases monotonously during each stage of optimization with constant weighting parameter. An example of time-optimal control fo a pendulum-cart system is solved. Copyright ~direct 2000 IFAC
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