The rapidly increasing computational demands for artificial intelligence (AI) have spurred the exploration of computing principles beyond conventional digital computers. Physical neural networks (PNNs) offer efficient neuromorphic information processing by harnessing the innate computational power of physical processes; however, training their weight parameters is computationally expensive. We propose a training approach for substantially reducing this training cost. Our training approach merges an optimal control method for continuous-time dynamical systems with a biologically plausible training method--direct feedback alignment. In addition to the reduction of training time, this approach achieves robust processing even under measurement errors and noise without requiring detailed system information. The effectiveness was numerically and experimentally verified in an optoelectronic delay system. Our approach significantly extends the range of physical systems practically usable as PNNs.

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