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Is there any research on the development of attacks against artificial intelligence systems?

For example, is there a way to generate a letter "A", which every human being in this world can recognize but, if it is shown to the state-of-the-art character recognition system, this system will fail to recognize it? Or spoken audio which can be easily recognized by everyone but will fail on the state-of-the-art speech recognition system.

If there exists such a thing, is this technology a theory-based science (mathematics proved) or an experimental science (randomly add different types of noise and feed into the AI system and see how it works)? Where can I find such material?

Sometimes if the rules used by an AI to identify characters are discovered, and if the rules used by a human being to identify the same characters are different, it is possible to design characters that are recognized by a human being but not recognized by an AI. However, if the human being and AI both use the same rules, they will recognize the same characters equally well.

A student I advised once trained a neural network to recognize a set of numerals, then used a genetic algorithm to alter the shapes and connectivity of the numerals so that a human could still recognize them but the neural network could not. Of course, if he had then re-trained the neural network using the expanded set of numerals, it probably would have been able to recognize the new ones.

Yes, there is some research on this topic, which can be called adversarial machine learning, which is more an experimental field.

An adversarial example is an input similar to the ones used to train the model, but that leads the model to produce an unexpected outcome. For example, consider an artificial neural network (ANN) trained to distinguish between oranges and apples. You are then given an image of an apple similar to another image used to train the ANN, but that is slightly blurred. Then you pass it to the ANN, which predicts the object to be an orange.

Several machine learning and optimization methods have been used to detect the boundary behaviour of machine learning models, that is, the unexpected behaviour of the model that produces different outcomes given two slightly different inputs (but that correspond to the same object). For example, evolutionary algorithms have been used to develop tests for self-driving cars. See, for example, Automatically testing self-driving cars with search-based procedural content generation (2019) by Alessio Gambi et al.