Dynamic event-triggered robust optimal tracking control for multi-player nonzero-sum games with mismatched uncertainties and asymmetric constrained inputs

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In this paper, a novel dynamic event-triggered robust optimal tracking control method is proposed for multi-player nonzero-sum game problem with mismatched uncertainties and asymmetric constrained inputs. First, the original asymmetric constrained-input multi-player system is transformed into a new multi-player system with symmetric constrained inputs implemented by the state-space transformation technique, and an augmented system is established based on the new system and the desired trajectory. Next, an auxiliary augmentation system is constructed to handle the robust tracking control problem. Then, a critic neural network with a novel modified weight updating law is established for each player to solve the event-triggered coupled Hamilton–Jacobi equations, which relaxes the restrictions of initial admissible control and persistence of excitation condition. Furthermore, efficient communication and computing are obtained by the newly established dynamic event-triggered mechanism, and the Zeno behavior can be excluded by introducing an exponential term. The uniformly ultimately bounded properties of all signals are proved. Finally, two numerical examples verify the effectiveness of the designed method.