In this paper, a novel adaptive dynamic programming (ADP)-based event-triggered safe control method is proposed to solve the zero-sum game problem of nonlinear safety-critical systems with safety constraints and input saturation. First, the barrier function-based system transformation, the zerosum game problem with safety constraints and input saturation is transformed into an equivalent input saturation zero-sum game problem, so as to guarantee that the system does not violate the safety constraints. Furthermore, the non-quadratic utility function is introduced into the performance function to solve input saturation. Then, a critic neural network (NN) is constructed to approximate the optimal safety value function. Subsequently, a novel event-triggered scheme is developed to determine the update instant of the control law and the disturbance law. Therefore, the proposed ADP-based event-triggered safe control method can ensure that the states of nonlinear safety-critical systems satisfy the safety constraints, while greatly reducing the amount of calculation and saving communication resources. In addition, during the learning process, the concurrent learning is used to relax the persistence of excitation (PE) condition. According to the Lyapuov theory, it is proved that the weight estimation error of the critic neural network and the states are uniformly ultimately bounded (UUB), and the Zeno behavior is excluded. Finally, a simulation example verifies the effectiveness of the proposed method.

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In this paper, the H ∞ tracking control problem of partially unknown linear systems with output constraints and disturbance is studied by reinforcement learning (RL) method. Firstly, an augmented system is established based on the reference trajectory dynamics and target system dynamics, and a special cost function is established to realize asymptotic tracking. In addition, the barrier function (BF) is used to transform the augmented system, and the output constraints is realized simultaneously by minimizing the quadratic cost function of the transformed system. Using only the obtained data and part of the system dynamics, the optimal control strategy and the worst disturbance strategy are obtained by integral reinforcement learning (IRL). Rigorous stability analysis shows that the proposed method can make the trajectories of the system states converge, and the output of the control strategy can make the tracking error asymptotically stable. Finally, a simulation example is conducted to verify the effectiveness of the proposed algorithm.INDEX TERMS Barrier function, H ∞ tracking control, Integral reinforcement learning, Output constraints

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In this paper, an event‐triggered safe control method based on adaptive critic learning (ACL) is proposed for a class of nonlinear safety‐critical systems. First, a safe cost function is constructed by adding a control barrier function (CBF) to the traditional quadratic cost function; the optimization problem with safety constraints that is difficult to deal with by classical ACL methods is solved. Subsequently, the event‐triggered scheme is introduced to reduce the amount of computation. Further, combining the properties of CBF with the ACL‐based event‐triggering mechanism, the event‐triggered safe Hamilton–Jacobi–Bellman (HJB) equation is derived, and a single critic neural network (NN) framework is constructed to approximate the solution of the event‐triggered safe HJB equation. In addition, the concurrent learning method is applied to the NN learning process, so that the persistence of excitation (PE) condition is not required. The weight approximation error of the NN and the states of the system are proven to be uniformly ultimately bounded (UUB) in the safe set with the Lyapunov theory. Finally, the availability of the presented method can be validated through the simulation.

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