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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. [ABSTRACT FROM AUTHOR]

In this article, the H∞$$ {H}_{\infty } $$ safe control problem of continuous‐time affine nonlinear safety‐critical systems is studied based on the barrier function (BF) and adaptive dynamic programming (ADP). We show that the safety constraints in this article occur under the condition that the system initial state is unsafe and have not been adequately addressed in the existing work. First, the H∞$$ {H}_{\infty } $$ control problem is transformed into a zero‐sum game problem, and a new safe Hamilton–Jacobi–Isaacs equation is proposed by combining with the BF, which makes the unsafe behavior be punished in the learning process. In addition, a damping coefficient is introduced into the BF to punish the unsafe behavior more flexibly. Aiming at the requirement that the initial system state must be strictly constrained in the safe set, a new weight updating method based on ADP is proposed, which can reasonably avoid the influence of the BF on neural network (NN) parameters when the initial system state is unsafe. Furthermore, based on the Lyapunov stability theory, it is proved that the system states of safety‐critical systems and the NN parameters are uniformly ultimately bounded under the safety constraints and disturbances effect. Finally, the effectiveness of the proposed method is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a new online model-free adaptive dynamic programming algorithm is developed to solve the H ∞ control problem of the continuous-time linear system with completely unknown system dynamics. Solving the game algebraic Riccati equation, commonly used in H ∞ state feedback control design, is often referred to as a two-player differential game where one player tries to minimize the predefined performance index while the other tries to maximize it. Using data generated in real time along the system trajectories, this new method can solve online the game algebraic Riccati equation without requiring the full knowledge of system dynamics. A rigorous proof of convergence of the proposed algorithm is given. Finally, simulation studies on two examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]