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.
Research has proven that light treatment, specifically red light radiation, can provide more clinical benefits to human health. Our investigation was firstly conducted to characterize the tissue morphology of mouse breast post 660 nm laser radiation with low power and long-term exposure. RNA sequencing results revealed that light exposure with a higher intervention dosage could cause a number of differentially expressed genes compared with a low intervention dosage. Gene ontology analysis, protein–protein interaction network analysis, and gene set enrichment analysis results suggested that 660 nm light exposure can activate more transcription-related pathways in HC11 breast epithelial cells, and these pathways may involve modulating critical gene expression. To consider the critical role of the Wnt/T-catenin pathway in light-induced modulation, we hypothesized that this pathway might play a major role in response to 660 nm light exposure. To validate our hypothesis, we conducted qRT-PCR, immunofluorescence staining, and Western blot assays, and relative results corroborated that laser radiation could promote expression levels of β-catenin and relative phosphorylation. Significant changes in metabolites and pathway analysis revealed that 660 nm laser could affect nucleotide metabolism by regulating purine metabolism. These findings suggest that the Wnt/β-catenin pathway may be the major sensor for 660 nm laser radiation, and it may be helpful to rescue drawbacks or side effects of 660 nm light exposure through relative interventional agents.
In this article, the H ∞ 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 ∞ 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.
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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