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This paper investigates a dynamic event-triggered robust safety control method for multiplayer fully cooperative games with mismatched uncertainties and asymmetric input constraints under continuous-time nonlinear systems. Firstly, to address the safety constraints on the system states, a suitable barrier function is proposed to transform the original constrained system into an unconstrained system. Subsequently, through the construction of an auxiliary system, the robust control (RC) problem is transformed into optimal control problem with auxiliary control laws. Secondly, the control laws are subjected to asymmetric constraints by designing a non-quadratic function. Unlike traditional static event-triggered control, a new dynamic event-triggered mechanism is introduced for updating the control laws. In addition, a new critic neural network (NN) weight update method is constructed to approximate the solution of the event-triggered Hamiltonian Jacobi Bellman (HJB) equation by using the concurrent learning technique. Furthermore, Lyapunov's theorem proves that the closed-loop system is uniformly ultimately bounded (UUB). Finally, a simulation example of a single-linked robotic arm is provided to verify the validity of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

In this paper, for the safety–critical systems with unmatched disturbances, a safe optimal robust control method based on neural network is proposed to ensure that the safety–critical system operates within its safe region and learns the optimal control strategy. The cost function which is the goal of the designers is augmented by a control barrier function (CBF) to achieve both safety and optimality. This method does not directly regard security as a constraint on the system state, but influences the cost function through a security penalty mechanism. An additional function is used to approximate the effect of the unmatched disturbances on the safety–critical systems. On the premise of satisfying the security and robustness, the neural network approximation method is used to learn the optimal control strategy. Based on Lyapunov stability theory, it is shown that the neural network-based safe optimal robust controller can guarantee all the signals of the resulting closed-loop systems to be uniformly ultimately bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive critic design is proposed to approximate the online Nash equilibrium solution for the robust trajectory tracking control of non-zero-sum (NZS) games for continuous-time uncertain nonlinear systems. First, the augmented system was constructed by combining the tracking error and the reference trajectory. By modifying the cost function, the robust tracking control problem was transformed into an optimal tracking control problem. Based on adaptive dynamic programming (ADP), a single critic neural network (NN) was applied for each player to solve the coupled Hamilton–Jacobi–Bellman (HJB) equations approximately, and the obtained control laws were regarded as the feedback Nash equilibrium. Two additional terms were introduced in the weight update law of each critic NN, which strengthened the weight update process and eliminated the strict requirements for the initial stability control policy. More importantly, in theory, through the Lyapunov theory, the stability of the closed-loop system was guaranteed, and the robust tracking performance was analyzed. Finally, the effectiveness of the proposed scheme was verified by two examples. [ABSTRACT FROM AUTHOR]

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Utilizing parallel learning technology and an event-triggering mechanism, we introduce an adaptive security tracking control approach for nonlinear systems with both matched and mismatched uncertainties. The methodology commences with an overview of the constraints imposed by the control barrier function (CBF) on the system state, followed by the selection of a suitable CBF. An augmented system is constructed by amalgamating the system state and tracking error, with the mismatched uncertainty being decomposed to introduce an auxiliary system. Incorporating the CBF into the performance metrics ensures that the system state remains within a secure region. Subsequently, the paper employs an event-triggering mechanism to derive an event-based secure Hamiltonian–Jacobi–Bellman (HJB) equation. An adaptive single-critic network, designed using parallel learning technology, approximates the solution to the event-based secure HJB equation. Lastly, the Lyapunov method is employed to demonstrate the uniform ultimate boundedness (UUB) of both the tracking error and weight error. The efficacy of the proposed method is validated through two nonlinear examples. [ABSTRACT FROM AUTHOR]