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The prescribed-time optimal control problem for nonlinear systems is investigated in this article. First, a transformation function is constructed, which includes the system state and a strictly decreasing auxiliary function related to the prescribed time and accuracy. Second, the control input and the transformation function are incorporated into a new performance index function. This encodes the prescribed-time control into the optimal control problem. Subsequently, a new Hamilton–Jacobi–Bellman (HJB) equation related to the prescribed time and accuracy is derived. To find a solution to the HJB equation, a fuzzy reinforcement learning algorithm is proposed. This algorithm successfully approximates the optimal cost and control policy while ensuring the system stability. Additionally, the system state can converge to a preassigned residual set within a prescribed time. Finally, an example of an electromechanical system is used to illustrate the efficacy of the suggested algorithm.

This article studies sampled-data stabilization for a class of fractional-order switched nonlinear systems (FOSNSs) with arbitrary switching. The feasibility of using a fuzzy-logic system (FLS) to approximate the fractional-order systems (FOSs) is proved. Using backstepping method, the fractional-order adaptive update laws and sampled-data controller for the discussed FOSNSs are designed based on the FLS. Under the proposed sampled-data control scheme, it is proved that solutions of the studied FOSNSs are semi-globally uniformly ultimately bounded (SGUUB). Two examples are given to verify the effectiveness of the proposed sampled-data control scheme.

A collision-free formation control problem for multiple unmanned aerial vehicles (UAVs) with directed switching topologies and disturbances is investigated. A novel distributed control algorithm that uses UAVs local directed switching information is proposed for achieving the required flight formation and ensuring a safe distance between UAVs; the algorithm involves the incorporation of the APF method in the virtual leader formation scheme. Two command signals generated by the virtual position controller are transmitted to the attitude subsystem. For each UAV, an adaptive composite controller is designed by combining a fuzzy system and fast terminal sliding mode control technique to guarantee that tracking errors converge to a stable area around zero. Finally, the feasibility of the proposed composite control algorithm is demonstrated through a simulation.

This article investigates multiasynchronous control for asymptotic stabilization (AS) in mean-square and nonweighted $\mathcal {L}_{2}$-gain for a class of switched Takagi–Sugeno fuzzy systems with both time-varying delay and infinite-time distributed delay (mixed delays) as well as cyber-attacks. The proposed event-triggered controller not only is mode-dependent but also excludes Zeno behavior automatically with two tunable parameters to adjust the event-triggering (ET) number. A novel Lyapunov–Krasovskii functional (LKF) with a negative term is established to greatly reduce the conservatism and simplify the analysis of nonweighted $\mathcal {L}_{2}$-gain by ensuring its increment at switching instants be smaller than one. Three main results are provided to guarantee the AS in mean-square and design the control gains and weights of the ET mechanism, as well as the optimal nonweighted $\mathcal {L}_{2}$-gain. Compared with existing results, the new asynchronous control techniques eliminate the limitation of divergence in mismatched intervals for LKF. Numerical simulations demonstrate the merits of the theoretical analysis.

This article puts forward an observer-based finite-time sampled-data stabilization scheme for a nonlinear time-delay system. To overcome the difficulties of stabilizing such nonlinear system under consideration, a reduced-order observer, whose role lies in estimating unavailable states, is formulated by relying on detectable sampled output, subsequently, a finite-time sampled-data output-feedback stabilizer (FSOS), which possesses suitable scalars and sampling period, can be developed with the help of adding a power integrator (AAPI) technique, such stabilizer can drive the formulating closed-loop system to be globally practically finite-time stable (GPFS) in the presence of uncertain time delays, which requires to be verified by means of established Lyapunov-Krasovskii functionals (LKFs). The availability of the developed scheme can be reflected by two simulations in the end.

This article presents a positivity analysis and exponential stabilization design for singular switched positive systems (SSPSs) with actuator saturation under a mode-dependent minimum dwell time (MDMDT) constraint. First, a necessary and sufficient positivity criterion is proposed for SSPSs using the singular value decomposition approach. Then, an exponential stability condition is provided for the closed-loop SSPSs via the mode-dependent state-feedback control using a novel discretized linear copositive Lyapunov function technique. Furthermore, by applying the matrix decomposition technique to the controller gain matrix and controller auxiliary gain matrix, an effective mode-dependent design scheme for a saturation controller in the solvable linear programming (LP) form is proposed for the SSPSs. For singular positive systems, an effective saturation control scheme in the solvable LP form can be obtained accordingly. Finally, three examples are provided to validate the results.

This article concerns optimal prescribed-time formation control for a class of nonlinear multiagent systems (MASs). Optimal control depends on the solution of the Hamilton–Jacobi–Bellman equation, which is hard to be calculated directly due to its inherent nonlinearity. To overcome this difficulty, the reinforcement learning strategy with fuzzy logic systems is proposed, in which identifier, actor, and critic are used to estimate unknown nonlinear dynamics, implement control behavior, and evaluate system performance, respectively. Different from the existing optimal control algorithms, a new performance index function considering formation error cost and control input energy cost is constructed to achieve optimal formation control of MASs within a prescribed time. The presented control strategy can ensure that the formation error converges to the desired accuracy within a prescribed time. Finally, the validity of the presented strategy is verified via a simulation example.

The problem of neural adaptive distributed formation control is investigated for quadrotor multiple unmanned aerial vehicles (UAVs) subject to unmodeled dynamics and disturbance. The quadrotor UAV system is divided into two parts: the position subsystem and the attitude subsystem. A virtual position controller based on backstepping is designed to address the coupling constraints and generate two command signals for the attitude subsystem. By establishing the communication mechanism between the UAVs and the virtual leader, a distributed formation scheme, which uses the UAVs’ local information and makes each UAV update its position and velocity according to the information of neighboring UAVs, is proposed to form the required formation flight. By designing a neural adaptive sliding mode controller (SMC) for multi-UAVs, the compound uncertainties (including nonlinearities, unmodeled dynamics, and external disturbances) are compensated for to guarantee good tracking performance. The Lyapunov theory is used to prove that the tracking error of each UAV converges to an adjustable neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.

The current paper is devoted to studying global asymptotic $H_{\infty }$ drive-response synchronization for a kind of switched nonlinear time-delay systems with output random injection attacks (IAs). An attack-decomposition method is proposed to derive an attack-free signal, by which an observer is designed to estimate the state of the driving system. Then, two mode-dependent event-triggering mechanisms (MDETMs) are respectively designed for observer-controller (O-C) and controller-actuator (C-A) channels to save the communication resources as much as possible. In order to analyze the effects of the switching on the $H_{\infty }$ performance, a mode-dependent discretized Lyapunov-Krasovskii functional (LKF) is developed, which has the merit of monotone decreasing on any time-interval and switching instants. Sufficient criteria are given to ensure the $H_{\infty }$ synchronization with non-weighted $\mathcal {L}_{2}$ -gain, whether the attack is related to the output or not. Numerical simulations are provided to verify the non-weighted $\mathcal {L}_{2}$ -gain performance with low conservatism.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov–Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.