In this article, an adaptive dynamic programming (ADP)-based optimal control strategy for a series of fractional-order nonlinear systems (FONS) with unknown control directions is investigated. To eliminate the challenges posed by unknown control directions, fractional-order Nussbaum-type functions are introduced for FONS, expanding the range of possible applications. Additionally, since system performance is compromised by disturbances, a fractional-order disturbance observer is designed to counteract the effects of external disturbances and enhance system robustness. Furthermore, differential geometric methods are employed to investigate FONS, constructing appropriate diffeomorphism that provide equivalent systems for decoupled linearization. Then, an optimal control method is studied for a class of strictly feedback FONS, in which Nussbaum-type functions are combined with ADP theory during the backstepping design process. Finally, based on fractional Lyapunov stability theory and backstepping method, it is guaranteed that all signals of the closed-loop FONS are uniformly ultimately bounded (UUB). Numerical simulation and a PMSM model are utilized to verify the effectiveness of the presented method.

This article is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order α ∈ (0,1) . First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and It∧ o differential formulation to design proper multiple Lyapunov-Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

In this article, a novel fault reconstruction algorithms for fractional-order nonlinear switching systems (FONSSs) with actuator and sensor faults are investigated. First, fractional-order nonlinear system (FONS) with faults, is transformed into two fast and slow subsystems using global differential homogeneous transformation, one of which is unaffected by the fault and the state is partially observable; the other subsystem is affected by the fault but the state is fully observable. After that, it is introduced for the first time that persistent dwell-time (PDT) switching is taken into consideration in the design process of the observer for FONSS, which overcomes the transient problem of the switching moment and ensures the stability of the error dynamics equations of the two fast and slow subsystems. In addition, to eliminate the impact of faults, an optimal adaptive fault-tolerant control strategy based on actor-critic architecture NN are designed to effectively compensate. Finally, the effectiveness of the proposed control strategy is verified by simulation results.

In this article, fractional-order nonautonomous system (FONAS) with the input delay and nonlinear terms are considered and investigated using adaptive fuzzy control method based on Q-learning. With the novel estimation model, the defined predictions for the error system determines the weights of the fuzzy logic system (FLS). On this basis, an error derivative-based cost function is introduced, which not only deals with the classic problem that quadratic term cost function is unbounded in infinite time, but also resolves the challenge that the exponential discount factor cost function fails to stabilize asymptotically. For the unmeasurable part of the state, the designed fuzzy observer eliminates the restriction on the gain parameters. Furthermore, based on the measured information and the actor–critic architecture of the online training FLSs, the improved adaptive fault-tolerant control (FTC) input approximate the optimal control. Utilizing a fractional-order Lyapunov method, the stability of FONAS with actuator faults is discussed, and a sufficient criterion for stability is obtained, which is easier to perform with convex optimization tools. Finally, numerical simulations are shown to display the effectiveness of the optimal adaptive fuzzy FTC strategy.

This article researches the sliding mode control (SMC) for fuzzy fractional-order multiagent system (FOMAS) subject to time-varying delays over directed networks based on reinforcement learning (RL),$\alpha\in(0,1).$First, since there is information communication between an agent and another agent, a new distributed control policy$\xi_{i}(t)$is introduced so that the sharing of signals is implemented through RL, whose propose is to minimize the error variables with learning. Then, different from the existed papers studying normal fuzzy MASs, a new stability basis of fuzzy FOMASs with time-varying delay terms is presented to guarantee that the states of each agent eventually converge to the smallest possible domain of$0$using Lyapunov–Krasovskii functionals, free weight matrix, and linear matrix inequality (LMI). Furthermore, in order to provide appropriate parameters for SMC, the RL algorithm is combined with SMC strategy, and the constraints on the initial conditions of the control input$u_i(t)$are eliminated, so that the sliding motion satisfy the reachable condition within a finite time. Finally, to illustrate that the proposed protocol is valid, the results of the simulation and numerical examples are presented.

This technical note discusses the design process of dynamic event-triggered control (DETC) with the mixed$H_{2}/H_\infty $for partially unknown nonlinear stochastic systems. The purpose of this problem is to design a controller to make the closed-loop system achieve the expected$H_{2}$performance under the condition that the$H_\infty $continuous attenuation level is protected. Firstly, a two-player non-zero-sum game for stochastic system is given. Then we prove the optimal control strategy and the worst interference, which constitute the Nash equilibrium solution and can be derived from the corresponding Hamiltonian functions. Furthermore, two neural networks (NNs) are used to realize Nash equilibrium. Under the condition of dynamic event-triggered mechanism (DETM), the control strategy only is updated at the trigger moment. In addition, the stability and weights convergence of the system are proved mathematically. Finally, two numerical example are given to prove it.Note to Practitioners—In the practice of control engineering, mixed$H_{2}/H_\infty $control can not only evaluate the$H_{2}$performance index of the transient behavior of the system, but also measure the$H_\infty $performance index of the system’s robustness to external disturbances and parameter uncertainty. And many useful signals and interference vary randomly. Therefore, the optimal control of stochastic systems and dynamics play an important role in the modern industry. Saving control resources is very important for actual production. Therefore DETC is considered in this paper. On the other hand, in practice, accurate system models are difficult to obtain. In order to tackle this difficulty, by designing a novel scheme via integral reinforcement learning technique, the system relaxes the requirement of drift dynamic and Zeno behavior is avoided.

This article focuses on the distributed robust fault estimation problem for a kind of discrete-time interconnected systems with input and output disturbances. For each subsystem, by letting the fault as a special state, an augmented system is constructed. Particularly, the dimensions of system matrices after augmentation are lower than some existing related results, which may help to reduce calculation amount, especially, for linear matrix inequality-based conditions. Then, a distributed fault estimation observer design scheme that utilizes the associated information among subsystems is presented to not only reconstruct faults, but also suppress disturbances in the sense of robust$H_{\infty }$optimization. Besides, to improve the fault estimation performance, a common Lyapunov matrix-based multiconstrained design method is first given to solve the observer gain, which is further extended to the different Lyapunov matrices-based multiconstrained calculation method. Thus, the conservatism is reduced. Finally, simulation experiments are shown to verify the validity of our distributed fault estimation scheme.

In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon H∞ optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3. Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.

For nonlinear systems, a novel adaptive dynamic programming (ADP) algorithm of self-triggered control (STC) strategy is proposed. This is a novel attempt to introduce self-triggering into the ADP algorithm. First, an identifier based on a generalized fuzzy hyperbolic model (GFHM) is established, which only uses input–output data to reconstruct the unknown system, thus reducing the requirements for system dynamics. Then, the critic neural network (NN) adjusts continuously, while actor NN updates the control strategy only at triggering instants. The event-triggered control (ETC) reduces the use of control resources and improves the anti-interference capability. However, it requires dedicated hardware to monitor whether triggering rules are violated, which is not feasible on most general-purpose devices. Hence, we propose a novel technique, which uses the current state of the device to determine the state measurement at the next moment, calculate the control law, and then abandon persistently monitoring of the plant. This technique is called STC. Finally, the closed-loop system is guaranteed to be ultimate uniform boundedness (UUBs). Furthermore, a simulation example is given.

This article concentrates on the neural network (NN)-based adaptive sliding-mode control (SMC) for fuzzy fractional-order system (FOS),$\alpha \in (0,1)$. First of all, a novel method of optimal SMC approach is developed for fuzzy FOSs by using the adaptive dynamic program (ADP), integral sliding mode, and NN with unmatched disturbances and time-varying delays. Next, to weaken the influence of the nonlinearities, the SMC strategy is proposed for the specific system, which is established on the corresponding SMD to ensure that the FOS reach the SMS in a finite time. Moreover, it shows that the matrix of SMS can be described by the linear matrix inequality (LMI). Furthermore, the Hamilton–Jacobi–Bell man (HJB) equation can be approximated by a single NN method, and the Lyapunov stability principle proves that the weight errors are convergent, further guaranteeing the asymptotically stability of the fuzzy FOS. Finally, to display that the above-presented policy is effective, simulation results are presented.

RGBT tracking has attracted increasing attention since RGB and thermal infrared data have strong complementary advantages, which could make trackers all-day and all-weather work. Existing works usually focus on extracting modality-shared or modality-specific information, but the potentials of these two cues are not well explored and exploited in RGBT tracking. In this paper, we propose a novel multi-adapter network to jointly perform modality-shared, modality-specific and instance-aware target representation learning for RGBT tracking. To this end, we design three kinds of adapters within an end-to-end deep learning framework. In specific, we use the modified VGG-M as the generality adapter to extract the modality-shared target representations. To extract the modality-specific features while reducing the computational complexity, we design a modality adapter, which adds a small block to the generality adapter in each layer and each modality in a parallel manner. Such a design could learn multilevel modality-specific representations with a modest number of parameters as the vast majority of parameters are shared with the generality adapter. We also design instance adapter to capture the appearance properties and temporal variations of a certain target. Moreover, to enhance the shared and specific features, we employ the loss of multiple kernel maximum mean discrepancy to measure the distribution divergence of different modal features and integrate it into each layer for more robust representation learning. Extensive experiments on two RGBT tracking benchmark datasets demonstrate the outstanding performance of the proposed tracker against the state-of-the-art methods.