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This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations. [ABSTRACT FROM AUTHOR]

This article is dedicated to model order reduction of linear time-invariant passive systems, i.e., positive real (PR) systems, based on the balanced truncation (BT) concept. The main feature of this article is that we have used the phase angle of the transfer function, $G(s)$ , in model order reduction for the first time in the proposed method, which results in more accurate reduced-order models. It is worth noting that this hypothesis has been never made before in any other model order reduction techniques. Furthermore, new gramians are calculated corresponding to their associated new Riccati equations and Lur’e equations, which are in turn achieved by using Kalman–Yakubovic–Popov (KYP) lemma and linear matrix inequalities (LMI). Thereafter, a novel passivity preserving model order reduction algorithm, which takes the phase angle of the transfer function, $G(s)$ , into account, is presented. It is demonstrated that the proposed method is a generalization of the positive real balanced truncation (PRBT) method, and it is perfectly capable of providing more accurate approximation error compared to PRBT. Finally, numerical examples are included to figure out the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive finite-time quantized tracking control problem for a class of full state-constrained nonlinear systems with unknown control directions based on a modified fractional-order dynamic surface control (FODSC) technique. First, fractional calculus is introduced to filter design to avoid the issue of the “explosion of complexity” exposed in the traditional backstepping technique. To facilitate the control design, barrier Lyapunov functions and Nussbaum gain technique are utilized to handle full state-constrained problem and the unknown control directions, respectively. In addition, the fuzzy logic systems are employed to approximate the unknown nonlinearity of the system. By integrating with the approximation errors and compensating signals, a composite adaptive quantized controllers is designed to guarantee all the signals of the closed-loop systems are bounded and tracking error converges to an arbitrarily small neighborhood of the zero within a finite time. Finally, a mechanical horizontal platform model and a Brusselator model are carried out to verify the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

This article considers the Nussbaum gain adaptive control issue for a type of nonlinear systems, in which some sophisticated and challenging problems, such as periodic disturbances, dead zone output, and unknown control direction are addressed. The Fourier series expansion and radial basis function neural network are incorporated into a function approximator to model time-varying-disturbed function with a known period in nonlinear systems. To deal with the problems of the dead zone output and unknown control direction, the Nussbaum-type function is recommended in the design of the control algorithm. Applying the Lyapunov stability theory and backstepping technique, the proposed control strategy ensures that the tracking error is pulled back to a small neighborhood of origin and all closed-loop signals are bounded. Finally, simulation results are presented to show the availability and validity of the analysis approach. [ABSTRACT FROM AUTHOR]

This article considers the decentralized fractional-order fault-tolerant control problem for unmanned aerial vehicles (UAVs) against wind disturbances and actuator faults in a directed communication network. A new composite adaptive disturbance observer-based decentralized fractional-order fault-tolerant control (CADOB-DFO-FTC) scheme, which incorporates fractional-order (FO) sliding-mode surfaces, nonlinear disturbance observers (NDOs), fuzzy wavelet neural networks (FWNNs), and robust controllers, is developed to achieve the attitude tracking control of networked UAVs in a decentralized way. Based on the FO sliding-mode surfaces, the NDOs are first developed to estimate the lumped uncertainties due to the aerodynamic parameter perturbations, wind disturbances, and actuator faults. Then, adaptive FWNNs with updating weighting matrices, mean vectors, and deviation vectors are constructed to effectively attenuate the adverse effects induced by the NDO estimation errors. Furthermore, to compensate the FWNN approximation errors, robust controllers are integrated into the developed control scheme to enhance the approximation abilities. It is shown that by using Lyapunov methods, all UAVs can track their attitude references. Finally, comparative simulation results are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a novel membership-function dependent approach for the stability/positivity investigation and controller design of a nonlinear, discrete-time system with time delay which is represented by a polynomial fuzzy model to enhance the accuracy of the approximation. The polynomial fuzzy controller is designed based on imperfect premise matching design concept and a set of sum of square (SOS)-based conditions is formulated to check the positivity and stability of the control system. To relax the conservative SOS-based conditions, we employ piecewise Taylor series membership functions (PTSMFs) and introduce the membership function knowledge into the stability conditions. Slack matrices are used to represent the membership function and premise variable knowledge, which contains: 1) regional approximation error between PTSMFs and original membership functions; 2) regional bounds of PTSMFs; and 3) the property knowledge of interpolation membership function of PTSMFs and regional bounds of premise variables. A simulation example is finally given to verify our novel stability/positivity conditions and discrete-time polynomial fuzzy (DPF) controller design. [ABSTRACT FROM AUTHOR]

This article addresses a filter-driven-approximation (FDA)-based design problem for the distributed containment control of multi-input–multi-output pure-feedback multiagent systems with completely unknown nonlinearities. Local filter-driven approximators are designed to compensate for unknown nonaffine nonlinear functions lumped in the local controller design procedure where the first-order filtered signals of the error surfaces, state variables, and control inputs are linearly combined for the design of the filter-driven approximators. A containment control scheme using the filter-driven function approximators is recursively constructed to ensure that the outputs of the followers converge to the convex hull spanned by multiple time-varying leaders. Compared with existing containment control results using adaptive neural-network-based or fuzzy-based approximators, the proposed FDA-based containment control scheme depends only on the relative output information among agents and does not require any adaptive techniques. Thus, the proposed control structure can be simplified. It is shown that the closed-loop signals, including approximation errors are semi-globally uniformly ultimately bounded. Simulation examples are provided to validate the effectiveness of the proposed theoretical strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic sliding mode control (SMC) approach to the robust voltage regulation of dc–dc boost converters by using interval type-2 fuzzy neural networks (IT2FNNs). First, uncertainties caused by the perturbation of the input inductor and the output capacitor are represented with some bounded approximation errors, by the utilization of a Takagi–Sugeno (T–S) fuzzy modeling approach. Based on the represented model of the boost converter, a new type of sliding surface is designed depending on the duty cycle and reference inputs of the converter. Then, a dynamic SMC law is designed, by considering that the perturbation of the uncertain parameters, including input inductor, output capacitor, load resistor, and input voltage, is bounded. Meanwhile, we adopt an exponential plus power approaching law in the sliding mode controller for fast reachability of the sliding surface and a small chattering in the duty cycle input. Moreover, in terms of the considered uncertainties, a novel IT2FNN-based dynamic SMC law is derived, by applying simplified ellipsoidal-type membership functions in the type-2 fuzzy neural network. To improve the capacity to manage the uncertainties, some online learning algorithms for the updating of the IT2FNN are designed by a gradient descent method (GDM), without the requirement of the boundedness of the uncertainties. The resulting tracking error system is synthesized to be bounded stable based on the designed IT2FNN-based dynamic SMC. Finally, the effectiveness of the proposed adaptive IT2FNN-based dynamic SMC method is verified by some comparative simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the position tracking control problem for an induction motor with completely unknown nonlinearities. A novel control scheme is presented by using the gradient descent algorithm, adaptive backstepping technique, neural networks (NNs), and extended differentiators. Differing from some existing results which only designed the adaption of weights of NNs, our proposed control strategy provides training for all the parameters of NNs, including the basis functions’ widths and centers. With the help of the gradient descent algorithm and Lyapunov stability criterion, the convergence of both the NN approximation error and the system tracking error can be guaranteed. Finally, a simulation example shows the advantages of our proposed method compared with direct adaptive NN control strategy. [ABSTRACT FROM AUTHOR]

The optimal control problem of discrete-time nonlinear systems depends on the solution of the Bellman equation. In this paper, an adaptive reinforcement learning (RL) method is developed to solve the complex Bellman equation, which balances value iteration (VI) and policy iteration (PI). By adding a balance parameter, an adaptive RL integrates VI and PI together, which accelerates VI and avoids the need of an initial admissible control. The convergence of the adaptive RL is proved by showing that it converges to the Bellman equation. Subsequently, the adaptive RL is realized by using the neural network (NN) approximation for value function and a least-squares scheme is developed for updating NN weights. Then, the convergence of NN-based adaptive RL is proved with considering NN approximation error. To further improve its performance, an adaptive rule is developed for tuning balance parameter in adaptive RL iteration by iteration. Finally, the effectiveness of the adaptive RL is validated with simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, a novel distributed ${{H}_{ \infty }}$ optimal tracking control scheme is designed for a class of physically interconnected large-scale nonlinear systems in the presence of strict-feedback form, external disturbance and saturating actuators. First, by designing feedforward control, the distributed ${{H}_{\infty }}$ optimal tracking control problem of a physically interconnected large-scale system is transformed into equivalent control of a decoupled multiagent system. Subsequently, a feedback control algorithm is designed to learn the optimal control input and the worst-case disturbance policy. The algorithm guarantees that the function approximation error and the distributed tracking error are uniformly ultimately bounded while the cost function converges to the bounded $ {L}_{{2}}$ -gain optimal value. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results of distributed control for the mobile multirobot system. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive neural network (NN) control scheme is proposed for a class of nonlinear systems with unknown control direction. By introducing some differentiable functions and high-order Lyapunov functions, the obstacle caused by unknown control direction in NN control is successfully circumvented and all closed-loop signals are shown to be uniformly bounded up to infinite time. Meanwhile, by introducing an error transformation technique, it is rigorously proved that the argument of the unknown nonlinearities remains within a compact set which can be explicitly calculated a priori, making the NN approximation always valid. Moreover, with the aid of a bound estimation approach, we effectively compress the impact of approximation errors and external disturbances and steer the tracking error into a predefined small residual set. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the expected rate of convergence to consensus in an asymmetric network represented by a weighted directed graph. The initial state of the network is represented by a random vector and the expectation is taken with respect to the random initial condition of the network. The proposed convergence rate is described in terms of the eigenvalues of the Laplacian matrix of the network graph. The generalized power iteration algorithm is then introduced based on the Krylov subspace method to compute the proposed expected convergence rate in a centralized fashion. To this end, the Laplacian matrix of the network is transformed to a new matrix such that existing techniques can be used to find the eigenvalue representing the expected convergence rate of the network. The convergence analysis of the centralized algorithm is performed with a prescribed upper bound on the approximation error of the algorithm. A distributed version of the centralized algorithm is then developed using the notion of consensus observer. The efficiency of the algorithms is subsequently demonstrated by simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the disturbance observer-based composite fuzzy control of a class of uncertain nonlinear systems with unknown dead zone. With fuzzy logic system approximating the unknown nonlinearities, composite learning is constructed on the basis of a serial–parallel identifier. By introducing the intermediate signal, the disturbance observer is developed to provide efficient learning of the compounded disturbance which includes the effect of time-varying disturbance, fuzzy approximation error, and unknown dead zone. Based on the disturbance estimation and fuzzy approximation, the adaptive fuzzy controller is synthesized with novel updating law. The stability analysis of the closed-loop system is rigorously established via Lyapunov approach. The performance of the proposed controller is verified via simulation that faster convergence and higher precision are obtained. [ABSTRACT FROM PUBLISHER]