Decentralized adaptive neural prescribed performance control for high-order stochastic switched nonlinear interconnected systems with unknown system dynamics

In this paper, the problem of decentralized adaptive neural backstepping control is investigated for high-order stochastic nonlinear systems with unknown interconnected nonlinearity and prescribed performance under arbitrary switchings. For the control of high-order nonlinear interconnected systems, it is assumed that unknown system dynamics and arbitrary switching signals are unknown. First, by utilizing the prescribed performance control (PPC), the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, at each recursive step, only one adaptive parameter is constructed to overcome the over-parameterization, and RBF neural networks are employed to tackle the difficulties caused by completely unknown system dynamics. At last, based on the common Lyapunov stability method, the decentralized adaptive neural control method is proposed, which decreases the number of learning parameters. It is shown that the designed common controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the prescribed tracking control performance is guaranteed under arbitrary switchings. The simulation results are presented to further illustrate the effectiveness of the proposed control scheme.     

Decentralized output feedback stabilization for switched stochastic high-order nonlinear systems with time-varying state/input delays

This paper investigates decentralized output feedback stabilization problem for a class of switched stochastic high-order systems with time-varying state/input delays. With the help of coordinate transformations, a scaling gain is incorporated into the observers and controllers for the nominal system. Based on the homogeneous domination approach and stochastic Lyapunov–Krasovskii stability theorem, it is shown that global asymptotic stability in probability of the closed-loop system can be implemented by tuning the scaling gain. Two examples are given to demonstrate the feasibility of the proposed control method.     

Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties

This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.     

Reduced-order observer based fault estimation and fault-tolerant control for switched stochastic systems with actuator and sensor faults

This paper addresses the problems of fault estimation and fault-tolerant control for a class of switched stochastic systems with sensor and actuator faults. A reduced-order fault estimation observer is designed to estimate the system states, actuator and sensor faults, simultaneously. In the observer design process, intermediate variables are introduced such that the differential information of the measurement output is not included in the designed observer. Compared with the existing results, the dimension of the proposed observer is reduced, and the sensor fault can be completely unknown and unbounded. An observer based fault-tolerant controller is designed to stabilize the switched stochastic systems. Under arbitrary switching signal, the designed observer and controller can ensure that both the estimation error system and the closed-loop system are mean-square exponentially stable with disturbance attenuation performance. At last, both a numerical example and a switched electrical circuit example verify the proposed method.     

Global adaptive output feedback control for a class of nonlinear time-delay systems

This paper addresses the problem of global output feedback control for a class of nonlinear time-delay systems. The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate. With a change of coordinates, a linear-like controller is constructed, which avoids the repeated derivatives of the nonlinearities depending on the observer states and the dynamic gain in backstepping approach and therefore, simplifies the design procedure. Using the idea of universal control, we explicitly construct a universal-type adaptive output feedback controller which globally regulates all the states of the nonlinear time-delay systems.     

Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression

This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system.     

Distributed robust adaptive control of high order nonlinear multi agent systems

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust.     

Global adaptive control for uncertain nonaffine nonlinear hysteretic systems

In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes.     

Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation

This paper is concerned with the adaptive bipartite output consensus tracking problem of high-order nonlinear coopetition multi-agent systems with input saturation under a signed directed graph. A distributed fuzzy-based command filtered backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by the fuzzy logic system (FLS). The errors compensation mechanism is constructed to eliminate the errors caused by filters. Under the proposed control scheme, we only need to design one adaptive law for each agent, and it is proved that the bipartite output tracking errors converge into the desired neighborhood and all the closed-loop signals are bounded although the input saturation exists. Two numerical examples are included to verify the effectiveness of given scheme.     

Decentralized adaptive control of interconnected nonlinear systems with unknown control directions

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations.     

Adaptive NN output-feedback stabilization for a class of stochastic nonlinear strict-feedback systems

In this paper, the adaptive neural network output-feedback stabilization problem is investigated for a class of stochastic nonlinear strict-feedback systems. The nonlinear terms, which only depend on the system output, are assumed to be completely unknown, and only an NN is employed to compensate for all unknown upper bounding functions, so that the designed controller is more simple than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the closed-loop system can be proved to be asymptotically stable in probability. The simulation results demonstrate the effectiveness of the proposed control scheme.     

Robust fault detection for nonlinear networked systems with stochastic interval delay characteristics

In this paper, the problem of observer-based robust fault detection (RFD) for nonlinear networked systems with stochastic interval delay is investigated. By employing the information of probabilistic distribution of networked-induced time-varying delay, the observer-based fault detection filter as residual generator and a proposed performance index as objective function, the RFD of nonlinear networked systems is formulated as an optimization problem. The desired fault detection filter is constructed in terms of certain linear matrix inequalities, which depend on not only delay-interval but also delay-interval-occurrence-rate. Especially, the sub-optimal trade-off of strong robustness from residual signal to disturbance and parameter uncertainty, as well as high sensitivity to fault is obtained by a repeated application of a two-objective optimization algorithm. Numerical simulations are given to illustrate the effectiveness of proposed techniques.     

An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs

Considering the performances of conventional Kalman filter may seriously degrade when it suffers stochastic faults and unknown input, which is very common in engineering problems, a new type of adaptive three-stage extended Kalman filter (AThSEKF) is proposed to solve state and fault estimation in nonlinear discrete-time system under these conditions. The three-stage UV transformation and adaptive forgetting factor are introduced for derivation, and by comparing with the adaptive augmented state extended Kalman filter, it is proven to be uniformly asymptotically stable. Furthermore, the adaptive three-stage extended Kalman filter is applied to a two-dimensional radar tracking scenario to illustrate the effect, and the performance is compared with that of conventional three stage extended Kalman filter (ThSEKF) and the adaptive two-stage extended Kalman filter (ATEKF). The results show that the adaptive three-stage extended Kalman filter is more effective than these two filters when facing the nonlinear discrete-time systems with information of unknown inputs not perfectly known.     

Finite-time stabilization for a class of stochastic nonlinear systems via output feedback

This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.     

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.     

Multilevel adaptive control of nonlinear interconnected systems

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks.     

Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint

In this paper, we aim to solve the control problem of nonlinear affine systems, under the condition of the input deadzone and output constraint with the external unknown disturbance. To eliminate the effects of the input deadzone, a Radial Basis Function Neural Network (RBFNN) is introduced to compensate for the negative impact of input deadzone. Meanwhile, we design a barrier Lyapunov function to ensure that the output parameters are restricted. In support of the barrier Lyapunov method, we build an adaptive neural network controller based on state feedback and output feedback methods. The stability of the closed-loop system is proven via the Lyapunov method and the performance of the expected effects is verified in simulation.     

Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective.