Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation

This paper studies the problem of adaptive neural network finite-time control for a class of non-triangular nonlinear systems with input saturation. Under the assumption that the nonlinearities have strict increasing smooth bounding functions, the backstepping technique can be used to design the state feedback controller and adaptive laws. Neural networks are adopted to approximate some unknown nonlinear functions. With the help of the finite-time Lyapunov stability theorem, it can be proved that the state of the closed-loop system can converge to an arbitrarily small neighborhood of the origin in a finite time. Finally, a numerical simulation example is given to show the effectiveness of the proposed design method.

     

Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems

This paper investigates the observer-based adaptive finite-time neural control issue of stochastic non-strict-feedback nonlinear systems. By establishing a state observer and utilizing the approximation property of the neural network, an adaptive neural network output-feedback controller is constructed. The controller solves the issue that the states of stochastic nonlinear system cannot be measured, and assures that all signals in the closed-loop system are bounded. Different from the existing adaptive control researches of stochastic nonlinear systems with unmeasured states, the proposed control scheme can guarantee the finite-time stability of the stochastic nonlinear systems. Furthermore, the effectiveness of the proposed control approach is verified by the simulation results.

     

Decentralised H∞ finite-time control equation of large-scale switched systems using robust performance minimisation

Many actual engineering applications can be modelled as large-scale switched system, while switching behaviours often occur in some short finite time intervals; thus, it is significant to ensure the finite-time boundedness of large-scale switched system in practical terms. In this paper, the problems of finite-time stability analysis and stabilisation for large-scale switched system are addressed. First, considering different switching signals for subsystems, the concepts of decentralised finite-time boundedness (DFTB) and decentralised finite-time H_∞ controllers are introduced, which focus on the dynamical transient behaviour of large-scale switched system during finite intervals. Under these concepts, several sufficient conditions are given to ensure a class of large-scale systems decentralised finite-time stable based on the decentralised average dwell times, and then the results are extended to H_∞ finite-time boundedness of large-scale switched system. Finally, based on the results on DFTB, optimal decentralised H_∞ controllers and average dwell times are designed under the minimum value of H_∞ performance. Numerical examples are given to illustrate the effectiveness of the proposed approaches in this paper.     

Adaptive Dynamic Surface Control for Finite-time Tracking of Uncertain Nonlinear Systems with Dead-zone Inputs and Actuator Faults

In this paper, a finite-time tracking control scheme for perturbed undetermined nonlinear systems governed by dead-zone inputs and actuator faults is investigated. By means of dynamic surface control technique, a suitable adaptive neural network controller is introduced, which guarantees that all signals in the closed-loop system are bounded, and that all state trajectories of the error dynamics converge to a small region in the sense of semi-globally practically finite-time stabilization. Finally, a numerical simulation is taken into consideration for the reliability of the proposed methodology.

     

一类非线性大系统分散自适应预设性能有限时间跟踪控制

研究一类非线性互联大系统的分散自适应预设性能有限时间跟踪控制问题.结合神经网络自适应技术、实际有限时间控制理论和预设性能控制方法,提出一种新的预设性能控制设计方法,以解决传统预设性能方法难以实现分散控制的问题.所设计的控制器能够保证大系统中各个子系统的跟踪误差被有限时间性能函数约束,在任意给定的停息时间内收敛到平衡点的一个给定的邻域内,且该闭环大系统的所有信号是实际有限时间稳定的.特别地,该停息时间与系统初始状态无关.两个仿真例子验证了所提出控制方法的有效性和优越性.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

Decentralised zero-sum differential game for a class of large-scale interconnected systems via adaptive dynamic programming

In this paper, a novel decentralised differential game strategy for large-scale nonlinear systems with matched interconnections is developed by using adaptive dynamic programming technique. First, the Nash-equilibrium solutions of the corresponding isolated differential game subsystems are found by appropriately redefining the associated cost functions accounting for the bounds of interconnections. Then, the decentralised differential game strategy is established by integrating all the modified Nash-equilibrium solutions of the isolated subsystems to stabilise the overall system. Next, the solutions of Hamilton–Jacobi–Isaaci equations are approximated online by constructing a set of critic neural networks with adaptation law of weights. The stability analysis of each subsystem is provided to show that all the signals in the closed-loop system are guaranteed to be bounded by utilising Lyapunov method. Finally, the effectiveness of the proposed decentralised differential game method is illustrated by a simple example.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

Observer-critic structure-based adaptive dynamic programming for decentralised tracking control of unknown large-scale nonlinear systems

In this paper, a decentralised tracking control (DTC) scheme is developed for unknown large-scale nonlinear systems by using observer-critic structure-based adaptive dynamic programming. The control consists of local desired control, local tracking error control and a compensator. By introducing the local neural network observer, the subsystem dynamics can be identified. The identified subsystems can be used for the local desired control and the control input matrix, which is used in local tracking error control. Meanwhile, Hamiltonian-Jacobi-Bellman equation can be solved by constructing a critic neural network. Thus, the local tracking error control can be derived directly. To compensate the overall error caused by substitution, observation and approximation of the local tracking error control, an adaptive robustifying term is employed. Simulation examples are provided to demonstrate the effectiveness of the proposed DTC scheme.     

Finite-time Adaptive Fault-tolerant Control for Nonlinear Systems With Multiple Faults

This paper focuses on the problem of adaptive finitetime fault-tolerant control for a class of non-lower-triangular nonlinear systems. The faults encountered in the control system include the actuator faults and the abrupt system fault. By applying backstepping design and neural networks approximation, an adaptive finite-time fault-tolerant control scheme is developed. It is shown that the proposed controller ensures that all signals in the closed-loop system are semi-globally practically finite-time stable and the track-ing error converges to a small neighborhood around the origin within finite time. The simulation is carried out to explain the validity of the developed strategy.      

A robotic system based on neural network controllers

In this paper, a control algorithm based on neural networks is presented. This control algorithm has been applied to a robot arm which has a highly nonlinear structure. The model based approaches for robot control (such as the computed torque technique) require high computational time and can result in a poor control performance, if the specific model-structure selected does not properly reflect all the dynamics. The control technique proposed here has provided satisfactory results. A decentralised model has been assumed here where a controller is associated with each joint and a separate neural network is used to adjust the parameters of each controller. Neural networks have been used to adjust the parameters of the controllers, being the outputs of the neural networks, the control parameters.     

Asymptotic sliding mode control approach to adaptive distributed tracking problem for multi-agent nonlinear delayed systems

In this article, a sliding mode coordinated decentralised state-feedback model reference adaptive control is developed for a class of large-scale uncertain multi-agent systems with time-varying delays in the nonlinear interconnections. The design procedure is based on a combination of the model coordination concept and a sliding mode control methodology. Novel decentralised controller parameterisations that are robust to unknown information exchange delays and to external disturbances with unknown bounds are proposed. Two different controllers are designed: one with discontinuous and one with continuous control action, respectively.     

Non-fragile robust finite-time H ∞ control for nonlinear stochastic it? systems using neural network

This paper deals with the problem of non-fragile robust finite-time H _?? control for a class of uncertain nonlinear stochastic It? systems via neural network. First, applying multi-layer feedback neural networks, the nonlinearity is approximated by linear differential inclusion (LDI) under statespace representation. Then, a sufficient condition is proposed for the existence of non-fragile state feedback finite-time H _?? controller in terms of matrix inequalities. Furthermore, the problem of nonfragile robust finite-time H _?? control is reduced to the optimization problem involving linear matrix inequalities (LMIs), and the detailed solving algorithm is given for the restricted LMIs. Finally, an example is given to illustrate the effectiveness of the proposed method.     

Finite-time fault-tolerant control for flutter of wing

In this paper, we use the radial basis function neural network and the finite-time H_∞ adaptive fault-tolerant control technique to deal with the flutter problem of wings with propulsion system, which is affected by input saturation, time delay, time-varying parameter uncertainties and external disturbances. Then sensor and actuator faults are both considered in the control design. The theory content of this article includes the trajectory optimization, modeling of wing flutter and fault-tolerant controller design. The stability of the finite-time H_∞ adaptive fault-tolerant controller is theoretically proved. Finally, simulation results are given to demonstrate the effectiveness of the scheme.     

Adaptive Finite-time Consensus for Second-order Nonlinear Multi-agent Systems with Input Quantization

In this paper, the adaptive finite-time consensus (FTC) control problem of second-order nonlinear multi-agent systems (MASs) with input quantization and external disturbances is studied. With the help of finite time control technology, a novel distributed adaptive control protocol is constructed to achieve FTC performance for second-order nonlinear MASs by using the recursive method. The control input is quantized through a hysteresis quantizer, which reduces the communication rate of arbitrary two agents. The unknown functions are approximated by adopting the radial basis function neural networks. Under the consensus protocols and adaptive laws, it can be proved that velocity errors of arbitrary two agents reach a small region of zero in finite time as well as position errors. Finally, the effectiveness of the proposed method is illustrated via a simulation example.

     

Adaptive fuzzy neural network finite-time command filtered control of n-link robotic systems with actuator saturation

The finite time tracking control of n-link robotic system is studied for model uncertainties and actuator saturation. Firstly, a smooth function and adaptive fuzzy neural network online learning algorithm are designed to address the actuator saturation and dynamic model uncertainties. Secondly, a new finite-time command filtered technique is proposed to filter the virtual control signal. The improved error compensation signal can reduce the impact of filtering errors, and the tracking errors of system quickly converge to a smaller compact set within finite time. Finally, adaptive fuzzy neural network finite-time command filtered control achieves finite-time stability through Lyapunov stability criterion. Simulation results verify the effectiveness of the proposed control.     

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.     

全局稳定的分散自适应神经网络反推跟踪控制

针对一类不确定大规模系统,研究其全局稳定的分散自适应神经网络反推跟踪控制问题.在假设不匹配的未知关联项满足部分已知的非线性Lipschitz条件下,采用神经网络作为前馈补偿器,逼近参考信号作为输入的未知关联函数;设计者可根据参考信号的界预先确定神经网络逼近域,同时保证了闭环系统的全局稳定性.仿真实例验证了控制算法的有效性.     

Output feedback adaptive DSC for nonlinear systems with guaranteed L-infinity tracking performance

In this paper, the problem of output tracking for a class of uncertain nonlinear systems is considered. First, neural networks are employed to cope with uncertain nonlinear functions, based on which state estimation is constructed. Then, an output feedback control system is designed by using dynamic surface control (DSC). To guarantee the L-infinity tracking performance, an initialization technique is presented. The main feature of the scheme is that explosion of complex- ity problem in backstepping control is avoided, and there is no need to update the unknown parameters including control gains as well as neural networks weights, the adaptive law with one update parameter is necessary only at the first design step. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the L-infinity performance of system tracking error can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.     

Feedback-Linearization-Based Neural Adaptive Control for Unknown Nonaffine Nonlinear Discrete-Time Systems

A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in affine-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input–output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings.