Nonlinear Systems In Lower Triangular Form Research Articles

Event-triggered impulsive control of lower-triangular large-scale nonlinear systems based on gain scaling technique

This paper investigates the event-triggered impulsive control problem for a class of large-scale nonlinear systems in lower-triangular form. Based on gain scaling technique and impulsive control theory, a novel decentralized event-triggered impulsive control strategy is first put forward by introducing a static scaling gain, where no control input exists between two consecutive triggering points. Moreover, when the large uncertainties exist in system nonlinearities, we further develop a new control strategy by introducing a time-varying scaling gain. It is proved that the proposed closed-loop control strategies exclude the Zeno behavior without sacrificing the global convergence of system states. Compared with the existing results, it is the first time to apply impulsive control to lower-triangular large-scale nonlinear systems, and the advantages of event-triggered impulsive control and gain scaling technique are subtly combined in the proposed control strategies. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed schemes.

Adaptive decentralized stabilization of infinite networks of interconnected nonlinear systems with uncontrollable linearization

We solve the problem of decentralized adaptive stabilization for infinite networks of interconnected nonlinear systems in lower-triangular form with power integrators with uncontrollable linearization and with uncertainties in the last equation in which the control input appears. The feedback law is adaptive and continuous but not necessarily smooth, and the decentralized adaptive backstepping algorithm is based on small gain approach and on suitable gain assignment for each node of the infinite network.

Neural Networks-Based Adaptive Exponential Quasi-Passification and Output Tracking Control for Uncertain Switched Nonlinear Systems

In this paper, we mainly study the adaptive exponential quasi-passivity and adaptive tracking control of lower triangular uncertain switched nonlinear systems, even though the adaptive output tracking control problem of individual subsystem is unsolvable. First, the exponential quasipassivity concept is proposed to describe the energy changing of the overall switched nonlinear systems without the exponential quasi-passivity property of all the subsystems. Then, for switched nonlinear systems, the semiglobally uniformly ultimate boundedness is achieved by using exponential quasipassivity. Second, this result is applied to solve adaptive tracking control problem uncertain switched nonlinear systems in lower-triangular form. A new adaptive tracking control technique is developed by combining quasi-passification methods with adaptive backstepping techniques. The unknown nonlinear functions are approximated by the radial basis function neural networks. In contrast to the existing results, the multiple storage functions method reduces the conservativeness caused by a common Lyapunov function for all subsystems. Finally, the effectiveness of the proposed method is verified by an example.

Neural Networks-Based Adaptive Finite-Time Fault-Tolerant Control for a Class of Strict-Feedback Switched Nonlinear Systems.

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

Approximation-based disturbance observer approach for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched disturbances

ABSTRACTThis paper presents an approximation-based nonlinear disturbance observer (NDO) methodology for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched external disturbances. Compared with existing control results using NDO for nonlinear systems in lower-triangular form, the major contribution of this study is to develop an NDO-based control framework in the presence of non-affine nonlinearities and disturbances unmatched in the control input. An approximation-based NDO scheme is designed to attenuate the effect of compounded disturbance terms consisting of external disturbances, approximation errors and control coefficient nonlinearities. The function approximation technique using neural networks is employed to estimate the unknown nonlinearities derived from the recursive design procedure. Based on the designed NDO scheme, an adaptive dynamic surface control system is constructed to ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a neighbourhood of the origin. Simulation examples including a mechanical system are provided to show the effectiveness of the proposed theoretical result.