Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network(NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.

Stability analysis of linear/nonlinear switching active disturbance rejection control based MIMO continuous systems

In this paper,a linear/nonlinear switching active disturbance rejection control(SADRC)based decoupling control approach is proposed to deal with some difficult control problems in a class of multi-input multi-output(MIMO)systems such as multi-variables,disturbances,and coupling,etc.Firstly,the structure and parameter tuning method of SADRC is introduced into this paper.Followed on this,virtual control variables are adopted into the MIMO systems,making the systems decoupled.Then the SADRC controller is designed for every subsystem.After this,a stability analyzed method via the Lyapunov function is proposed for the whole system.Finally,some simulations are presented to demonstrate the anti-disturbance and robustness of SADRC,and results show SADRC has a potential applications in engineering practice.

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.

Robust H-infinity integral sliding mode control for a class of uncertain switched nonlinear systems

This paper develops a new method to deal with the robust H-infinity control problem for a class of uncertain switched nonlinear systems by using integral sliding mode control.A robust H-infinity integral sliding surface is constructed such that the sliding mode is robust stable with a prescribed disturbance attenuation level γ for a class of switching signals with average dwell time.Furthermore,variable structure controllers are designed to maintain the state of switched system on the sliding surface from the initial time.A numerical example is given to illustrate the effectiveness of the proposed method.

H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems. Each switched system in this class is composed of a zero-mput asymptotically stable nonlinear part, which is also a switched system, and a linearizable part which is controllable. Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively. The nonlinear state feedback and switching law are designed. We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law. The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.

Broad-Band All-Optical Wavelength Conversion of Differential Phase-Shift Keyed Signal Using an SOA-Based Nonlinear Polarization Switch

Broad-band all-optical wavelength conversion of differential phase-shift keyed （DPSK） signal is experimentally demonstrated. This scheme is composed of a one-bit delay interferometer demodulation stage followed by a semiconductor optical amplifier （SOA） based nonlinear polarization switch. A wavelength converter for the 10 G b/s DPSK signal is presented, which has a wide wavelength range of more than 30 nm. The converted signals experience small power penalties less than 1.4 dB compared with the original signal, at a bit error rate of 10-9. Additionally, the optical spectra, the measured waveforms and the open eye diagrams of the converted signals show a high quality wavelength conversion performance.

Periodic Modulation of Nonlinearity in a Fiber Bragg Grating:A Numerical Investigation

We present numerical studies on the switching characteristics of a fiber Bragg grating (FBG) with modulation in the third order nonlinear index of refraction along it’s length. The FBG is operating in a continuous wave regime (CW). This study was done taking into account the possible asymmetry brought by the non harmonic modulation of the nonlinearity, leading to different reflection and transmission characteristics, that depend on the direction of propagation along the modulated nonlinear FBG. This phenomenon may be useful for applications like an optical isolator. It was found that for a set of values of the modulation parameter, the FBG can exhibit multistable states. The numerical studies were obtained starting from the coupled-mode equations solved from the coupled-mode theory and simulated using the fourth-order Runge-Kutta method.

Adaptive Tracking Control for Output-Constrained Switched MIMO Pure-Feedback Nonlinear Systems with Input Saturation

In this paper,an adaptive neural tracking control scheme for a class of uncertain switched multi-input multi-output(MIMO)pure-feedback nonlinear systems is proposed.The considered MIMO pure-feedback nonlinear system contains input and output constraints,completely unknown nonlinear functions and time-varying external disturbances.The unknown nonlinear functions representing system uncertainties are identified via radial basis function neural networks(RBFNNs).Then,the Nussbaum function is utilized to deal with the nonlinearity issue caused by the input saturation.To prevent system outputs from violating prescribed constraints,the barrier Lyapunov functions(BLFs)are introduced.Also,a switched disturbance observer is designed to make the time-varying external disturbances estimable.Based on the backstepping recursive design technique and the Lyapunov stability theory,the developed control method is verified applicable to ensure the boundedness of all signals in the closed-loop system and make the system output track given reference signals well.Finally,a numerical simulation is given to demonstrate the effectiveness of the proposed control method.

Connectivity-preserving consensus of nonlinear switched multi-agent systems with predefined accuracy

This paper focuses on the connectivity-preserving consensus of nonlinear switched multi-agent systems with predefined accuracy.Accordingly,a unified error transformation is adopted to preserve the initial interaction pattern determined by agents’limited communication ranges and initial states.Meanwhile,the so-called congelation of variables method is used to handle the unknown aperiodically time-varying parameters,which are fast-varying in an unknown compact set with only their radii known a priori.In addition,a series of continuously differentiable functions are incorporated into the Lyapunov function to design the controller.Based on Lyapunov stability theory,the proposed control algorithm guarantees that the consensus errors converge with a predefined accuracy,whereas most existing connectivity-preserving results can only ensure uniform ultimate boundedness.Simultaneously,all closed-loop signals remain bounded.Finally,two simulations are provided to validate the effectiveness of the proposed control protocol.

Non-fragile stabilisation of nonlinear switched systems with actuator saturation

For nonlinear continuous-time switched systems,the problem ofhowto overcome the controller vulnerability is studied when the saturating actuator is considered.The sufficient condition of non-fragile stabilisation of the system is derived by using the method of multiple Lyapunov functions.Then,a switching law and the non-fragile state feedback controllers are designed such that the closed-loop system can be asymptotically stabilised at the origin.Finally,when some scalar parameters of the closed-loop system are given,the design issue of the non-fragile state feedback controllers and the switching law,which aim at enlarging the estimation of domain of attraction for closed-loop system,is transformed into a convex optimisation issue with linear matrix inequalities(LMI)constraints,and a numerical example is given to verify the effectiveness of the proposed method.

Output Feedback Stabilization of Switched Stochastic Nonlinear Systems Under Arbitrary Switchings

This paper is concerned with the problem of global output feedback stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings. The subsystems are assumed to be in output feedback form and driven by white noise. By introducing a common Lyapunov function, the common output feedback controller independent of switching signals is constructed based on the backstepping approach. It is proved that the zero solution of the closed-loop system is fourth-moment exponentially stable. An example is given to show the effectiveness of the proposed method.

Attitude tracking control for variable structure near space vehicles based on switched nonlinear systems

An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle （VSNSV） in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control （DSC） approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.

Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.

State tracking model reference adaptive control for switched nonlinear systems with linear uncertain parameters

Model reference adaptive control （MRAC） is considered for a class of switched nonlinear systems in which the unknown parameters appear linearly. The linear uncertain parameters in each subsystem can be expressed as a vector and the uncertain vectors in different subsystems are estimated individually by different vector variables. Update laws are designed such that the parameter estimation will ＇freeze＇ until its corresponding subsystem is active. Controllers for subsystems are given to ensure asymptotic states tracking under arbitrary switchings. Two examples are presented to validate the proposed method.

Output Feedback Tracking Control for a Class of Switched Nonlinear Systems with Time-varying Delay

This paper studies the problem of tracking control for a class of switched nonlinear systems with time-varying delay. Based on the average dwell-time and piecewise Lyapunov functional methods, a new exponential stability criterion is obtained for the switched nonlinear systems. The designed output feedback H∞controller can be obtained by solving a set of linear matrix inequalities(LMIs).Moreover, the proposed method does not need that a common Lyapunov function exists for the switched systems, and the switching signal just depends on time. A simulation example is provided to demonstrate the effectiveness of the proposed design scheme.

Data-Driven Leader-Follower Output Synchronization for Networked Non-Linear Multi-Agent Systems with Switching Topology and Time-Varying Delays

This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs,a leader is introduced whose connectivity to the followers varies with time, and a novel data-driven consensus protocol based on model free adaptive control is proposed, where the reference input of each follower is designed to be the time-varying average of the neighboring agents＇ outputs. Both the case when the leader is with a prescribed reference input and the case otherwise are considered.The proposed protocol allows for time-varying delays, switching topology, and does not use the agent structure or the dynamics information implicitly or explicitly. Sufficient conditions are derived to guarantee the closed-loop stability, and conditions for consensus convergence are obtained, where only a joint spanning tree is required. Numerical simulations and practical experiments are conducted to demonstrate the effectiveness of the proposed protocol.

Global Disturbance Rejection of Switched Nonlinear Systems with Switched Internal Model

This paper investigates the problem of global disturbance rejection for a class of switched nonlinear systems where the solvability of the disturbance rejection problem for subsystems is not assumed. The disturbances are assumed to be sinusoidal with completely unknown frequencies, phases and amplitudes. First, as an extension of the classic concept of internal model for non-switched systems, a switched internal model is proposed. Second, in order to solve the problem under study, an adaptive control method is established on the basis of the multiple Lyapunov functions method. Also,adaptive state-feedback controllers of subsystems are designed and incorporated with a switching law to asymptotically reject the unknown disturbances. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.

The Tolerance of All-Optical Switching Based on Cascaded Second-Order Nonlinearity in PPLN APE Waveguide

Based on solving the couple mode equation numerically, the characterization of the signal power on the gate power was analyzed. And the relationship of the tolerance of the grating period and the bulk temperature on the interaction length was analyzed.