Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

Fuzzy-Model-Based Finite Frequency Fault Detection Filtering Design for Two-Dimensional Nonlinear Systems

This article studies the fault detection filtering design problem for Roesser type two-dimensional(2-D)nonlinear systems described by uncertain 2-D Takagi-Sugeno(T-S)fuzzy models.Firstly,fuzzy Lyapunov functions are constructed and the 2-D Fourier transform is exploited,based on which a finite frequency fault detection filtering design method is proposed such that a residual signal is generated with robustness to external disturbances and sensitivity to faults.It has been shown that the utilization of available frequency spectrum information of faults and disturbances makes the proposed filtering design method more general and less conservative compared with a conventional nonfrequency based filtering design approach.Then,with the proposed evaluation function and its threshold,a novel mixed finite frequency H_(∞)/H_(-)fault detection algorithm is developed,based on which the fault can be immediately detected once the evaluation function exceeds the threshold.Finally,it is verified with simulation studies that the proposed method is effective and less conservative than conventional non-frequency and/or common Lyapunov function based filtering design methods.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Event-Triggered Asymmetric Bipartite Consensus Tracking for Nonlinear Multi-Agent Systems Based on Model-Free Adaptive Control

In this paper,an asymmetric bipartite consensus problem for the nonlinear multi-agent systems with cooperative and antagonistic interactions is studied under the event-triggered mechanism.For the agents described by a structurally balanced signed digraph,the asymmetric bipartite consensus objective is firstly defined,assigning the agents'output to different signs and module values.Considering with the completely unknown dynamics of the agents,a novel event-triggered model-free adaptive bipartite control protocol is designed based on the agents'triggered outputs and an equivalent compact form data model.By utilizing the Lyapunov analysis method,the threshold of the triggering condition is obtained.Subsequently,the asymptotic convergence of the tracking error is deduced and a sufficient condition is obtained based on the contraction mapping principle.Finally,the simulation example further demonstrates the effectiveness of the protocol.

Optimal Control of Nonlinear Systems Using Experience Inference Human-Behavior Learning

Safety critical control is often trained in a simulated environment to mitigate risk.Subsequent migration of the biased controller requires further adjustments.In this paper,an experience inference human-behavior learning is proposed to solve the migration problem of optimal controllers applied to real-world nonlinear systems.The approach is inspired in the complementary properties that exhibits the hippocampus,the neocortex,and the striatum learning systems located in the brain.The hippocampus defines a physics informed reference model of the realworld nonlinear system for experience inference and the neocortex is the adaptive dynamic programming(ADP)or reinforcement learning(RL)algorithm that ensures optimal performance of the reference model.This optimal performance is inferred to the real-world nonlinear system by means of an adaptive neocortex/striatum control policy that forces the nonlinear system to behave as the reference model.Stability and convergence of the proposed approach is analyzed using Lyapunov stability theory.Simulation studies are carried out to verify the approach.

Neuro-Based Higher Order Sliding Mode Control for Perturbed Nonlinear Systems

One of the great concerns when tackling nonlinear systems is how to design a robust controller that is able to deal with uncertainty.Many researchers have been working on developing such type of controllers.One of the most effi-cient techniques employed to develop such controllers is sliding mode control(SMC).However,the low order SMC suffers from chattering problem which harm the actuators of the control system and thus unsuitable to be used in many practical applications.In this paper,the drawbacks of low order traditional sliding mode control(FOTSMC)are resolved by presenting a novel adaptive radial basis function neural network–based generalized rth order sliding mode control strategy for nth order uncertain nonlinear systems.The proposed solution adopts neural networks for their excellent capability in function approximation and thus used to approximate the nonlinearities and uncertainties for systems under considera-tion.The approximation errors are completely considered in the developed approach.The proposed approach can be used with any order of sliding mode and thus can be generally used with various types of applications.The global sta-bility of the proposed control approach is proved through Lyapunov stability cri-terion.The proposed approach is validated and assessed through simulations on the nonlinear inverted pendulum system with severe modeling uncertainties.The simulations results show that the proposed approach provide superior perfor-mance compared with other approaches in the literature.

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link,and propose a new six-dimensional system,which exhibits some hidden attractors.The parameter switching algorithm is used to numerically study the dynamic behaviors of the system.Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors.A self-excited attractor with the change of its parameters is also recognized.In addition,numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra,Lyapunov dimensions,bifurcation diagrams,phase space orbits,and basins of attraction.Consequently,the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable.These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems,and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

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.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method.

Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

Robust adaptive dynamic surface control for nonlinear uncertain systems

We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.

Adaptive Nonlinear PID Control and Rule-Based Compensation for Systems with Backlash

The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for canceling the effect of backlash. Adaptive nonlinear PID controller together with rule? based backlash compensator was developed and a satisfactory tracking performance was achieved. Simulation results demonstrated the effectiveness of the proposed method.

ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL

The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique.

ADAPTIVE TRACKING CONTROL FOR A CLASS OF NONLINEAR COMPOSITE SYSTEMS *

In this paper, the problem of adaptive tracking control for a class of nonlinear large scale systems with unknown parameters entering linearly is discussed. Based on the theory of input output linearization of nonlinear systems, direct adaptive control schemes are presented to achieve bounded tracking. The proposed control schemes are robust with respect to the uncertainties in interconnection structure as well as subsystem dynamics. A numerical example is given to illustrate the efficiency of this method.

Decentralized Control Based on FNNSMC for Interconnected Uncertain Nonlinear Systems

A new type controller, fuzzy neural networks sliding mode controller (FNNSMC), is developed for a class of large scale systems with unknown bounds of high order interconnections and disturbances. Although sliding mode control is simple and insensitive to uncertainties and disturbances, there are two main problems in the sliding mode controller (SMC): control input chattering and the assumption of known bounds of uncertainties and disturbances. The FNNSMC, which incorporates the fuzzy neural networks (FNN) and the SMC, can eliminate the chattering by using the continuous output of the FNN to replace the discontinuous sign term in the SMC. The bounds of uncertainties and disturbances are also not required in the FNNSMC design. The simulation results show that the FNNSMC has more robustness than the SMC.