Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.     

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.     

Observer design for a class of nonlinear fractional-order systems with unknown input

A full order fractional-order observer is designed for a class of Lipschitz continuous-time nonlinear fractional-order systems with unknown input. Sufficient conditions of existence for the designed observer and stability of state estimation error system are developed by reconstructing state and using general quadratic Lyapunov function. By applying fractional-order extension of Lyapunov direct method, the stability of the fractional-order state estimation error system is analyzed. Due to the conditions involving a nonlinear matrix inequality, a new sufficient condition with linear matrix inequality (LMI) is reformulated, which makes the full order fractional-order observer implemented easily by using Matlab LMI toolbox. Examples are taken to show the effectiveness of the proposed approach by numerical simulations.     

Quantized asynchronous extended dissipative observer-based sliding mode control for Markovian jump TS fuzzy systems

This article is dedicated to the issue of asynchronous adaptive observer-based sliding mode control for a class of nonlinear stochastic switching systems with Markovian switching. The system under examination is subject to matched uncertainties, external disturbances, and quantized outputs and is described by a TS fuzzy stochastic switching model with a Markovian process. A quantized sliding mode observer is designed, as are two modes-dependent fuzzy switching surfaces for the error and estimated systems, based on a mode dependent logarithmic quantizer. The Lyapunov approach is employed to establish sufficient conditions for sliding mode dynamics to be robust mean square stable with extended dissipativity. Moreover, with the decoupling matrix procedure, a new linear matrix inequality-based criterion is investigated to synthesize the controller and observer gains. The adaptive control technique is used to synthesize asynchronous sliding mode controllers for error and SMO systems, respectively, so as to ensure that the pre-designed sliding surfaces can be reached, and the closed-loop system can perform robustly despite uncertainties and signal quantization error.Finally, simulation results on a one-link arm robot system are provided to show potential applications as well as validate the effectiveness of the proposed scheme.     

Disturbance observer-based robust missile autopilot design with full-state constraints via adaptive dynamic programming

This paper aims to develop a robust optimal control method for longitudinal dynamics of missile systems with full-state constraints suffering from mismatched disturbances by using adaptive dynamic programming (ADP) technique. First, the constrained states are mapped by smooth functions, thus, the considered systems become nonlinear systems without state constraints subject to unknown approximation error. In order to estimate the unknown disturbances, a nonlinear disturbance observer (NDO) is designed. Based on the output of disturbance observer, an integral sliding mode controller (ISMC) is derived to counteract the effects of disturbances and unknown approximation error, thus ensuring the stability of nonlinear systems. Subsequently, the ADP technique is utilized to learn an adaptive optimal controller for the nominal systems, in which a critic network is constructed with a novel weight update law. By utilizing the Lyapunov's method, the stability of the closed-loop system and the convergence of the estimation weight for critic network are guaranteed. Finally, the feasibility and effectiveness of the proposed controller are demonstrated by using longitudinal dynamics of a missile.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Robust observer design for multi-motor web-winding system

This paper develops a novel observer design method for multi-motor web-winding system. Firstly, the multi-motor web-winding system is regarded as a synthetic system with several subsystems, where the dynamic model for each subsystem is given. Then, the nonlinear diffeomorphism transformation is introduced to obtain a transformed system with block triangular structure and the interconnections among the subsystems are allowed. Next, a decentralized high-gain observer with sliding mode is designed for the transformed system, based on which the estimation error dynamics can be got. Sufficient condition of asymptotic stability for estimation error dynamics is derived by the Lyapunov stability theory and the observer gain is obtained. After that, the observer for original multi-motor web-winding system is achieved via inverse transformation. Finally, the simulation and analysis are performed in the three-motor web-winding system to verify the effectiveness of the proposed observer.     

Dynamical robust H∞ filtering for nonlinear uncertain systems: An LMI approach

In this paper, a new approach to robust H_∞ filtering for a class of nonlinear systems with time-varying uncertainties is proposed in the LMI framework based on a general dynamical observer structure. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions and appear in both state and measured output equations. The admissible Lipschitz constants of the nonlinear functions are maximized through LMI optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics with prespecified disturbance attenuation level and is robust against time-varying parametric uncertainties as well as Lipschitz nonlinear additive uncertainty.     

Dissipative observers for discrete-time nonlinear systems

This paper addresses the problem of designing a state observer for a class of nonlinear discrete-time systems using the dissipativity theory. We show that the dissipative observation methodology, originally proposed by one of the authors for continuous-time nonlinear systems, can be extended to the discrete-time case. For constructing a convergent observer, the methodology is applied to the nonlinear estimation error dynamics, which is decomposed into a discrete-time Linear Time-Invariant (LTI) subsystem in the forward loop, connected to a time-varying static nonlinearity in the feedback loop. In order to assure asymptotic stability of the closed-loop, complementary dissipativity conditions are imposed on each of the subsystems: (i) the static nonlinearity is required to be dissipative with respect to a quadratic supply rate, and (ii) the observer gains are designed such that the LTI system is dissipative with respect to a complementary supply rate. As in the continuous time framework, the proposed method includes as special cases, unifies and generalizes some observer design methods proposed previously in the literature. A great advantage of the Dissipative Observer Design Method proposed here is that it leads to Matrix Inequalities for the design of the observer gains, and these can be usually converted into Linear Matrix Inequalities (LMI’s). The results are illustrated using Chua’s Chaotic system.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Actuator fault diagnosis for a class of bilinear systems with uncertainty

In this paper, the actuator fault diagnosis problem for a class of bilinear systems with uncertainty is discussed. The system is transformed into two different subsystems. One is not affected by actuator fault, so an adaptive observer can be designed such that, under certain conditions, the observer error dynamics is stable. The other whose states can be measured is affected by the faults. The observation scheme is then used for model-based fault diagnosis. Finally, an example of a semiactive suspension system is used to illustrate the applicability of the proposed method.     

Command filtered adaptive output feedback design with novel Lyapunov-based analysis for nonlinear systems with unmodeled dynamics

This paper presents a novel Lyapunov function-based backstepping controller design to tackle the tracking problems for nonlinear systems with unmodeled dynamics and unmeasurable states. The coexistence of unmodeled dynamics and unmeasurable states is the main challenge, which calls for novel techniques to take these two factors into account simultaneously. First, the classical Luenberger observer is extended with a novel transformation function to decouple the original system state and state estimation error. In this way, the effect of unmodeled dynamics on system stability can be separately considered. On this basis, a command-filtered controller is designed to simplify the backstepping design procedures. It is worthy to pointed out that, a novel Lyapunov function is developed to simplify the stability analysis with command filter, where the filter errors, the observer error, compensated tracking errors, and parameter estimation errors can be guaranteed to be semi-globally uniformly ultimate bounded. The simulation studies are investigated to validate the effectiveness of the presented design scheme.     

A variable gain impulsive observer for Lipschitz nonlinear systems with measurement noises

This paper investigates the variable gain impulsive observer design problem for Lipschitz nonlinear systems. It is assumed that the measurements are contaminated by noise and received by observer at aperiodic instants. To establish a tractable design condition for impulsive observers, the piecewise linear interpolation method is used to construct the variable gain function. To quantify the impact of the measurement noises and exogenous disturbance on the estimation error, a Lyapunov-based condition for establishing exponential input-to-state stability (EISS) property of the observation error dynamics is presented. Then it is shown that the EISS condition can be expressed as a set of linear matrix inequalities (LMIs) by introducing a piecewise quadratic Lyapunov function. A convex optimization problem is proposed in which the EISS gain is minimized. Comparisons with the existing methods show the effectiveness of the proposed design technique.     

Observer-based output feedback control for networked systems with dual-channel event-triggered sampling and quantization

This paper investigates the problem of observer-based output feedback control for linear networked systems with dual-channel event-triggered mechanisms and quantization. Both continuous-time and discrete-time event detection cases are discussed. In the continuous-time case, the stability of observer error dynamics and closed-loop system are analyzed respectively, and it is proved that Zeno behavior would not occur. In order to approach engineering practice, in the discrete-time case, two types of network attacks including denial-of-service (DoS) and fault data injection (FDI) attacks are considered, whose nature property is characterized by Bernoulli variables. By combining these factors and transmission delay, a novel augmented system model is proposed, and some sufficient conditions are derived based on Lyapunov functional approach and linear matrix inequalities (LMIs). Compared with the existing results, this framework is more comprehensive and practical, and the global uniform ultimate boundedness of closed-loop systems can be guaranteed. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.     

一类不确定时延非线性大系统的分散控制

本文研究了一类具有关联延迟和系统参数不确定的非线性大系统的分散控制问题,系统的匹配/非匹配不确定参数范数有界。首先基于状态观测器设计时延独立的动态输出反馈控制律，并根据 稳定性理论推导并证明了在该控制律作用下系统稳定的充分条件。最后给出一个数值例子来说明本文结果的可行性，仿真结果表明设计出的控制器不仅使得闭环系统稳定而且保证系统不受参数不确定和时延的影响。     

Sampled-data sliding mode observer for robust fault reconstruction: A time-delay approach

A sliding mode observer in the presence of sampled output information and its application to robust fault reconstruction is studied. The observer is designed by using the delayed continuous-time representation of the sampled-data system, for which sufficient conditions are given in the form of linear matrix inequalities (LMIs) to guarantee the ultimate boundedness of the error dynamics. Though an ideal sliding motion cannot be achieved in the observer when the outputs are sampled, ultimately bounded solutions can be obtained provided the sampling frequency is fast enough. The bound on the solution is proportional to the sampling interval and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under sampled outputs and system uncertainties. It is shown that actuator or sensor faults can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology compared to existing sliding mode observer design approaches.     

Adaptive event-triggering distributed filter of positive Markovian jump systems based on disturbance observer

This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Output feedback control with performance recovery analysis for a class of time-delay nonlinear systems

A class of nonlinear systems is considered in this paper which contains multiple time-varying delays and additional disturbances. Motivated by a robust model-free state-feedback controller, an observer-based output-feedback controller is designed to achieve uniformly ultimately bounded tracking. A high-gain-like observer is designed to estimate the unmeasurable current states utilizing the delayed output, and the estimated states are further used to facilitate the development of the output-feedback controller. The control input is saturated to avoid the side effects resulting from the high-gain-like observer’s peaking phenomenon. Under some sufficient conditions, it is proved that the saturation of the controller will no longer take place after a specific time, and both the estimation error and the tracking error will be uniformly ultimately bounded. In the stability analysis, Lyapunov–Krasovskii functionals are implemented to alleviate the difficulties resulting from the delays. Relationships among the delays, the desired trajectories, and the maximal tolerable error are identified. Behaviors of the closed-loop system under different observation and control gains are also analyzed. A two-link revolute robotic arm is taken as an example to conduct a series of simulations, and the results show that the output-feedback controller can recover the performance of the corresponding state-feedback controller.     

Fractional-order control with second-order sliding mode algorithm and disturbance estimation for vibration suppression of marine riser

Suppression of the vibration caused by environmental loads in marine risers is critical to prevent irreparable damages. This paper addresses this issue by proposing a novel boundary control for a flexible riser connected to a vessel at its top. In this regard, initially, a sliding mode observer (SMO)-based disturbance estimator is constructed to estimate the uncertainty of the vessel's dynamics. Next, using backstepping, a suitable virtual control along with the respective error dynamics are derived. A fractional-order error surface is defined to achieve Mittag-Leffler convergence for the control error variable. A second-order sliding mode (SOSM) control law is used to stabilize this error surface. The boundedness and ultimate boundedness of the riser's deflection under the proposed boundary control is shown by Lyapunov analysis. Comparative simulations demonstrate the robust vibration suppression performance of the proposed controller.