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.     

Parameters estimation using sliding mode observer with shift operator

In different areas of engineering, mathematical models are used to describe real life phenomena and experiments are conducted to validate them. It is common that these models may contain a number of parameters that cannot be measured directly or calculated. Thus, parameter estimation is an important step in the process of modeling based on empirical data of the system.In the control system’s literature, one can find considerable amount of research in the area of system parameters identification. Most of these techniques are based on minimizing the estimation error in some statistical framework such as least square error based methods. In most cases, using these techniques, one can prove the uniform exponential stability of the state and parameter estimation error, but the convergence rate can be too low. However, when designing control systems, knowledge of unknown immeasurable (or even time varying) parameters might be crucial for the operation of the controller and thus have to be accurately estimated with a desired rate of convergence. In this paper, we demonstrate a way to provide an estimation technique with tunable convergence rate using sliding mode with linear operators such as time delay.     

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.     

Rapid fault reconstruction using a bank of sliding mode observers

This paper deals with the design of a model-based rapid fault detection and isolation strategy using sliding mode observers. To address this problem, a new scheme is proposed by adaptively combining the information provided by a bank of observers. In this regard, a new structure for sliding mode observers is considered. Then, the well-known recursive least square algorithm is utilized to merge individual state estimations suitably such that the system fault is detected faster. The required condition for enhancing perfect state estimation is derived, and the stability of the overall system is proven via Lyapunov’s direct method. The supremacy of proposed scheme is fully discussed through mathematical analyses as well as simulations.     

Fault reconstruction using a LPV sliding mode observer for a class of LPV systems

This paper proposes a new sliding mode observer for fault reconstruction, applicable for a class of linear parameter varying (LPV) systems. Observer schemes for actuator and sensor fault reconstruction are presented. For the actuator fault reconstruction scheme, a virtual system comprising the system matrix and a fixed input distribution matrix is used for the design of the observer. The fixed input distribution matrix is instrumental in simplifying the synthesis procedure to create the observer gains to ensure a stable closed-loop reduced order sliding motion. The ‘output error injection signals’ from the observer are used as the basis for reconstructing the fault signals. For the sensor fault observer design, augmenting the LPV system with a filtered version of the faulty measurements allows the sensor fault reconstruction problem to be posed as an actuator fault reconstruction scenario. Simulation tests based on a high-fidelity nonlinear model of a transport aircraft have been used to demonstrate the proposed actuator and sensor FDI schemes. The simulation results show their efficacy.     

Event-based state and fault estimation for stochastic nonlinear system with Markov packet dropout

This paper investigates the event-based state and fault estimation problem for stochastic nonlinear system with Markov packet dropout. By introducing the fictitious noise, the fault is augmented to the system state. Then combining the unscented Kalman filter (UKF) with event-triggered and Markov packet dropout, the modified UKF is proposed to estimate the state and fault. Meanwhile, the stochastic stability of the proposed filter is also discussed. Finally, two simulation results illustrate the performance of the proposed method.     

Event-based state and fault estimation for nonlinear systems with logarithmic quantization and missing measurements

This paper mainly focuses on the event-based state and fault estimation problem for a class of nonlinear systems with logarithmic quantization and missing measurements. The sensors are assumed to have different missing probabilities and a constant fault is considered here. Different from a constant threshold in existing event-triggered schemes, the threshold in this paper is varying in the state-independent condition. With resort to the state augmentation approach, a new state vector consisting of the original state vector and the fault is formed, thus the corresponding state and fault estimation problem is transmitted into the recursive filtering problem. By the stochastic analysis approach, an upper bound for the filtering error covariance is obtained, which is expressed by Riccati difference equations. Meanwhile, the filter gain matrix minimizing the trace of the filtering error covariance is also derived. The developed recursive algorithm in the current paper reflects the relationship among the upper bound of the filtering error covariance, the varying threshold, the linearization error, the probabilities of missing measurements and quantization parameters. Finally, two examples are utilized to verify the effectiveness of the proposed estimation algorithm.     

Hybrid sliding mode observer for switched linear systems with unknown inputs

This paper addresses the state observation and unknown input estimation of a class of switched linear systems with unknown inputs. This class of systems may have modes in which the state is not fully observable. A state transformation allows implementing two suitable reduced-order observers. The first one, based on second order sliding mode techniques, is proposed to reconstruct the discrete state in the presence of unknown inputs. The second one, based on gathering partial information from individual modes of the switched system and on higher order sliding mode techniques, is introduced to estimate the continuous state. Then, the observer injection signal of the first second order sliding mode observer is used to estimate the unknown inputs. Simulation results highlight the efficiency of the proposed method.     

Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer

Over the last decade, considerable interest has been shown from industry, government and academia to the design of Vertical Take-Off and Landing (VTOL) autonomous aerial vehicles. This paper uses the recently developed sliding mode control driven by sliding mode disturbance observer (SMC-SMDO) approach to design a robust flight controller for a small quadrotor vehicle. This technique allows for a continuous control robust to external disturbance and model uncertainties to be computed without the use of high control gain or extensive computational power. The robustness of the control to unknown external disturbances also leads to a reduction of the design cost as less pre-flight analyses are required. The multiple-loop, multiple time-scale SMC-SMDO flight controller is designed to provide robust position and attitude control of the vehicle while relying only on knowledge of the limits of the disturbances. Extensive simulations of a 6 DOF computer model demonstrate the robustness of the control when faced with external disturbances (including wind, collision and actuator failure) as well as model uncertainties.     

Distributed event-triggered state estimation and fault detection of nonlinear stochastic systems

This paper is devoted to investigate the designs of the event-based distributed state estimation and fault detection of the nonlinear stochastic systems over wireless sensor networks (WSNs). The nonlinear stochastic systems as well as the filters corresponding to the multiple sensors are represented by interval type-2 Takagi–Sugeno (T–S) fuzzy models. (1) A new type of fuzzy distributed filters based on event-triggered mechanism is established corresponding to the nodes of the WSN. (2) The overall stability and performance, that is mean-square asymptotic stability in H_∞ sense, of the event-driven fault detection system is analyzed based on Lyapunov stability theory. (3) New techniques are developed to cope with the problem of parametric matrix decoupling for solving the distributed filter gains. (4) Finally, the desired event-based distributed filter matrices are designed subject to the numbers of the fuzzy rules and a series of matrix inequalities. A simulation case is detailed to show the effectiveness of the presented event-based distributed fault detection filtering scheme.     

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.     

Distributed fuzzy learning sliding mode cooperative control for non-affine nonlinear multi-missile guidance systems via a prescribed performance observer

This paper focuses on the distributed fuzzy learning sliding mode cooperative control issue for non-affine nonlinear multi-missile guidance systems. The dynamics of each follower is non-affine form with unknown lumped factor. To estimate the unknown lumped factor, a generalized fuzzy hyperbolic model (GFHM) based prescribed performance observer (PPO) is proposed. Different from the traditional disturbance observers, a residual set of error transient behavior is incorporated additionally so that the peak phenomenon can be avoided. Meanwhile, an auxiliary system is employed to convert the system of each follower to augmented affine form. Then, a distributed fuzzy learning sliding mode cooperative control approach is designed which consists of two parts. The adaptive sliding mode control (SMC) part is designed to force the states to move along the predefined integral sliding surface. For the equivalent sliding dynamics, the distributed optimal control part with GFHM is developed to minimize the cooperative performance function. Thus, the stability and the optimality of the closed-loop system are guaranteed synchronously. Finally, all signals of closed-loop system are rigorously proved bounded and the multi-missile cooperative guidance scenario is applied to verify the effectiveness of proposed method.     

Optimization-based adaptive neural sliding mode control for nonlinear systems with fast and accurate response under state and input constraints

The high-performance control requires the system to be stable, fast and accurate simultaneously. However, various systems (e.g., motors, industrial robots) generally face technical challenges such as nonlinearities, uncertainties, external disturbances and physical constraints, which make it difficult to reach the hardware potential of the systems to track the desired trajectories when satisfying the high-performance control requirements. Therefore, take a two-order nonlinear system for example, an optimization-based adaptive neural sliding mode control based on a two-loop control structure is proposed in this paper, where the outer and inner loops are designed separately to achieve different control requirements. Namely, the outer loop is designed as a model predictive control (MPC)-based optimization problem, which can optimize the desired trajectories to meet the state and input constraints, and maximize the converging speed of transient response as fast as possible, and the inner loop is designed with a recurrent neural network (RNN)-based adaptive neural sliding mode controller, which can guarantee the tracking of the replanned desired trajectories from outer loop as accurate as possible. The stability of the system is guaranteed by Lyapunov theorem, the optimal tracking performance is achieved under nonlinearities, uncertainties, external disturbances and physical constraints, and comparative simulation with a motor system is carried out to verify the effectiveness and superiority of the proposed approach.     

Distributed fault detection for nonlinear multi-agent systems under fixed-time observer

This paper mainly investigates the fault detection problem for nonlinear multi-agent systems with actuator faults. For fault detection, a fixed-time observer is proposed by employing auxiliary variable received from neighbor agents. Then, with the aid of the observer, a residual vector is introduced by the auxiliary variable to detect the faults occurring on any followers, and each observer can estimate the whole state of followers. Moreover, the convergence time is dependent on the parameters of the designed observer and independent of initial condition of system state. Finally, the theoretical result is verified by a simulation example.     

Trajectory tracking of a quadrotor using extend state observer based U-model enhanced double sliding mode control

This paper develops a novel U-model enhanced double sliding mode controller (UDSMC) for a quadrotor based on multiple-input and multiple-output extended-state-observer (MIMO-ESO). UDSMC is designed using Lyapunov synthesis and Hurwitz stability to not only cancel the complex dynamics and nonlinearity, but also stabilize the uncertainty and external disturbance of the underlying quadrotors. MIMO-ESO is designed to estimate the unmeasurable velocities which can reduce the impact of sensor measurement errors in practice. The difficulties associated with quadrotor velocity's measurement disturbances and uncertain aerodynamics are successfully addressed in this control design. Rigorous theoretical analysis has been carried out to determine whether the proposed control system can achieve stable trajectory tracking performance, and a comparative real-time experimental study has also been carried out to verify the better effectiveness of the proposed control system than the built-in PID control system.     

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T²)$O\left(T^2\right)$ where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF).     

Filtering based parameter estimation for observer canonical state space systems with colored noise

This paper surveys the identification of observer canonical state space systems affected by colored noise. By means of the filtering technique, a filtering based recursive generalized extended least squares algorithm is proposed for enhancing the parameter identification accuracy. To ease the computational burden, the filtered regressive model is separated into two fictitious sub-models, and then a filtering based two-stage recursive generalized extended least squares algorithm is developed on the basis of the hierarchical identification. The stochastic martingale theory is applied to analyze the convergence of the proposed algorithms. An experimental example is provided to validate the proposed algorithms.