High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction

This paper develops a high gain observer with multiple sliding modes for simultaneous state and fault estimations for MIMO nonlinear systems. The novelty lies in the observer design that employs the combination of high-gain observer and sliding mode observer. The proposed observer does not impose the small-Lipschitz-constant condition on the system nonlinearity. By imposing a structural assumption on the nonlinear fault distribution matrix, the observability of the faults/unknown inputs w.r.t. the outputs is safeguarded and sliding modes are utilized for their reconstruction. The reconstruction of the faults from the sliding mode only relies on the output estimation error and thus can be implemented online together with the state estimation. Finally, an application to flexible joint robotic arm is used to illustrate the proposed method.     

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.     

Combined state and parameter estimation for a bilinear state space system with moving average noise

This paper considers the identification problem of bilinear systems with measurement noise in the form of the moving average model. In particular, we present an interactive estimation algorithm for unmeasurable states and parameters based on the hierarchical identification principle. For unknown states, we formulate a novel bilinear state observer from input-output measurements using the Kalman filter. Then a bilinear state observer based multi-innovation extended stochastic gradient (BSO-MI-ESG) algorithm is proposed to estimate the unknown system parameters. A linear filter is utilized to improve the parameter estimation accuracy and a filtering based BSO-MI-ESG algorithm is presented using the data filtering technique. In the numerical example, we illustrate the effectiveness of the proposed identification methods.     

Unknown input observer for linear non-minimum phase systems

An unknown input observer is to estimate the system state of a dynamic system subject to unknown input excitations. In this note, by assuming that at each time instant, the unknown input can be approximated by a polynomial over a local time interval, a finite-time observer is proposed to achieve approximate joint state and input estimation. Both the obtained state and input estimates are moving averages of the present and past output signals. The advantage of the proposed design is that it can be applied to non-minimum phase systems or systems with non-unity relative degree. Notice that most previous unknown input observer designs require the system to be minimum-phase and relative degree one.     

High-gain fractional disturbance observer control of uncertain dynamical systems

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs. The proposed fractional PI-like structure yields precise conditions for feedback gain tuning. Remarkably, the resulting controller rejects non-differentiable disturbances with a smooth controller, guaranteeing robustness, an outstanding features for tracking tasks, under a prescribed practical stability regimen. A comparison to a fractional sliding mode observer is conducted via simulations to highlight the reliability of the proposed scheme.     

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.     

Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs

The paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with unknown inputs. The fault and the unknown inputs affect both the state and the output. However, if the dynamical evolution models of the fault and the unknown inputs are available the filtering problem will be solved by the Optimal three-stage Kalman Filter (OThSKF). The OThSKF is obtained after decoupling the covariance matrices of the Augmented state Kalman Filter (ASKF) using a three-stage U–V transformation. Nevertheless, if the fault and the unknown inputs models are not perfectly known the Robust three-stage Kalman Filter (RThSKF) will be applied to give an unbiased minimum-variance estimation. Finally, a numerical example is given in order to illustrate the proposed filters.     

Zonotopic set-membership state estimation for switched systems

This paper proposes a new approach for set-membership state estimation of switched discrete-time linear systems subject to bounded disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed and a new criterion is proposed to reduce the size of the zonotope at each sample time. The zonotopic set-membership estimator design for switched systems is provided within the LMI framework. The extension of the proposed scheme to deal with unknown inputs is also presented. An application to vehicle lateral dynamics state estimation is provided. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.     

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.     

Model predictive tracking control with disturbance compensation for wheeled mobile robots in an environment with obstacles

This paper explores the trajectory tracking control problem for a wheeled mobile robot (WMR) in an environment with obstacles and unknown disturbances. A fixed-time extended state observer is presented, which is utilized to estimate unknown disturbances and improve the convergence speed of estimation errors. By introducing the obstacle avoidance cost, a model predictive controller with disturbance compensation is proposed to guarantee desired tracking performance in the presence of obstacles. The proposed method is analyzed for recursive feasibility and closed-loop system stability subject to unknown disturbances and obstacles. Finally, both simulation and experiment are conducted to express the satisfactory tracking effect of the developed approach.     

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.     

State and unknown input estimations for discrete-time switched linear systems with average dwell time

In this paper, the problem of state and unknown input estimations for a class of discrete-time switched linear systems with average dwell time switching is investigated. First, a proportional integral observer with an exponential H_∞ performance is constructed to estimate the system state and unknown input simultaneously. Second, both of the observability and the stability of the estimation error system are analyzed, then the derivation of the observer gain matrices is transformed into the calculation of linear matrix inequalities. Third, the obtained results are extended to the systems with output disturbances. Finally, two simulation examples are provided to show the validity and effectiveness of the proposed methods.     

Additive-state-decomposition-based model predictive tracking control for PMSM servo system with multiple disturbances

This paper presents an additive-state-decomposition-based model predictive tracking control and disturbance rejection method for a permanent magnet synchronous motor (PMSM) servo system subject to unknown parameter perturbations, unmodeled dynamics, and time-varying load torque. The basic idea of this method is to equivalently decompose the original system into a primary system for handling the tracking control subproblem and a secondary system for dealing with the robust stabilization subproblem. A model predictive controller is designed for the primary system to achieve high-accuracy tracking of the reference speed. As for the secondary system, a novel high-order generalized extended state observer (HGESO) is constructed to estimate the multiple disturbances simultaneously, and a state feedback control law incorporating a disturbance compensator is developed to eliminate the adverse effect of the multiple disturbances on the system output. By combining the control inputs of the two subsystems together, the control objectives of the original system can be achieved. Both the stability criterion and design procedure of the closed-loop control system are developed. Finally, hardware-in-the-loop-based comparative experiments are conducted to demonstrate that the proposed method effectively suppresses the influence of the multiple disturbances on motor speed tracking accuracy and that the control system has both satisfactory dynamic performance and robustness.     

Parameter fault detection and estimation of a class of nonlinear systems using observers

The focus of this paper is on the detection and estimation of parameter faults in nonlinear systems with nonlinear fault distribution functions. The novelty of this contribution is that it handles the nonlinear fault distribution function; since such a fault distribution function depends not only on the inputs and outputs of the system but also on unmeasured states, it causes additional complexity in fault estimation. The proposed detection and estimation tool is based on the adaptive observer technique. Under the Lipschitz condition, a fault detection observer and adaptive diagnosis observer are proposed. Then, relaxation of the Lipschitz requirement is proposed and the necessary modification to the diagnostic tool is presented. Finally, the example of a one-wheel model with lumped friction is presented to illustrate the applicability of the proposed diagnosis method.     

A reset observer with discrete/continuous measurements for a class of fuzzy nonlinear systems

This paper proposes the design of a reset fuzzy observer for the class of nonlinear systems able to be described by a Takagi–Sugeno fuzzy model. The observer uses both continuous and discrete measurements and in contrast with the observers based on the First Order Reset Element (FORE), it updates its states resetting the initial condition of the integrator at each instant when the discrete measurements are available. The proposed fuzzy observer is applied to estimate the substrate and biomass concentration of an anaerobic wastewater treatment process and the effectiveness of the proposed method is tested by simulations comparing the results of a reset fuzzy observer with two fuzzy observers using continuous measurements only. Finally, the estimation scheme is validated using experimental data from an actual anaerobic digestion process, suggesting that the proposed reset fuzzy observer is a practical and encouraging approach to the state estimation of the class nonlinear processes under study.     

Fixed-time anti-saturation grouped cooperative guidance law with state estimations of multiple maneuvering targets

The problem of a grouped multiple missiles cooperative attack on multiple high maneuvering targets with a limited driving force is achieved by an anti-saturation fixed-time grouped cooperative guidance (FxTCG) law based on a sliding mode fixed-time disturbance observer (SM-FxTDO) in this study. First, the state estimation of each high maneuvering target within a fixed time is achieved by designing a sliding mode fixed-time disturbance observer. Second, the group cooperative guidance law is designed by using fixed-time theory, which can ensure the group consensus of multiple missiles strike times within a fixed time under the condition of input saturation. Then, the fixed time stability of the multi-missiles system is proven by using the bi-limit homogeneous theory and the Lyapunov function. Finally, the simulation results show the superiority of the designed observer and cooperative guidance law. The proposed observer can more effectively and accurately estimate the state of the high maneuvering target than the ESO. The proposed cooperative guidance law expands the number of attack targets and makes each group of multiple missiles attack the corresponding high maneuvering target under the conditions of an input saturation within a fixed time compared to the single-target cooperative law.     

Neural dynamic sliding mode control of nonlinear systems with both matched and mismatched uncertainties

Mismatched uncertainty and chattering appear as two challenges in sliding mode control. To overcome the problem of mismatched uncertainty, multiple sliding surfaces with virtual inputs are proposed. Accordingly, we have proposed two new methods based on designed neural observer: sliding mode control (SMC) and dynamic sliding mode control (DSMC) methods. Although, the proposed SMC can significantly cope with the mismatched uncertainties, but it suffers from chattering phenomenon. The chattering problem can be removed in DSMC, because an integrator is placed before the system. This results in increased number of the system states. This new state can be identified with the proposed neural observer. Note that in both proposed approaches, the robust performance (invariance property) of system is reserved, even in the presence of mismatch uncertainties. Then, to have a valid comparison the proposed DSMC is also designed using loop transfer recovery observer (LTRO). This comparison shows the good performance of the DSMC based neural networks. Moreover, the upper bound of uncertainties is not used in SMC and DSMC controllers and also in the neural observer and LTRO, which is important in practical implementation. Finally, comparing the equations, one can see the simplicity of DSMC in concept and also in realization.     

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.     

Adaptive fuzzy output feedback fault-tolerant tracking control of switched uncertain nonlinear systems with sensor faults

This paper investigates the adaptive fuzzy output feedback fault-tolerant tracking control problem for a class of switched uncertain nonlinear systems with unknown sensor faults. In this paper, since the sensor may suffer from an unknown constant loss scaling failure, only actual output can be used for feedback design. A failure factor is employed to represent the loss of effectiveness faults. Then, an adaptive estimation coefficient is introduced to estimate the failure factor, and a state observer based on the actual output is constructed to estimate the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Based on the Lyapunov function method and the backstepping technique, the proposed control scheme with average dwell time constraints can guarantee that all states of the closed-loop system are bounded and the tracking error can converge to a small neighborhood of zero. Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.