Robust unknown input observer based fault detection for high-order multi-agent systems with disturbances

This paper is devoted to fault detection (FD) for high-order multi-agent systems with disturbances. In order to detect the fault occurred in one agent, the unknown input observer (UIO) is constructed in its neighbor. Two cases are considered, if the perfect UI decoupling condition is satisfied, the UI does not affect the residual; if the condition is not satisfied, this paper proposes a method of partitioning the UI into two parts, such that a subset of the UI does not appear in residual dynamics, and the influence of the other UI is constrained. Simulations are given to demonstrate the effectiveness of the proposed method.     

Observation and sliding mode observer for nonlinear fractional-order system with unknown input

The main purpose of this paper is twofold. First, the observability and the left invertibility properties and the observable canonical form for nonlinear fractional-order systems are introduced. By using a transformation, we show that these properties can be deduced from an equivalent nonlinear integer-order system. Second, a step by step sliding mode observer for fault detection and estimation in nonlinear fractional-order systems is proposed. Starting with a chained fractional-order integrators form, a step by step first-order sliding mode observer is designed. The finite time convergence of the observer is established by using Lyapunov stability theory. A numerical example is given to illustrate the performance of the proposed approach.     

A probabilistic damage identification approach for structures with uncertainties under unknown input

To avoid the false positives of damages in the deterministic identification method induced by uncertainties in measurement noise, a probabilistic method is proposed to identify damages of the structures with uncertainties under unknown input. The proposed probabilistic method is developed from a deterministic simultaneous identification method of structural physical parameters and input based on dynamic response sensitivity. The deterministic simultaneous identification method is first derived. The effect of uncertainties caused by measurement noise on the identified parameters is then investigated. The statistical parameters of the identified structural parameters are calculated. The damage index is derived from the statistical parameters of the physical parameters of intact and damaged structure. The probability of identified damage, defined as the probability of identified structural stiffness smaller than that of intact structure, is further derived using the probability method. A twelve-story building and a nine-bay three-dimensional frame structure are, respectively, analyzed numerically and experimentally using the proposed method. The research results indicate that the probabilistic simultaneous identification method for damage and input can decrease the false positives of damages in contrast with the deterministic method under intensive measurement noise, and it can also achieve an accurate identification for structural unknown input.     

Eigenstructure assignment for linear systems with probabilistic uncertainties

In this paper, S (stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties is proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design schemes are illustrated by numerical examples, and applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on S-eigenstructure assignment.     

Filtering in linear discrete systems with unknown perturbations

This paper considers an algorithm for the synthesis of an optimal filter providing a state vector estimator for a discrete linear dynamic system with additive perturbations containing an unknown constant component. The algorithm does not use perturbation estimators. Results of a computation experiment are given.     

Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input

This article focuses on robust adaptive sliding mode control law for uncertain discrete systems with unknown time-varying delay input, where the uncertainty is assumed unknown. The main results of this paper are divided into three phases. In the first phase, we propose a new sliding surface is derived within the Linear Matrix Inequalities (LMIs). In the second phase, using the new sliding surface, the novel Robust Sliding Mode Control (RSMC) is proposed where the upper bound of uncertainty is supposed known. Finally, the novel approach of Robust Adaptive Sliding ModeControl (RASMC) has been defined for this type of systems, where the upper limit of uncertainty which is assumed unknown. In this new approach, we have estimate the upper limit of uncertainties and we have determined the control law based on a sliding surface that will converge to zero. This novel control laws are been validated in simulation on an uncertain numerical system with good results and comparative study. This efficiency is emphasized through the application of the new controls on the two physical systems which are the process trainer PT326 and hydraulic system two tanks.     

Linear estimation for discrete-time periodic systems with unknown measurement input and missing measurements

This paper considers the estimation problem for periodic systems with unknown measurement input and missing measurements. The missing measurements phenomenon is described by an independent and identically distributed Bernoulli process. The quality of the estimation achieved by an admissible filter is measured by a performance criterion described by the Cesaro limit of the mean square of the deviation between the remote signal and the estimated signal. By employing the minimum variance unbiased estimation technique, the periodic unbiased estimator is obtained, where the estimator gain is designed in terms of the unique periodic solution of a Lyapunov equation together with the periodic stabilizing solution of a Riccati equation. Finally, a numerical example is provided to show the effectiveness of the proposed estimation approach.     

New simple approach for enhanced rejection of unknown disturbances in LTI systems with input delay

This work proposes the extension of the simplified filtered Smith predictor (SFSP) for state-space systems to improve rejection of matched and unmatched unknown disturbances in LTI systems with input delay. The proposed structure is simpler than others recently proposed in the literature and can be applied to continuous-time or discrete-time systems. Furthermore, it allows improving rejection of both matched and unmatched disturbances, while also enhancing noise attenuation and robustness characteristics. Finite spectrum assignment (FSA) based implementation is used in order to guarantee the internal stability of the proposed controller. Simulation and experimental results are used to show the usefulness of the proposal.     

Partial state estimation for linear systems with output and input time delays

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov–Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.     

Observer-based adaptive fuzzy-neural control for a class of uncertain nonlinear systems with unknown dead-zone input

Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper.     

A natural observer for optimal state estimation in second order linear structural systems

A state observer for mechanical and structural systems is derived in the context of the second order differential equation of motion of linear structural systems. The proposed observer possesses similar characteristics to the Kalman filter in the sense that it minimizes the trace of the state error covariance matrix within the predefined structure of the feedback gain. The main contribution of the paper consists of the fact that the proposed observer can be implemented directly as a modified linear finite element model of the system, subject to collocated corrective forces proportional to the measured response. The proposed algorithm is effectively illustrated in two different types of second order systems; a close-coupled spring–mass–damper multi-degree of freedom system and a plate subject to transverse vibrations.     

Multi-thresholds for fault isolation in the presence of uncertainties

Monitoring of the faults is an important task in mechatronics. It involves the detection and isolation of faults which are performed by using the residuals. These residuals represent numerical values that define certain intervals called thresholds. In fact, the fault is detected if the residuals exceed the thresholds. In addition, each considered fault must activate a unique set of residuals to be isolated. However, in the presence of uncertainties, false decisions can occur due to the low sensitivity of certain residuals towards faults. In this paper, an efficient approach to make decision on fault isolation in the presence of uncertainties is proposed. Based on the bond graph tool, the approach is developed in order to generate systematically the relations between residuals and faults. The generated relations allow the estimation of the minimum detectable and isolable fault values. The latter is used to calculate the thresholds of isolation for each residual.     

On robust stability of linear time invariant fractional-order systems with real parametric uncertainties

In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results obtained by the lemma and theorems presented in the paper.     

Robust prevention of limit cycle for nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity

A new method is proposed to compute all feasible robust stabilizing controllers for preventing the generation of limit cycle of nonlinear control systems with parametric uncertainties both in the linear plant and nonlinearity. The describing function analysis method is employed to approximate the behaviors of the nonlinearity. The Kharitonov theorem is utilized to characterize parametric uncertainties in the linear plant and nonlinearity. Necessary conditions for limit cycles are established. Boundaries for the generation of limit cycle and boundaries for asymptotic stability are portrayed exploiting the stability equation method. The region for prescribed limit cycle behavior and the region for asymptotic stability are located. An admissible specification-oriented Kharitonov region is found directly on the controller parameter plane. The region is non-conservative and constitutes all of the feasible controller gain sets to achieve robust prevention of limit cycle for the considered uncertain nonlinear control systems. The way to tune the controller gains is suggested. Finally, for comparison purpose, two illustrative examples proposed in the literature are given to show how the proposed algorithm can be effectively applied to tune a robust controller to achieve a prescribed limit cycle behavior and accomplish robust limit cycle amplitude suppression and prevention.     

A robust disturbance reduction scheme for linear small delay systems with disturbances of unknown frequencies

A robust disturbance reduction scheme for linear small delay systems with disturbances of unknown frequencies is presented in this paper. Unlike other methods, the proposed scheme does not require disturbance frequencies to be known. The linear systems modeled in this study are nominally stable and minimum phase systems with relative degree. The control structure is an integration of Astrom's modified Smith predictor and the proposed scheme. The proposed scheme consists of an input disturbance reduction controller (IDRC) and a residual disturbance reduction controller (RDRC). The IDRC using an artificial neural network (ANN) is proposed to reduce unknown load disturbances and modeling uncertainties in stable systems and unstable systems. The ANN can appropriately approximate the product of an inverse time delay and a nonnegative gain in the IDRC. The residual signals including residual disturbances and residual uncertainties are suppressed by the RDRC based on a disturbance observer. Simulation examples are illustrated to show the effectiveness of the proposed robust disturbance reduction scheme for linear delay uncertain systems with periodic or non-periodic unknown load disturbances.     

Autonomous space systems control incorporating automated maneuvers strategies in the presence of parameters uncertainties

The research attempts to deal with the autonomous space systems incorporating new automated maneuvers strategies in the presence of parameters uncertainties. The main subject behind the investigation is to realize the high-resolution small amplitude orbital maneuvers via the first control strategy. And subsequently to realize the large amplitude orbital maneuvers via the second control strategy, as well. There is a trajectory optimization to provide the three-axis referenced commends for the aforementioned overactuated autonomous space system to be able to transfer from the initial orbit to its final ones, in finite burn, as long as the uncertainties of key parameters of the system such as the thrust vector, the center of the gravity, the moments of the inertia and so on are taken into real consideration. The strategies performances are finally considered through a series of experiments and a number of benchmarks to be tangibly verified.     

Identification of linear regression models in the presence of errors in input and output data

The problem of constructing linear regression models in the presence of errors in input and output data is considered. A statistical test for detecting measurement errors in input data is proposed that does not require a preliminary consistent estimation of the coefficients under the assumption of the presence of errors. The test is validated by Monte-Carlo statistical simulation.     

Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint

In this paper, we aim to solve the control problem of nonlinear affine systems, under the condition of the input deadzone and output constraint with the external unknown disturbance. To eliminate the effects of the input deadzone, a Radial Basis Function Neural Network (RBFNN) is introduced to compensate for the negative impact of input deadzone. Meanwhile, we design a barrier Lyapunov function to ensure that the output parameters are restricted. In support of the barrier Lyapunov method, we build an adaptive neural network controller based on state feedback and output feedback methods. The stability of the closed-loop system is proven via the Lyapunov method and the performance of the expected effects is verified in simulation.     

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.