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The robust control problem of a class of nonlinear systems subject to external disturbances, control gain uncertainty, and nonlinear uncertainties is investigated in this paper using a nonlinearity estimator-based control approach. Different from the existing results, the crucial but highly restrictive hypothesis on the boundedness of nonlinear uncertainties is removed from this paper by means of the tools of semiglobal stabilization. By delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful level sets, the rigorous qualitative robustness performance is presented for the closed-loop system. Finally, an example of a single-link manipulator is utilized to demonstrate the performance specification claimed by the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper develops a new high-gain observer design method for nonlinear systems that has a lower gain compared to the standard high-gain observer. This new observer, called HG/LMI observer, is obtained by combining the standard high-gain methodology with the LMI-based observer design technique. Through analytical developments, this paper shows how the new observer provides lower gains, shows how it applies to systems with multinonlinear functions, and analyzes performance in the presence of measurement noise and/or delayed output measurements. A numerical example is given to illustrate the increasing advantage of the new HG/LMI observer with increase in the observer's “compromise index.” Finally, the applicability and performance of the observer is demonstrated for a real-world application consisting of a train's magnetic levitation system. [ABSTRACT FROM AUTHOR]

The paper proposes a technique to estimate the angular velocity of a rigid body from single vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector measurements are directly filtered through a nonlinear observer estimating the angular velocity. Convergence is established using a detailed analysis of a linear-time varying dynamics appearing in the estimation error equation. This equation stems from the classic Euler equations and measurement equations. As is proven, the case of free-rotation allows one to relax the persistence of excitation assumption. Simulation results are provided to illustrate the method. [ABSTRACT FROM PUBLISHER]

This paper considers the observer-based output feedback stabilization of coupled parabolic PDEs with spatially-varying coefficients and different diffusion coefficients subject to distinct constant input and output delays. By representing the delays in the form of homodirectional hyperbolic systems, a hyperbolic-parabolic PDE-PDE-PDE cascade is obtained. The state feedback controller design for this system is based on a Fredholm backstepping transformation mapping the closed-loop system into a stable PDE-PDE-PDE target system. With this, a minimum control time is achieved for the hyperbolic subsystem in the target dynamics. Then, this approach is extended to the design of a state observer for delayed measurements to obtain an observer-based output feedback controller. Exponential stability of the resulting closed-loop system is verified. Furthermore, it is shown that the Fredholm and backstepping transformations related to the hyperbolic subsystems are attainable in closed form. The new design procedure is demonstrated for the output feedback stabilization of two coupled parabolic PDEs with different input and output delays. [ABSTRACT FROM AUTHOR]

This paper proposes a novel robust fault detection (FD) approach and designs a set-theoretic unknown input observer (SUIO) for linear parameter-varying (LPV) systems with both state and output equations scheduled by inexact scheduling variables. First, for such LPV systems, we propose a novel robust FD method by combing the set theory with the unknown input observer, which considers the bounds of measurement errors of scheduling variables to generate FD-oriented sets. In general, as long as sensors with sufficiently high precision are equipped to measure the scheduling variables, the bounds of measurement errors of scheduling variables can be less conservative than those direct bounds of scheduling variables, which can reduce robust FD conservatism in this way. Second, we give the unknown input decoupling condition of SUIO for such LPV systems and propose an SUIO design method under this condition for robust state estimation (SE). Besides, stability conditions for the proposed methods are established via matrix inequalities. At the end of this paper, a case study is used to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper addresses a supervisory control problem for time invariant hybrid dynamical systems based on the $l$-complete approximation scheme by Moor and Raisch (“Discrete supervisory control of hybrid systems based on $l$-complete approximations,” 2002) and partial observation. An underlying hybrid plant is realized by a hybrid state machine with an infinite state space, and its external behavior is described by discrete input/output signals with finite range, and some output signal is assumed to be unmeasurable. For the strongest $l$-complete approximation of the plant, which is realized by a finite state machine, we present a method to design a finite state supervisor to achieve a given specification. The supervisor cannot observe the unmeasurable output signal. Finally, we show that the finite state supervisor also meets the specification for the underlying hybrid plant. [ABSTRACT FROM AUTHOR]

This paper addresses the stabilization problem for nonlinear Markovian jump systems (MJS) with output disturbances, actuator and sensor faults simultaneously. This kind of plants are common in practical systems, such as mobile manipulators with switching joints. In this paper, a sliding mode observer design scheme is proposed for a new descriptor augmented plant. By employing the developed observer, the effects of actuator and sensor faults can be eliminated. It is shown that the stabilization of the overall closed-loop plant can be guaranteed by the proposed fault tolerant control (FTC) scheme. Finally, an example concerning mobile manipulators with Markovian switching joints is presented to show the effectiveness and applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this “log-linear” property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set, in the presence of silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). First, we demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets); subsequently, this observation is used to construct (offline) a marking observer under appropriate boundedness assumptions. Using the marking observer we show how to derive, at design time, a state feedback control law under the assumption that all transitions sharing a label can be enabled or disabled simultaneously as a group; this way, the most burdensome part of the computations is performed offline. [ABSTRACT FROM AUTHOR]

In this paper, a full-order observer design method is proposed for port-Hamiltonian systems. The proposed method is based on the notion of contractive port-Hamiltonian systems. It is the first structure preserving observer design for a broad class of input-state-output port-Hamiltonian systems. The design procedure consists of solving a matching equation, similar to the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for controller design. The matching equation, as shown in the paper, has some closed-form solutions for general class of mechanical and electromechanical systems. As another feature of the proposed method, it is shown that the existence of solution of the corresponding matching equation for a linear port-Hamiltonian system is equivalent to the detectability property of that system. Upon these facts, the proposed method can be considered as a counterpart of IDA-PBC for observer design. Simulations for some benchmark examples, including ball and beam, magnetic levitation, and permanent magnetic synchronous motor, show the potency and applicability of the method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new state observer design technique for nonlinear systems. It combines the well-known Kazantzis–Kravaris–Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it—extending the realm of applicability of both methods. A second contribution of this paper is the proof that these designs can be recast as particular cases of immersion and invariance observers—providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented. [ABSTRACT FROM AUTHOR]

An observer for simultaneous localization and mapping is considered in this paper. The proposed observer is based on recent theoretical foundations in a gradient-based observer design on Lie groups. As such, the form of the observer is similar to recently developed nonlinear attitude and pose observers. Translational and angular velocity measurements, as well as relative position measurements of nearby landmarks, are used directly within the observer structure. The case of biased translational and angular velocity measurements is also considered. Stability results are presented that demonstrate an asymptotic convergence of the pose and map estimates. The proposed algorithm is implemented successfully in experiment. [ABSTRACT FROM AUTHOR]

This paper addresses the actuator fault estimation sliding-mode observer (SMO) design problem of linear continuous-time systems over digital communication channels. This problem frequently occurred in a network environment where data has to be quantized before being transmitted via digital communication channels. Traditional observers (linear Luenberger observer, Walcott–ZaK SMO) are not effective to solve this design issue since the effects of signal quantization will degrade estimation performances evidently. In this paper, a new descriptor SMO method is presented to overcome this difficult problem. It is shown that, if the quantizer density is larger than $\sqrt{2}-1$ , the designed observer can compensate quantization errors completely, and the fault vector can be reconstructed despite of signal quantization. Finally, a simulation example with the F-404 aircraft engine model is proposed to demonstrate the effectiveness of the proposed robust digital observer design approach. [ABSTRACT FROM AUTHOR]

Our prior work has studied the enforcement of opacity security properties using insertion functions. Given a system that is not opaque, the so-called All Insertion Structure (AIS) is a game structure, played by the system and the insertion function, that embeds all valid insertion functions. In this paper, we first propose a more compact AIS that can be constructed with lower computational complexity. We then introduce the maximum total cost and the maximum mean cost, and use them as quantitative objectives to solve for optimal insertion functions. Specifically, we first determine if an insertion function with a finite total cost exists. If such an insertion function exists, we synthesize an optimal total-cost insertion function. Otherwise, we construct an optimal mean-cost insertion function. In either case, we find an optimal insertion strategy on the AIS, with respect to the corresponding cost objective. The algorithmic procedures are adapted from results developed for minimax games and mean payoff games. The resulting optimal strategy is represented as a subgraph of the AIS that consists of all the system actions and the optimal insertion actions. Finally, we use this subgraph to synthesize an optimal insertion function that is encoded as an I/O automaton. [ABSTRACT FROM PUBLISHER]

This note points out certain limitations of our results from the paper mentioned in the title, and provides a modified approach to overcome these limitations. Specifically, the observer design addressed in the aforementioned paper is, in general, only applicable to switched linear systems with invertible state reset maps and this note presents a modified algorithm for state estimation that can also handle non-invertible state reset maps. In the process, we also identify some equalities from that paper which may not hold in general for arbitrary state reset maps. [ABSTRACT FROM PUBLISHER]

Nonlocal terms have been the mainstay of the applications of partial differential equation (PDE) backstepping methods to parabolic PDEs. The problem of similar nonlocal terms for wave equations is still open. For wave equations, similar nonlocal terms have not been studied. In this paper, we open the topic of exploration of control of wave PDEs with nonlocal terms. This paper is concerned with the wave equation with in-domain feedback/recirculation of a boundary velocity with a spatially constant coefficient. Due to this nonlocal term, the passivity of the wave equation is destroyed. We first design an explicit state feedback controller to achieve exponential stability for the closed-loop system. Then, we design the output feedback by using infinite-dimensional observer. The backstepping approach is adopted in investigation. It is shown that by using two measurements only, the output feedback makes the closed-loop system exponentially stable. [ABSTRACT FROM AUTHOR]

This paper studies the online fault detection for stochastic discrete-event systems (DESs) under partial observability of events. Prior works have only studied the verification of the stochastic diagnosability (S-Diagnosability) property. To the best of our knowledge, this is a first paper that investigates the online detection schemes and also introduces the notions of their missed detections (MDs) and false alarms (FAs). Due to the probabilistic nature of the problem, MDs and FAs are possible even for S-Diagnosable systems, and we establish that S-Diagnosability is a necessary and sufficient condition for achieving any desired levels of MD and FA rates. We also provide a detection scheme, that can achieve the specified MD and FA rates, based on comparing a suitable detection statistic, that we define, with a suitable detection threshold, that we algorithmically compute. We also algorithmically compute the corresponding detection delay bound. The detection scheme also works for non-S-Diagnosable systems, with the difference that in this case there exists a lower bound for achievable MD rate, that increases as the FA rate requirement is made more stringent by decreasing it. [ABSTRACT FROM AUTHOR]

In this paper, two control schemes producing a continuous control signal are presented for a perturbed triple integrator: The continuous twisting algorithm (3-CTA) and the output feedback continuous twisting algorithm (3-OFCTA). The first one is a state feedback controller that ensures global finite-time stability of the origin, despite of Lipschitz, nonvanishing, and matched disturbances. It provides steady-state precision of fourth order of the output w.r.t. sampling step. The second one is an output feedback controller, which uses a third-order robust and exact differentiator as an observer. By requiring only information of the measurable output, the 3-OFCTA preserves all features of robustness, convergence, and precision of the state feedback 3-CTA. Moreover, it is proven that a separation principle applies, so that the gains of the controller and of the observer can be selected independently to assure stability. [ABSTRACT FROM AUTHOR]

In this paper, we propose an observer for a dynamical system for which the states on the frontier of its domain are not observable, and all trajectories converge to the frontier. The proposed case study, a bioreactor in batch operating conditions with a single microbial reaction and gas production, is standard and largely encountered in practical situations. We also show how to extend this observer to obtain an observer in higher dimension that is robust with respect to unbiased noise. [ABSTRACT FROM AUTHOR]

In this paper, we design a novel observer for a class of semilinear heat one dimmensional (1-D) equations under the delayed and sampled point measurements. The main novelty is that the delay is arbitrary. To handle any arbitrary delay, the observer is constituted of a chain of subobservers. Each subobserver handles a fraction of the considered delay. The resulting estimation error system is shown to be exponentially stable under a sufficient number of subobservers is used. The stability analysis is based on a specific Lyapunov–Krasovskii functional and the stability conditions are expressed in terms of linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

This paper proposes a global sliding mode observer for a class of nonlinear mechanical systems with two degrees of freedom. For the observer design, besides the usual Coriolis and centrifugal forces, we consider (discontinuous) dry and viscous friction and non vanishing uncertainties/perturbations. Moreover, the system is not required to be bounded-input-bounded-state, rendering the observer design problem challenging. For this class of systems, a dissipativity-based sliding-mode observer, with theoretically exact global finite-time convergence to the actual velocities, is proposed. To illustrate the effectiveness of the proposed observer, experimental results on a cart-pendulum system are presented. [ABSTRACT FROM AUTHOR]

This paper considers an iterative procedure to design a minimum possible order unknown input functional observer for linear time-invariant systems. Necessary and sufficient conditions for the existence of the observer are given. The proposed procedure is simple and is based neither on the solution of a generalized Sylvester equation nor canonical forms. This procedure can be easily implemented due to its incremental form. The main feature of our procedure is then the simplicity of the design. Moreover, in the case of a single functional to be observed, a minimum order stable linear unknown input functional observer is obtained. [ABSTRACT FROM AUTHOR]

This paper presents a systematical reduced-order observer design method for a class of switched descriptor systems containing unknown inputs (UIs) in both the dynamic and the output equations. Generally speaking, when the output of the system contains UIs, the reduced-order observer design will become much more challenging. In order to overcome the difficulty brought by the UIs in the output, first, by introducing a new UI vector, a new equivalent system is obtained, which does not contain UIs in the corresponding output any more. Then, for the purpose of reduced-order observer design, the observer matching condition (OMC) and the minimal phase condition (MPC) are discussed, and it is shown that the new general system maintains both the OMC and the MPC. Subsequently, based on the discussions on the existence conditions, a reduced-order unknown input observer is developed to asymptotically estimate the state of the original system. Finally, an electronic circuit example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that, under some mild assumptions, it is possible to design observers for linear time-invariant continuous-time and discrete-time systems by feeding classical linear observers (e.g., the Kalman filters and the Luenberger observer) with the successive integrals and the moving average of the measured output, respectively. The main interest in these observers relies on the fact that both the integral and the moving average exhibit low-pass behaviors, thus allowing the design of observers that are less sensitive to high-frequency noise. Examples are reported all throughout this paper to corroborate the theoretical results and to highlight the improved filtering properties of the proposed observers. [ABSTRACT FROM AUTHOR]

This paper considers the fully distributed tracking consensus problem for general nonlinear multiagent systems with a leader whose control input is nonzero and bounded. First, a new class of distributed state observer for the leader is proposed without the knowledge of the upper bound of the leader's input. Then, the situations that followers are affected by disturbances with unknown upper bound or disturbances generated by exosystems are investigated. Specifically, two distributed control protocols based on the distributed state observer, neural networks, and adaptive laws are proposed. Finally, simulation examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fault and state estimation problem for Markovian jump systems (MJSs) with simultaneous actuator and sensor faults. To deal with the design issues, we propose a novel descriptor reduced-order sliding mode observer (SMO), based on which the estimation of the actuator faults, sensor faults, and the states can be obtained simultaneously. Compared with the traditional SMO design issues in MJSs, we reconstruct the actuator faults directly without employing the equivalent output error injection method. Thus, the reachability analysis of the sliding surface is not necessary. The superiority of this kind of the SMO method is that the sliding surface switching problem is avoided. Finally, the effectiveness (as suggested by the theoretical results) of the approach described is tested on a mobile manipulator by simulation studies. [ABSTRACT FROM AUTHOR]

This paper is concerned with the rate at which a discrete-time, deterministic, and possibly large network of nonlinear systems generates information, and so with the minimum rate of data transfer under which the addressee can maintain the level of awareness about the current state of the network. While being aimed at development of tractable techniques for estimation of this rate, this paper advocates benefits from directly treating the dynamical system as a set of interacting subsystems. To this end, a novel estimation method is elaborated that is alike in flavor to the small gain theorem on input-to-output stability. The utility of this approach is demonstrated by rigorously justifying an experimentally discovered phenomenon. The topological entropy of nonlinear time-delay systems stays bounded as the delay grows without limits. This is extended on the studied observability rates and appended by constructive upper bounds independent of the delay. It is shown that these bounds are asymptotically tight for a time-delay analog of the bouncing ball dynamics. [ABSTRACT FROM AUTHOR]

This paper studies the time-varying output formation (TVOF) tracking problems for heterogeneous linear multiagent systems with a nonautonomous leader on directed topologies, where the dynamics of the agents can be different in the aspects of both parameters and dimensions, and the leader can have unknown control input. A TVOF tracking protocol and a design algorithm are presented using the neighboring interaction. In the proposed protocol, a distributed observer with adaptive updating mechanism is constructed for each follower to asymptotically estimate the state of the leader under the influences of the leader's unknown input first. Then, a local formation controller is presented by utilizing the distributed observer, the local state observer, and the desired formation vector. Based on the Lyapunov stability theory, it is proved that the expected TVOF tracking can be accomplished by the heterogeneous multiagent systems in the presence of the leader's unknown input. Furthermore, a continuous TVOF tracking protocol with $\sigma$ -modification adaptive law is proposed to avoid the large chattering phenomenon. [ABSTRACT FROM AUTHOR]

Secure state estimation for cyber-physical systems under sparse sensor attacks is the problem of estimating the state from the corrupted measurements. Although such problem can be addressed by brute force search, combinatorial candidates lead to excessive time requirement, which hinders the scalability. For reducing the computational complexity, this paper provides an alternative approach (called set cover approach) to reduce the number of candidates by at least half with the help of a greedy algorithm. Then, a switched observer, with less candidate observers, is designed to estimate the state from the corrupted measurements under the basic observability requirement. Meanwhile, a modified greedy algorithm is proposed to reduce the number of candidates further based on the observer design conditions. Finally, the effectiveness of the proposed set cover approach is demonstrated by two simulations showing an order of magnitude decrease in execution time. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose a filtering strategy for max-plus linear systems with bounded disturbances without the direct calculation of the a posteriori state probability. The strategy is based on the inversion of the expectation of the measure with respect to the state variable. Among the possible solutions, the closest to the prediction is chosen. An algorithm, based on interval propagation, is proposed to solve this problem. Simulations are performed to show the consistence of the proposed methodology with other approaches in the literature. [ABSTRACT FROM AUTHOR]

This paper presents the development of a full-state observer for an Euler-Bernoulli beam system with simply supported boundary conditions. This problem is motivated by the necessity of estimators in control and diagnostic applications. The observer is developed using a backstepping procedure. The full state observer cannot be completed with a single observer system, and hence this paper presents the synthesis of two observer structures that together provide the desired convergence. The necessary feedback information is limited to the slope and the sheer force of the beam at one boundary, which are practically measurable values on a physical system. The observer estimates the full infinite dimensional beam system without any discretization of the model. The result of the technique developed in this paper is that the infinite dimensional observer estimates converge to the plant system states (representing the actual beam displacement) at an arbitrary exponential rate; numerical simulation results validating this behavior are provided. [ABSTRACT FROM AUTHOR]

This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables. For a given plant and partition, we establish a characterization of all error behaviors that can be achieved by interconnecting the plant with some observer. The main result of this paper is a very general, behavioral formulation of an internal model principle for observers. We will show that a nonintrusive observer achieves a stable error behavior if and only if, in addition to a detectability condition on the observer, the observer behavior contains the anti-stabilizable part of the plant behavior. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global stabilization of a rather general class of MIMO nonlinear systems is addressed. The systems considered in the paper are invertible, have a trivial zero dynamics and possess a “normal form” in which certain multipliers are functions of the state vector of a special kind. While special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization (via full-state feedback, though), the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability (thus making the design of observers possible) and to the property of uniform invertibility, relations never established before in the literature. As a result, for this class of MIMO nonlinear systems, a dynamic output feedback law can be designed, yielding semiglobal (and even global, under appropriate assumptions) asymptotic stability. [ABSTRACT FROM PUBLISHER]

This paper aims at designing a nonasymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's observable canonical form of pseudo-state space representation with unknown initial conditions. First, this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output, based on which the modulating functions method is applied. Then, the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to nonasymptotically estimate the pseudo-state of the system in noisy environment. Second, the pseudo-state estimator is studied in discrete noisy case, which contains the numerical error due to a used numerical integration method, and the noise error contribution due to a class of stochastic processes. Then, the noise error contribution is analyzed, where an error bound useful for the selection of design parameter is provided. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator, where some comparisons with the fractional order Luenberger-like observer and a new fractional order \mathcalH\infty-like observer are given. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of state estimation in nonlinear Lagrangian dynamical systems with frictionless unilateral constraints using the position measurement as output. The discontinuous velocity variable in such systems is modeled as a function of bounded variation (so that Zeno phenomenon is not ruled out). Since the derivative of such functions is represented with the Lebesgue-Stieltjes measure, the framework of measure differential inclusions (MDIs) is used to describe the dynamics. A class of estimators is proposed, which also uses the framework of MDIs, and is shown to generate asymptotically converging state estimates. The existence and uniqueness of solutions for the proposed estimators is rigorously proven. The global stability of error dynamics is analyzed using the generalized Lyapunov methods for functions of bounded variation. As particular cases of our estimators, we provide an explicit construction of a full-order observer, and a reduced-order observer. [ABSTRACT FROM AUTHOR]

Classical methods for estimating additive faults are based on state-space models, e.g., moving horizon estimation (MHE) and unknown input observers (UIOs). This paper contributes new direct design methods from closed-loop I/O data for systems with stable inversion, which do not require building a state-space model by first principles, nor require identifying it. Inspired by subspace identification, we use the input and output (I/O) relationship of a plant in a Vector ARX (VARX) form to parameterize least-squares (LS) problems for estimating faults. We prove that with the order of the VARX descriptions tending to infinity, the fault estimates are unbiased. Under lower relative degrees, we prove that our new methods are equivalent to system-inversion-based estimation for both LTI and LTV systems. We will show more general unbiased estimation conditions for higher relative degrees. These require that the underlying inverted system from faults to outputs is stable. Algorithms of identifying unbiased fault estimation filters from data will be developed in this paper based on single LS. Moreover, covariance of the fault estimates can also be extracted from data. [ABSTRACT FROM AUTHOR]

This paper deals with output-feedback-based state consensus of homogeneous linear multiagent systems. A novel reduced-order dynamic output-feedback protocol is proposed, which does not need the absolute output information of neighboring agents. Necessary and sufficient conditions for the solvability of the consensus problem under the proposed protocol are derived, and it is shown that the protocol state is convergent if consensus is reached. A design algorithm is then constructed for computing the protocol gains. Furthermore, the protocol specialized for leader–follower consensus is addressed. In addition, the solvability of a truncated version of the proposed protocol without controller interaction is discussed from a low-gain perspective. A numerical example is finally presented to demonstrate the effectiveness of the proposed protocol and design method. [ABSTRACT FROM AUTHOR]

This paper investigates the positive edge-consensus problem via output feedback protocols for undirected networks and directed networks whose edge dynamics are defined on nonnegative spaces. First, the definition and topology of the line graph are presented based on a given nodal graph with positive edge dynamics. Two observer-type positive edge-consensus protocols are introduced, and sufficient conditions of positive consensus for uncertain positive systems are proposed without utilizing the information of algebraic connectivity. Furthermore, necessary and/or sufficient conditions of positive consensus for the nominal systems are derived. The analysis illustrates that the error variables defined in this paper are nonnegative in both protocols. Finally, the illustrative simulation examples are presented to verify the effectiveness of the proposed observer-type positive edge-consensus protocols. [ABSTRACT FROM AUTHOR]

This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in. In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input–output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified. [ABSTRACT FROM AUTHOR]

This paper provides an extension of the observability rank condition to nonlinear systems driven by both known and unknown inputs. In particular, the systems here considered are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input (or disturbance) and multiple known inputs. Additionally, it is assumed that the unknown input is a differentiable function of time (up to a given order). The goal of the paper is not to design new observers for these systems but to provide the analytic condition in order to check the weak local observability of the state. This condition is simple and can be easily and automatically applied to the nonlinear systems mentioned above, independently of their complexity and type of nonlinearity. In particular, the complexity of the analytic condition is comparable to the complexity of the standard method to check the state observability in the case without unknown inputs (i.e., the observability rank condition). This is a fundamental practical (and unexpected) advantage. As for the observability rank condition, the proposed analytic condition is based on the computation of the observable codistribution. Similarly to the case of only known inputs, the observable codistribution is obtained by recursively computing the Lie derivatives of the outputs along the vector fields that characterize the dynamics. However, in correspondence of the unknown input, the corresponding vector field must be suitably rescaled. Additionally, the Lie derivatives of the outputs must also be computed along a new set of vector fields that are obtained by recursively performing suitable Lie bracketing of the vector fields that define the dynamics. In practice, the entire observable codistribution is obtained by a very simple recursive algorithm. Finally, it is shown that the recursive algorithm converges in a finite number of steps, and the criterion to establish that the convergence has been reached is provided. The proposed analytic extension of the observability rank condition is illustrated by checking the weak local observability of several nonlinear systems driven by known inputs and a single disturbance. [ABSTRACT FROM AUTHOR]

An adaptive distributed observer was recently proposed to solve the cooperative output regulation problem for discrete-time linear multi-agent systems. The validity of this approach relies on the assumptions that all the eigenvalues of the leader's system matrix are inside or on the unit circle and the solution to the regulator equations is unique. Besides, the range of the observer gains of the adaptive distributed observer is determined by the spectrum of a graph matrix of the communication network, which is not desirable in applications. To overcome these drawbacks, in this paper, we will first propose a new type of the discrete-time adaptive distributed observer for the leader system, whose observer gains are fixed and hence are independent of the communication network, and moreover, this observer allows the eigenvalues of the leader's system matrix to be inside a circle with radius strictly greater than one. Then, we will strengthen the existing adaptive control approach so that it can handle the case where the solution to the regulator equations is not unique. These improvements have not only made our approach more practical, but also enlarged the systems that can be handled by the existing approach. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed event-triggered consensus problem for a class of nonlinear multiagent systems subject to actuator saturation. A new distributed event-based dynamic output feedback controller is put forward via the relative output measurements of neighboring agents. It removes the impractical assumptions that the controllers for agents have to update continuously and the observers embedded in agents have to share information with their neighbors, thus the energy consumptions of agents are significantly reduced. Two event-triggered strategies for the cases with and without continuous communication among neighboring agents are established. Sufficient conditions are derived in terms of matrix inequalities to guarantee the exponential leader-following consensus. The problem of designing a distributed event-triggered control law such that the domain of attraction for consensus errors is enlarged, formulated, and solved as an optimization problem with matrix inequality constraints. Simulation results are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the design of observers for systems with slow and fast modes. The existing methods are able to design independent slow and fast observers with $O(\epsilon)$ accuracy only, where $\epsilon$ is a small positive singular perturbation parameter that indicates separation of system state-space variables into slow and fast. In this paper, the design of independent slow and fast reduced-order observers was performed with very high accuracy $O(\epsilon ^{i}), i=2,3,....$. The results obtained are extended to the design of corresponding observer driven controllers. The design allows complete time-scale separation for both the observer and controller through the decomposition into slow and fast time scales. This method reduces both offline and online computations. The effectiveness of the new methods is demonstrated through both theoretical and simulation results. [ABSTRACT FROM AUTHOR]

This paper formulates and studies the concept of quasi-Disturbance-to-Error Stability (qDES) which characterizes robustness of a nonlinear observer to an output measurement disturbance. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. We use these conditions to show that several well-known observer designs yield qDES observers, while some others do not. Our results also enable the design of novel qDES observers, as we demonstrate with examples. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. [ABSTRACT FROM AUTHOR]

In this paper, we present a procedure for the state estimation and fault diagnosis of a labeled Time Petri net system. Starting from the State Class Graph defined by Berthomieu and Diaz, we introduce a new graph called Modified State Class Graph (MSCG) that allows an exhaustive representation of the evolution of the timed system. Then, we present a procedure that, given a timed observation, i.e., a sequence of labels with their firing time instants, and a time instant $\tau$, allows one to determine in which states the system can be at time $\tau$ by using the MSCG and solving a certain number of linear programming problems. Finally, we present a procedure to perform fault diagnosis using the MSCG. [ABSTRACT FROM AUTHOR]

This paper presents a new design approach to nonlinear observers for Itô stochastic nonlinear systems with guaranteed stability. A stochastic contraction lemma is presented which is used to analyze incremental stability of the observer. A bound on the mean-squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity. The observer design is based on a non-unique state-dependent coefficient (SDC) form, which parametrizes the nonlinearity in an extended linear form. The observer gain synthesis algorithm, called linear matrix inequality state-dependent algebraic Riccati equation (LMI-SDARE), is presented. The LMI-SDARE uses a convex combination of multiple SDC parametrizations. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances. Two variations of LMI-SDARE algorithm are also proposed. One of them named convex state-dependent Riccati equation (CSDRE) uses a chosen convex combination of multiple SDC matrices; and the other named Fixed-SDARE uses constant SDC matrices that are pre-computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre-computed by a convex LMI optimization problem. A connection between contraction analysis and \cal L2 gain of the nonlinear system is established in the presence of noise and disturbances. Results of simulation show superiority of the LMI-SDARE algorithm to the extended Kalman filter (EKF) and state-dependent differential Riccati equation (SDDRE) filter. [ABSTRACT FROM PUBLISHER]

We propose in this paper a Petri net approach to online diagnosis of discrete event systems (DESs) modeled by finite state automata. The diagnosis method is based on the construction of a Petri net diagnoser (PND) which is constructed in polynomial time and requires less memory than other methods proposed in the literature. We also present methods for the conversion of the PND to both sequential function chart and ladder diagram for implementation on a programmable logic controller (PLC). Implementation issues are also addressed in the paper. [ABSTRACT FROM PUBLISHER]

This paper is devoted to the problem of nonlinear state estimation under multirate sampling in presence of disturbance inputs. Considering a general description of a nonlinear sampled-data system, we establish a prescriptive framework for multirate observer design via an approximate discrete-time model of the plant. This framework is shown to be input-to-state stable in a semiglobal practical sense with respect to the estimation error for the unknown exact discrete-time model. A numerical example of an aerospace vehicle with input and output channels of various sampling rates demonstrates how the multirate observer can drastically improve performance compared with the single-rate observer. [ABSTRACT FROM PUBLISHER]

This paper addresses output feedback stabilization via event-triggered output feedback. In the first part of the paper, linear systems are considered, whereas the second part shows that a dynamic event-triggered output feedback control law can achieve feedback stabilization of the origin for a class of nonlinear systems by employing dynamic high-gain techniques. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of secure state estimation for cyber-physical systems modeled by continuous or discrete-time linear systems when some sensors are corrupted by an attacker. A novel state observer is proposed with adaptive switching mechanism. Attack tolerance principle is established based on adaptively truncating the injection channels of attacks. To implement it, a switching function matrix is introduced into the observer design. Driven by a well-defined performance index, the switching function matrix automatically reaches and remains in the desired entry mode and turns off the input channels of attacks. Based on the equivalence between $s$ -strong detectability of the observation error system and $2s$ -sparse detectability of the original system, the observation error system is proven to be asymptotically stable even under the cyber attacks. Compared with the existing complex static batch optimization algorithms, the proposed adaptive observer can be derived only by offline solving a set of simple linear matrix inequalities. Simulation examples are given to illustrate the estimation performance and the computational efficiency of the proposed method. [ABSTRACT FROM AUTHOR]