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In this paper, we explore the decentralized control problem through the lens of adaptive dynamic programming for continuous-time nonlinear systems, particularly those with unknown mismatched interconnections and asymmetric input constraints. First, the unknown interconnection term is addressed by approximating it with a radial basis function neural network. This approximation relies on the local states of isolated subsystems and the reference states of coupled subsystems, thus sidestepping the common assumption that interconnections are matched and upper bounded. Following this, the challenge of designing a decentralized optimal controller design is reframed as a series of local optimal controller design problems. This reframing is facilitated by adaptive critic networks and considers the asymmetric constraints of subsystems. The application of the Lyapunov stability theorem demonstrates that controllers, even with asymmetric input constraints, can rapidly stabilize the large-scale system. More importantly, we conclude that the control laws designed here serve as the decentralized control strategies for large-scale nonlinear systems. Our methodology employs the radial basis function neural network and the critic neural network. The former approximates interconnection terms, while the latter deals with cost functions, enabling to derive optimal decentralized control strategies under asymmetric constraints. The uniform ultimate boundedness of observation error and weight approximation error are assured by using the Lyapunov theorem. This is further supported by the introduction of a state observer to estimate the state of the interconnected subsystems and the use of the critic neural network to approximate an improved cost function. This approach allows for an approximate solution to the Hamilton–Jacobi–Bellman equation, resulting in optimal decentralized control strategies satisfying the asymmetric input constraints. At the same time, based on the weight updating rules of the critic neural network, we can guarantee that weight approximation errors are uniformly ultimately bounded by selecting the suitable Lyapunov function. The selection of neural networks in this study is driven by considerations of convergence speed and computational burden, leading to the choice of two specific types of networks. The effectiveness of the developed control method is then rigorously tested through simulation and comparative experiments implemented in a MATLAB environment. Comparative experiments underscore the advancements made by the algorithm developed in this paper, especially under asymmetric control constraints. Contrasting our approach with unimproved cost functions and strategies lacking control constraints, we showcase significant improvements. The simulation results are shown in Figs. 1–9, which fully verify the effectiveness of our established scheme. We can derive that the developed control method significantly enhances stabilization speed and performance.

The problem of designing event-triggered natural second-order state observers for second-order vector systems subject to external disturbances is considered in this paper. In this work, state observer is constructed using discrete measurements at instants when an event-triggered condition is satisfied. Due to the errors that arise by using the event-triggered mechanism and the external disturbance, the method in this paper only robustly estimates the state position and the state velocity of the second-order vector observers instead of estimating them asymptotically. Instead of using the method based on a parameter-dependent Lyapunov function in investigating the stability of the dynamic error system of natural second-order observers, a convex optimization problem is established in this paper to give an event-triggered mechanism and minimized levels in evaluating the boundedness of the dynamic error system of the event-triggered natural second-order observers. An automobile suspension and two numerical examples demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we construct a general observer theory for differential delay systems based on different types of symmetries (exact symmetry or asymptotic symmetry), ending up with a certain number of semi‐global and global observers, with bounded or unbounded system's solutions. We introduce the notions of symmetry for a differential delay system, being inspired by well‐known definitions of symmetry for an ordinary or partial differential system, and variational symmetry for the associated variational differential delay system. We illustrate observer design procedures in details, by proving that the existence of a (variational asymptotic) symmetry with system's detectability in the first approximation have a central role in the design of a state observer. The symmetry is a one‐parameter group of transformations which maps the system into itself (exact symmetry) or into a different system (asymptotic symmetry), approximating the original one with better and better accuracy as the parameter of the symmetry is larger. The types of symmetries we consider here show an important contractive action on the state and input spaces for which the system's solutions are mapped into arbitrarily small neighbourhoods of the origin in which the transformed system can be well‐approximated by its linearization. The parameter of the symmetry may be constant (semiglobal observers) or updated on‐line by a state norm estimator (global observers). [ABSTRACT FROM AUTHOR]

During the hypersonic flight process of rigid hypersonic flight vehicles (HFVs), the flight-path angle and angle of attack are usually small and sensitive to flight condition variation, the accurate measurements are difficult, subsequently the formulation of states observers is an urgent issue. A distributed high-gain observer is proposed to reconstruct the admissible system state dynamics based on limited measured output. First, a distributed observer is proposed for the cascade strict-feedback system to ensure the global convergence of the state estimation errors between the estimated state in each local observer and system states, for the prescribed system initial values. Second, the distributed high-gain observer-based nonlinear control is investigated on the longitudinal dynamics of HFVs with partial measurable states. The rigid body system dynamic is divided into the altitude subsystem and the velocity subsystem. In the altitude subsystem, the proposed distributed high-gain observer is formulated to exact estimate the flight-path angle and angle of attack, and then the back-stepping design is proposed for constructing the controllers. The nonlinear dynamic inversion controller is introduced to accomplish the velocity tracking. Finally, simulation examples are served to verify that the proposed output feedback control possesses the superior properties of high tracking performance, fast convergence of state estimation error and easy-implementation. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method. [ABSTRACT FROM AUTHOR]

The paper presents an iterative identification method dedicated for industrial processes. The method consists of two steps. In the first step, a MISO system is identified with the Modulating Functions Method to obtain sub-models with a common denominator. In the second step, the obtained subsystems are re-identified. This procedure enables to obtain the set of models with different denominators of the transfer functions. The algorithmwas used for on-line identification of a glass conditioning process. Identification window is divided into intervals, in which the models can be updated based on recent process data, with the use of the integral state observer. Results of the performed simulations for the identified models are compared with the historical process data.

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results. [ABSTRACT FROM AUTHOR]

This article considers the use of linear state observers to infer the unknown state (density matrix) of a closed quantum system using generalized quantum measurement—positive operator-valued measures (POVMs). An efficient test for observability is described in terms of two quantum observability matrices. The main contribution of this work is the development of a canonical quantum state observer, which may be utilized to estimate the state of any closed quantum system using POVM measurements. The observer ensures that the state estimation error tends to the unobservable space of the system, which is exactly zero when the system is observable. The space of Hermitian matrices is shown to be invariant with respect to the dynamics of the canonical observer, which allows one to project the observer's state onto the space of valid quantum density operators while retaining convergence to the true state.

The paper presents an iterative identification method dedicated for industrial processes. The method consists of two steps. In the first step, a MISO system is identified with the Modulating Functions Method to obtain sub-models with a common denominator. In the second step, the obtained subsystems are re-identified. This procedure enables to obtain the set of models with different denominators of the transfer functions. The algorithmwas used for on-line identification of a glass conditioning process. Identification window is divided into intervals, in which the models can be updated based on recent process data, with the use of the integral state observer. Results of the performed simulations for the identified models are compared with the historical process data. [ABSTRACT FROM AUTHOR]

This paper investigates the state estimation problem for switched linear systems involving additive disturbance and measurement noise, whose modes need not to be cooperative. Under the assumption that there exist nonsingular matrices that transform the observer error system matrices into Metzler ones, by using multiple Lyapunov functions and average dwell time method, hybrid state observers, which can produce a framer covering all possible state trajectories, are designed in two cases, that is, all the subsystems are stable and some of the subsystems may be unstable. The constructed interval observer for the considered systems are hybrid dynamical systems and the initialized states of the upper and lower observers at each switching instants are coupled, since the transformation matrices for different subsystems are different. Compared with the robust observer design for switched systems with arbitrary switching sequences in the literature, the difficulty consists in proposing new observer design conditions related to the state reset at the switching instants for switched systems under average dwell time scheme. Finally, two examples are given to show the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Online monitoring of fermentation processes is a necessary task to determine concentrations of key biochemical compounds, diagnose faults in process operations, and implement feedback controllers. However, obtaining the signals of all-important variables in a real process is a task that may be difficult and expensive due to the lack of adequate sensors, or simply because some variables cannot be directly measured. From the above, a model-based approach such as state observers may be a viable alternative to solve the estimation problem. This work shows a comparative analysis of the real-time performance of a family of sliding-mode observers for reconstructing key variables in a batch bioreactor for fermentative ethanol production. These observers were selected for their robust performance under model uncertainties and finite-time estimation convergence. The selected sliding-mode observers were the first-order sliding mode observer, the proportional sliding mode observer, and the high-order sliding mode observer. For estimation purposes, a power law kinetic model for ethanol production by Saccharomyces cerevisiae was performed. A hybrid methodology allows the kinetic parameters to be adjusted, and an approach based on inference diagrams allows the observability of the model to be determined. The experimental results reported here show that the observers under analysis were robust to modeling errors and measurement noise. Moreover, the proportional sliding-mode observer was the algorithm that exhibited the best performance. [ABSTRACT FROM AUTHOR]

This paper proposes some methods for estimating the order of nonlinear systems having non-integer order. First, the stability of time-varying order systems is studied. Afterward, the multivariable systems with time-varying incommensurate order are studied and an estimation scheme is proposed to approximate the order. In the next step, considering the pseudo-states of a system to be unknown, an order/pseudo-state estimator is designed for a category of nonlinear systems. It is shown that the method is extendible to form order/pseudo-state estimators for other classes of nonlinear systems using other traditional nonlinear observers. One of the advantages of the proposed methods is that a compact time interval is enough to guarantee bounded estimation error. • Proposes an adaptive order estimator for incommensurate variable order systems. • Designs a state/order estimator for a category of variable order nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper proposes a Kazantzis–Kravaris–Luenberger (KKL) observer design for discrete-time nonlinear systems whose output is affected by a time-varying measurement delay. Relying on an injective state transformation, a chain of observers is designed in the latent coordinates with exponential stability guarantees through the inverse map in the original coordinates. Moreover, the relationship between the number of sub-predictors and the lower and upper bounds of the delay is derived. The transformations involved in the design of the KKL observer are identified using an unsupervised learning-based approach that relies on neural networks. A disturbance rejection and robustness analysis against measurement noise and neural network approximation error are presented, respectively. Finally, we illustrate the performance and robustness of the proposed learning-based design KKL chain observer through numerical simulations. [ABSTRACT FROM AUTHOR]

Set-membership state estimation problem for a certain class of discrete-time nonlinear systems is tackled in this work. First, this problem is formulated as a reachability analysis problem. Then, to avoid the wrapping effect, explicit expression of the general solution of this class of systems is used to design new set-valued state estimation schemes. Moreover, for practical considerations, two periodically re-initialized algorithms based on both interval analysis and zonotope computation are introduced. The merit of the proposed approach is illustrated on a numerical example and its performance is compared to that of other methods borrowed from the literature. [ABSTRACT FROM AUTHOR]

This article considers the problem of designing robust event-triggered functional observers for linear interconnected systems with disturbances. The considered system comprises $N$ interconnected subsystems where each subsystem is subject to unknown-but-bounded input disturbances that do not necessarily satisfy the observer matching condition. First, novel Zeno-free event-triggered mechanisms (ETMs) for $N$ subsystems of the considered interconnected system are proposed. Then, robust distributed functional observers are designed based on the proposed ETMs. The designed event-triggered functional observers are robust such that the observer error for each subsystem is $\epsilon _i$ -convergent. This ensures that the $i$ th estimated state vector of the $i$ th subsystem converges robustly within an $\epsilon _i$ -bound of the true state vector of the $i$ th subsystem. Numerical examples are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results.

This article undertakes the problem of simultaneous estimation of state and process faults in linear parameter varying systems. For this purpose, a novel strategy that exploits recent results on the design of observers for quadratic parameter varying systems is developed, and a complete design procedure is described. First, it is shown that by treating the process faults as additional states to be estimated, the arising augmented state‐space model is indeed expressed as a quadratic parameter varying system. Hence, the estimates provided by a quadratic parameter varying observer based on the so‐called linear output error injection principle would comprise both the actual state and the process faults estimates. Robust design conditions that minimize the effect of disturbances and measurement noise on some linear, and possibly parameter‐varying, combination of error variables are obtained using a Lyapunov‐based approach. Then, it is shown that the design problem can be reduced to a finite set of linear matrix inequalities that can be solved using available computational tools. The final part of the article exhibits an illustrative example, which clearly exposes the potential applicability and performance of the developed approach. [ABSTRACT FROM AUTHOR]

This paper develops a theory of output feedback control for a class of nonlinear, nonstandard two-time-scale systems using a controller and a state observer with guaranteed closed-loop stability. Using insights from geometric singular perturbation theory, a sequential controller is designed over two time-scales. For different choices of measurements, Lyapunov-based observer designs are investigated. Both the controller and the observer are designed to guarantee Lyapunov stability of the lower-order reduced subsystems. Using an extension of the composite Lyapunov analysis, it is proved that the full-order nonlinear system with the controller and the observer remains globally asymptotically stable up to a bound of the time-scale separation parameter. In addition, the composite Lyapunov analysis yields sufficient conditions as guidelines to select the gains. The approach and analysis are demonstrated on a nonlinear two-time-scale system for which the reduced subsystems are linear, but the composite Lyapunov analysis handles the nonlinearity present in the full-order dynamics. [ABSTRACT FROM AUTHOR]

Online monitoring of fermentation processes is a necessary task to determine concentrations of key biochemical compounds, diagnose faults in process operations, and implement feedback controllers. However, obtaining the signals of all-important variables in a real process is a task that may be difficult and expensive due to the lack of adequate sensors, or simply because some variables cannot be directly measured. From the above, a model-based approach such as state observers may be a viable alternative to solve the estimation problem. This work shows a comparative analysis of the real-time performance of a family of sliding-mode observers for reconstructing key variables in a batch bioreactor for fermentative ethanol production. These observers were selected for their robust performance under model uncertainties and finite-time estimation convergence. The selected sliding-mode observers were the first-order sliding mode observer, the proportional sliding mode observer, and the high-order sliding mode observer. For estimation purposes, a power law kinetic model for ethanol production by Saccharomyces cerevisiae was performed. A hybrid methodology allows the kinetic parameters to be adjusted, and an approach based on inference diagrams allows the observability of the model to be determined. The experimental results reported here show that the observers under analysis were robust to modeling errors and measurement noise. Moreover, the proportional sliding-mode observer was the algorithm that exhibited the best performance.

This article presents a new droop-based supervisory-level controller for nanogrids (NGs) in the islanded mode of operation. The proposed control system is able to significantly improve the dynamics of power electronic interfaces in NGs. Unlike the existing techniques, the proposed controller takes into account the input-side (i.e., source-side) and the output-side (i.e., load-side) parameters as well as the dc-bus voltage dynamics. Theoretical analysis, simulation results, and experimental results confirm the feasibility of the proposed control system and demonstrate its superior performance. [ABSTRACT FROM AUTHOR]

In this paper, a model reference control strategy is proposed in order to perform trajectory tracking in Takagi–Sugeno–Lipschitz (TSL) systems. Since the state vector is assumed not to be completely available for measurement, a proportional observer is added to the control scheme in order to apply an estimate‐feedback control action instead of a state‐feedback one. The overall design of both the controller and the observer gains are performed using a Lyapunov‐based quadratic boundedness specification, in order to improve the robustness against unknown exogenous disturbances. It is shown that the conditions that ensure convergence within ellipsoidal regions of the tracking and estimation errors can be expressed in the form of a linear matrix inequality (LMI) formulation. The effectiveness of the developed control strategy is demonstrated by means of simulation results. [ABSTRACT FROM AUTHOR]

Fluid temperature predictions of geothermal borefields usually involve temporal superposition of its characteristic g-function, using load aggregation schemes to reduce computational times. Assuming that the ground has linear properties, it can be modelled as a linear state-space system where the states are the aggregated loads. However, the application and accuracy of these models is compromised when the borefield is already operating and its load history is not registered or there are gaps in the data. This paper assesses the performance of state observers to estimate the borefield load history to obtain accurate fluid predictions. Results show that both Time-Varying Kalman Filter (TVKF) and Moving Horizon Estimator (MHE) provide predictions with average and maximum errors below 0.1 ∘ C and 1 ∘ C, respectively. MHE outperforms TVKF in terms of n-step ahead output predictions and load history profile estimates at the expense of about five times more computational time. [ABSTRACT FROM AUTHOR]

The design problem of an adaptive state observer for linear time-varying systems is considered. Some parameters of a time-varying plant are assumed to be unknown numbers multiplied by known functions of time. The approach proposed below is based on identification methods of adaptation. In other words, the main idea is to transform a mathematical model in the form of a linear time-varying differential equation to a static linear regression model containing unknown parameters. In this case, both the unknown parameters of the plant and its initial conditions are the unknown parameters of the regression model under consideration. Further, standard gradient methods or other parametric identification approaches are used to estimate the unknown parameters of the regression model and to construct the observer. The results of computer simulations illustrate the effectiveness of the new state observer design method. [ABSTRACT FROM AUTHOR]

This paper presents a new set-membership observer design method for discrete-time linear parameter varying systems. The real process is assumed to be perturbed by unknown but bounded disturbances. The proposed set-membership observer provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation errors bounds. The observer design process is based on the offline solution of a finite number of linear matrix inequalities conditions that provide both the observer parameters and the ellipsoidal robustly positive invariant (RPI) sets for the estimation error dynamics. The main feature of the proposed approach concerns the fact that these RPI sets are used to frame, at every time-instant, the estimation error in an explicit way. Another novelty concerns the fact that the approach includes uniformly distributed random disturbances which belongs to the family of bounded disturbances. The a posteriori steady-state covariance matrix of the estimation error dynamics, perturbed by such disturbances, is used during the observer synthesis providing small RPI sets. Two numerical examples illustrate the behaviour of such observer and its easy implementation. [ABSTRACT FROM AUTHOR]

In this article, a phase-locked loop (PLL) rotor position and speed observer, including an integrated decoupled stator current observer, is proposed for wide-speed-range sensorless control of permanent magnet synchronous motor (PMSM) drives. This new PLL scheme consists of two interconnected observers: 1) a second-order PLL position observer using the direct current error as correction term and 2) a third-order extended Luenberger speed observer, based on the mechanical model of the drive, using the quadrature current error as the correction term. The estimated speed is just an unrefined reference for the position integrator, and it is further corrected by the PLL. The current observer is a subsystem integrated as a PLL phase detector. Key relations between the current errors and the position and speed errors are proven, and a practical two-step observer design method is presented. A method for real-time identification of the stator resistance at low speeds and of the permanent magnet flux at high speeds is proposed, using the current errors in the current reference frame. Experimental results for a 0.5-kW surface-mounted PMSM drive confirm the effectiveness, excellent dynamic performance, and robustness of the new PLL observer. Stable motor and generator operation at 15 r/min (0.01 p.u.) with ramp and step speed reversals, high-speed operation, and stator resistance adaptation is shown. [ABSTRACT FROM AUTHOR]

This article proposes a speed observer algorithm for the sensorless control of a doubly fed induction generator based on classical adaptive backstepping technique. The sensorless control is shown using classic stator field oriented control, which is use to active and reactive power control. Performance of the proposed algorithm of a speed observer is validated by simulation and experimental results obtained using a small-rating generator and bidirectional voltage source converter. The stability analysis of the presented solution with regard to observer gains changes is also considered. [ABSTRACT FROM AUTHOR]

This paper deals with the fixed-time tracking control problem of extended nonholonomic chained-form systems with state observers. According to the structure characteristic of such chained-form systems, two subsystems are considered to design controllers, respectively. First of all, using the fixed-time control theory, a controller is proposed to make the first tracking error subsystem converge to zero in bounded time independent initial state. Second, a state observer is proposed to estimate the unmeasurable states of the second subsystem. And the precise state estimation can be presented from the observer within finite time; moreover, the upper bound of time is a constant independent on the initial estimation error. Third, a fixed-time controller is designed to drive all states of the second chained-form subsystem to zero within pre-calculated time. Finally, the effectiveness of the proposed control scheme is validated by simulation results. [ABSTRACT FROM AUTHOR]

This paper presents a new harmonic compensation system along with a hybrid load observer used for micro-grids in the islanded mode. The proposed control system includes an online hybrid load observer, which is able to precisely estimate the harmonic contents of the load as well as the equivalent load impedance in the islanded mode. One of the main features of the proposed control system is its capability to deal with unknown load harmonics, which is a big challenge in micro-grids. Basically, the proposed control system is able to detect, estimate, and compensate various load disturbances and harmonics (e.g., synchronous and asynchronous harmonics, and dc components). Theoretical analysis, simulation results, and experimental results verify the feasibility and performance of the proposed control system. [ABSTRACT FROM AUTHOR]

In this paper, we address problem of distributed functional interval observers for a class of nonlinear fractional-order interconnected systems with bounded uncertainties. The system under consideration is formed by N ( N ≥ 2) interconnected subsystems. We first design N stand-alone distributed functional interval observers for the system. The designed interval observer for each subsystem is based on the local outputs, known bounds of the local uncertainty and additional outputs from other subsystems but without the need to exchange the state estimates among the observers. Then, conditions for the existence of such distributed functional interval observers are derived and an effective algorithm for computing unknown observer matrices is provided. Finally, two numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This study is concerned with the output feedback stabilisation problem for a class of large‐scale non‐linear time‐delay systems with unknown measurement sensitivities. The non‐linear terms are assumed to be bounded by states or delayed states multiplied by outputs polynomial functions. The state observers are given by the dynamic gain control design technique. By constructing an appropriate Lyapunov–Krasovskii functional, the global asymptotic stability of the closed‐loop control system is analysed. A numerical example is given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new nonlinear attitude observer based on high-grade rate gyros and single body-fixed vector measurements of a constant inertial vector, in contrast with typical solutions that require two of these vectors. The structure is cascaded, where in the first block a vector that is related to the angular velocity of the Earth is estimated and in the second block the attitude itself is obtained. The attitude is directly estimated on the special orthogonal group and the estimation error is shown to converge to zero, with a region of convergence that is best described as semi-global, with local exponential convergence. Simulation results illustrate the achievable performance of the proposed solution and the robustness to sensor noise. [ABSTRACT FROM AUTHOR]

The synthesis of externally positive filters that can be used to modulate control signals of output‐feedback sliding mode controllers is presented. These filters are useful to estimate the norm of unmeasured signals in systems with parametric uncertainties. These norm observers are a robust alternative to state observers, that may be difficult to design for uncertain systems. The first step of the synthesis is the search of the envelope function, which is an upper bound for the norm of each admissible impulse response of the uncertain system. After this step, the approximation of a positive filter with an impulse response that is an upper bound for the envelope function is carried out. The search of the envelope function and the synthesis of the approximation filters are formulated as non‐convex optimisation problems that can be solved by genetic algorithms. It is important to design norm observers that are not too conservative, because the modulation signals should be kept small in order to reduce the amplitude of the control signals, power losses, and undesirable chattering effects that may occur in sliding‐mode control. The proposed methods are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

The knowledge of tire-ground interaction forces is valuable for intelligent vehicles technologies. However, tire forces transducers are expensive and not suitable for ordinary passenger cars. An alternative is to estimate these forces using less sophisticated sensors. This paper presents a new delayed interconnected cascade-observer structure to reconstruct the forces acting on each tire in all directions. The addition of delayed interconnections overcomes the mutual dependence problem in the cascade estimator. Observers are developed based on nonlinear vehicle dynamic models. The Extended Kalman Filter and the Unscented Kalman Filter algorithms are applied for comparison purposes. Two experimental data are used to validate the estimator: a driving in ordinary urban streets and a high-speed slalom maneuver in a banked road. The results are compared with force measurements obtained with transducers and with an existing estimator from the literature. [ABSTRACT FROM AUTHOR]

We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

Abstract In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. Specifically, the reconstruction of the force is carried out from the estimates of the series coefficients, which in fact are part of the dynamical system that composes the observer. Adams-Bashforth-Moulton method is used to compute the fractional derivatives of the observer in the Liouville-Caputo sense. Experiments based on real data are presented to show the advantages of using a fractional observer in the reconstruction of forces. Highlights • Design of a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system. • Fourier series approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. • Numerical evaluation of the fractional state observer, using experimental data. [ABSTRACT FROM AUTHOR]

Summary: A fuzzy adaptive optimal output‐feedback control problem is investigated for nonlinear continuous‐time interconnected systems with saturation constraints. The system dynamics and the mismatched interconnections of each subsystem are unknown, and each subsystem contains unavailable states. Based on fuzzy logic systems, a fuzzy state observer is designed to approximate the unknown system states and the interconnections of the nonlinear interconnected system. By using adaptive dynamic programming technology, the decentralized optimal controller of each subsystem is given and the saturation control input is updated via the critic fuzzy logic systems. The proposed fuzzy adaptive observer‐based optimal control scheme can guarantee that the closed‐loop interconnected system is ultimately uniformly bounded stable. A simulation example validates the effectiveness of the presented scheme. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the complete moment convergence of double-indexed randomly weighted sums of negatively superadditive-dependent (NSD, for short) random variables, which is stronger than complete convergence. In addition, the convergence of double-indexed randomly weighted sums of NSD random variables is also obtained. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors, and study the almost sure convergence and mean square convergence of the state observers of linear-time-invariant systems. [ABSTRACT FROM AUTHOR]

This paper presents a fresh approach to the design of state observers for a class of time-delay systems with one time delay in the state and output vectors. By proposing a new coordinate state transformation, the system is first transformed into the new coordinates where all the delay terms associated with the state variables are injected into the system's output and input. Thus, in the new coordinate system, a Luenberger-type state observer can be easily designed. Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system. Conditions for the existence of the state transformations and an algorithm for computing them are provided in this paper. We show that our approach works for a wider class of time-delay systems in the sense that when some existing state observer design methods fail to reconstruct the state vector, the proposed new change of coordinates and the observer scheme in this paper can still reconstruct the original state vector. Numerical examples and simulation results are given to illustrative the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]