Impulsive Observer Research Articles

Observer-Based Suboptimal Controller Design for Permanent Magnet Synchronous Motors: State-Dependent Riccati Equation Controller and Impulsive Observer Approaches

Permanent Magnet Synchronous Motors (PMSMs) with high energy efficiency, reliable performance, and a relatively simple structure are widely utilised in various applications. In this paper, a suboptimal controller is proposed for PMSMs without sensors based on the state-dependent Riccati equation (SDRE) technique combined with customised impulsive observers (IOs). Here, the SDRE technique facilitates a pseudo-linearised display of the motor with state-dependent coefficients (SDCs) while preserving all its nonlinear features. Considering the risk of non-available/non-measurable states in the motor due to sensor and instrumentation costs, the SDRE is combined with IOs to estimate the PMSM speed and position states. Customised IOs are proven to be capable of obtaining quality, continuous estimates of the motor states despite the discrete format of the output signals. The simulation results in this work illustrate an accurate state estimation and control mechanism for the speed of the PMSM in the presence of load torque disturbances and reference speed changes. It is clearly shown that the SDRE-IO design is superior compared to the most popular existing regulators in the literature for sensorless speed control.

A variable gain impulsive observer for perturbed Lipschitz nonlinear systems with delayed discrete measurements

This paper addresses the impulsive observers design problem of perturbed Lipschitz nonlinear systems subject to noisy delayed discrete measurements. The transmission delay, state perturbation, and measurement noise simultaneously hinder the convergence of impulsive observer. To deal with the difficulty, the observation error system with delayed impulses is represented as an augmented system with switching delay-free impulses. By taking into account the switching structure of the impulse dynamics, the impulse observation gain matrix is modelled as a function of the time interval between two consecutive sampling instant and update instant. Such a structure of the observation gain matrix is able to adapt to the variation of sampling period and transmission delay. To obtain a tractable design condition, the idea of piecewise linear interpolation is applied to represent the impulse observation gain matrix as a piecewise linear form, which is determined by finite static impulse gains. A piecewise Lyapunov function which matches the piecewise linear structure of the observation gain is constructed to analyze the exponential input-to-state stability (EISS) property of the observation error system. The EISS gain quantifies the robustness performance of the designed impulsive observer. Sufficient conditions for the existence of the proposed variable gain impulsive observers are presented. Two numerical examples are provided to illustrate the effectiveness of the developed impulsive observation strategy.

Discrete Impulsive Signal Observer for Fractional-Order Control Systems and Its Consumer Electronic Circuit Application

In the process of actual electronic equipment signal transmission, interference is inevitable. How to accurately estimate the device status to ensure valid signal travelling is very meaningful. This paper mainly investigates a new transmission signal estimation strategy for fractional order control systems with unknown inputs. Compared with integer order modeling, fractional order modeling can better describe and report the essential process of system signal transmission. By using the fractional order output derivative-based method and convex optimization technique, an effective discrete-time impulsive observer design algorithm is proposed to stabilize the error dynamic systems. Especially, the resulting criterion reflects well the relationship between the fractional order and the pulse signal, and then is applied on a fractional order electronic circuit. It implies that the given conclusions are of significance in signal estimation.

Leader-Following Consensus of Linear Multiagent Systems With Aperiodically Sampled Outputs: A Distributed Impulsive-Observer-Based Approach.

This article studies the leader-following consensus problem for a class of linear multiagent systems over a directed graph with aperiodically sampled outputs. First, a novel distributed impulsive-observer-based consensus protocol is designed. This protocol requires only the output measurements at sporadic time instants for the observer and control gain design. Second, by using time-varying Lyapunov function techniques, sufficient conditions for exponential stability of a class of linear impulsive systems are established; subsequently, these stability results are applied for the distributed impulsive observer design. Different from the existing related works, the impulsive observer gain designed in this work is decoupled from the graph properties. As a result, once the impulsive observer gain is designed for one network topology, it can be directly used for other network topologies, as long as the graph properties and the dynamics of local agents satisfy certain conditions. Furthermore, the resilience of the designed protocol is tested under denial of service (DoS) attacks. It is shown that the protocol is robust with respect to low-frequency DoS attacks occurring in the observer communication network. Finally, two examples illustrating the validity and effectiveness of the proposed protocol are included.

Event-triggered impulsive observer with [formula omitted]-asymptotic gain for DC microgrids

This paper studies the problem of the state estimate of a class of DC microgrids with both disturbed states and disturbed outputs via event-triggered impulsive observer (ETIO). First, a mathematical model is established for such class of DC microgrids, and then the notion of impulsive observer including impulsive observer with K-asymptotic gain is proposed. Then, by using two Lyapunov-like functions, a scheme of event-triggered impulsive control (ETIC) via three layers of event-triggering conditions is designed for ETIO to track the state of the DC microgrid. And an algorithm is given for the implementation of ETIC in practice. The ETIC scheme is then extended to the sampling-based ETIC (S-ETIC) to reduce the calculation and improve the effectiveness of the ETIC. Both theoretical proofs and numerical simulations are given to show that the proposed ETIO via both ETIC and S-ETIC can track the state of the DC microgrid within K-asymptotic gain. Specifically, when the disturbance tends to zero, the tracking is accurate. Moreover, the simulation is given for comparisons between ETIO and other observers including the classic impulsive observer, Luenberger observer, sliding mode observer, and extended state observer. It is shown that the designed ETIO has advantages of lower impulse frequency, lower control cost, and smaller tracking error than the other observers.

Bounded Antisynchronization of Multiple Neural Networks via Multilevel Hybrid Control.

The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.

Impulsive observer-based admissibilization for delayed degenerate jump systems and application to DCM-IP device

This paper researches the impulsive observer-based admissibilization for delayed degenerate Markovian jump systems with completely known or partly unknown transition rates. In contrast with the normal continuous-time observer, the advantage of the impulsive observer is that it uses only the measurement outputs at the impulses moments to estimate the states of the controlled system. In order to make the obtained results more universalist, a novel piecewise differentiable Lyapunov–Krasovskii functional with piecewise linear impulse auxiliary functions is established, which can grasp the mixed characteristics of impulses instants information and Markovian jumping modes information. At the same time, singular value decomposition (SVD) technology is used to surmount the influence of the internal impulses of the degenerate system. Improved sufficient conditions about stochastic admissibilization for delayed degenerate impulsive Markovian jump systems are obtained in the form of linear matrix inequalities (LMIs) via mode-dependent impulsive observer-based state feedback controller. Direct current motor-controlled inverted pendulum (DCM-IP) device and a numerical example are utilized to verify the validity and practicability of the results acquired in this paper.

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.

Full‐order impulsive observers for impulsive systems with unknown inputs

AbstractThis paper studies full‐order impulsive observers for impulsive systems with unknown inputs. Two types of full‐order impulsive observers are designed respectively. The first type is Luenberger‐type impulsive observer (LIO). The second type is for the observed system with eliminable unknown input, where the impulsive observer is allowed to have nonidentical dynamic structure with the observed system. The conditions via the average dwell time technique are derived for the existence of these two types of impulsive observers. It is shown that in the LIO, the observer's state tracks the observed system's state in the sense of input‐to‐state stability (ISS). Specifically, the observer's state track completely the observed system's state if the unknown input trends to zero. While in the second type of impulsive observer, the observer's state tracks completely the observed system's state regardless of the unknown input trends to zero. Finally, three examples with simulations are presented to demonstrate the effectiveness of the theoretical results.

Granular-based state estimation for nonlinear fractional control systems and its circuit cognitive application

The issue of continuous observer design for integer order nonlinear systems has been widely studied in existing works. Yet, there are few works that closely related to granular computing theory and discrete signal to better estimate system states. In this paper, by using the granular function description, we propose a novel impulsive observer design algorithm to ensure the cognitive convergence of error dynamic systems. Especially, the resulting criterion reflects well the relationship between the fractional order and the pulse signal. A numerical simulation is provided to illustrate effectiveness of the given method.

A variable gain impulsive observer for Lipschitz nonlinear systems with measurement noises

This paper investigates the variable gain impulsive observer design problem for Lipschitz nonlinear systems. It is assumed that the measurements are contaminated by noise and received by observer at aperiodic instants. To establish a tractable design condition for impulsive observers, the piecewise linear interpolation method is used to construct the variable gain function. To quantify the impact of the measurement noises and exogenous disturbance on the estimation error, a Lyapunov-based condition for establishing exponential input-to-state stability (EISS) property of the observation error dynamics is presented. Then it is shown that the EISS condition can be expressed as a set of linear matrix inequalities (LMIs) by introducing a piecewise quadratic Lyapunov function. A convex optimization problem is proposed in which the EISS gain is minimized. Comparisons with the existing methods show the effectiveness of the proposed design technique.

Partial impulse observability of linear descriptor systems

A research paper in this journal vol. 61, no. 3, pp. 427-434, 2012, by M. Darouach, provides a functional observer design for linear descriptor systems under the partial impulse observability condition. The observer design is correct, but there was a flaw in the algebraic criterion characterizing partial impulse observability. In the present paper, we derive a novel characterization of partial impulse observability in terms of a simple rank condition involving the system coefficient matrices and an alternative characterization in terms of the Wong sequences.

Observers for Differential Algebraic Equation Models of Power Networks: Jointly Estimating Dynamic and Algebraic States

Phasor measurement units (PMUs) have become instrumental in modern power systems for enabling real time, wide-area monitoring and control. Accordingly, many studies have investigated efficient and robust dynamic state estimation (DSE) methods in order to accurately compute the dynamic states of generation units. Nonetheless, most of them forego the dynamic-algebraic nature of power networks and only consider their nonlinear dynamic representations. Motivated by the lack of DSE methods based on power network’s differential-algebraic equations (DAEs), this article develops a novel observer-based DSE framework in order to perform simultaneous estimation of the dynamic and algebraic states of multimachine power networks. Specifically, we leverage the DAE dynamics of a power network around an operating point and combine them with a PMU-based measurement model capable of capturing bus voltages and line currents. The proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> observer, which only requires detectability and impulse observability conditions that are satisfied for various power networks, is designed to handle various noise, unknown inputs, and input sensor failures. The results obtained from performing extensive numerical simulations on IEEE 9-bus and 39-bus systems showcase the effectiveness of the proposed approach for DSE purposes.

On design of adaptive impulsive observer based on comparison system: modifications in stability theory and feasibility centralization

On design of adaptive impulsive observer based on comparison system: modifications in stability theory and feasibility centralization

Co-Estimation of State and FDI Attacks and Attack Compensation Control for Multi-Area Load Frequency Control Systems Under FDI and DoS Attacks

This paper proposes a co-estimation and resilient compensation control framework for multi-area load frequency control (LFC) systems in the presence of false data injection (FDI) attacks and denial-of-service (DoS) attacks. To relax the requirement on existing DoS attack models, which are usually considered under the assumption that both its frequency and duration are constrained, a new DoS model within a known bounds of the sleeping and active period of the attack signal is proposed. The injected FDI attack signal is generated by an external dynamic systems. A switching impulsive observer and a switching state observer are constructed to estimate the unknown FDI attack signal and the system state, respectively. Moreover, a new exponential stability criteria of the output feedback multi-area LFC systems under DoS and FDI attacks is first derived by using attack parameter dependent time varying Lyapunov function method. Then, a co-design method of a resilient attack compensation controller, state estimator, and attack estimator is developed. Finally, case studies are considered for verification of the effectiveness of the proposed theoretical results.

Event-triggered impulsive observers for continuous-time dynamical systems

This paper studies the issue of impulsive observers via event-triggered impulsive control (ETIC) for continuous-time dynamical systems (CDS). By using three levels of event conditions, the schemes of output-based ETIC including sampling-based ETIC are designed and full-order event-triggered impulsive observers are obtained. The impulse frequency and control strength of ETIC are also estimated. Moreover, in the case of CDS with unknown input, the notion of impulsive observer with K-asymptotic gain is proposed. And it is shown that the state from the observer can track the state of observed system within an error bound and the impulsive observer is with K-asymptotic gain. Specifically, when the unknown input trends to zero, the track can be completely achieved. Finally, based on the chaotic Lorenz system, an example is given to demonstrate the effectiveness of the theoretical results. And it is shown that for a same observer via impulsive control, the designed ETIC can achieve better performances with much lower impulse frequency and much less control strength than the classic impulsive control.

Robust impulsive observer design for infinite‐dimensional cell population balance models

AbstractThe observer design problem for a class of cell population balance models, describing the time evolution of the cell mass density distribution function and the substrate concentration in a continuous‐stirred tank bioreactor with irregular discrete‐time measurements of the cell mass distribution is considered. The model consists of a partial integro‐differential equation coupled with an ordinary differential equation. Using the theory of impulsive systems sufficient conditions for the input‐to‐state‐stability (ISS) of the observation error in the state‐space with respect to the measurement uncertainty are derived in terms of the maximum time between successive measurements and the ISS gain. In absence of measurement uncertainty the convergence conditions imply exponential stability of the observation error dynamics. Besides these rigorous conditions, application‐oriented tuning guidelines are established. The theoretical results are illustrated with numerical simulations including a comparison with a continuous–discrete extended Kalman filter based on the numerical approximation, showing that a similar accuracy is achieved when using a finite‐dimensional approximation of the proposed impulsive observer scheme with a considerably lower computational effort.

Finite-time impulsive observers for nonlinear systems represented by Takagi–Sugeno models: Application to a chaotic system

In this paper, observer design for nonlinear systems represented by Takagi Sugeno models (T-S) is investigated. The first main contribution concerns the finite time convergence of the estimations, ensured by an impulsive observer with state updates. The second contribution, lies with taking into account unmeasurable parameters, using the Differential Mean Value Theorem (DMVT) to express the disturbed error dynamics into a Linear Parameter Varying system. The stability conditions are formulated in terms of Linear Matrix Inequalities (LMI). To prove the efficiency of the proposed procedure, applications are performed on a chaotic system. The obtained results are pretty satisfying.

Qualitative properties for the 1 − D impulsive wave equation: controllability and observability

In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain ω and at one instant of time τ ∈ (0, T). Afterward, we study impulse observability.

Impulsive observer-based design for state estimation of a class of nonlinear singularly perturbed systems with discrete measurements

The state estimation problem of a class of nonlinear singularly perturbed systems with discrete measurements is investigated. The fast dynamics is assumed to be linear and exponentially stable. Under this assumption and some additional conditions, an asymptotic representation of the fast state is obtained in terms of the slow state and the known input. Then the full state estimation problem reduces to the slow state estimation problem. Based on this observation, an impulsive observer based estimation scheme is presented in the framework of singular perturbation. The continuous part of the proposed impulsive observer is a copy of the reduced-order slow dynamics of the observed system, while the impulse part is responsible for the implementation of the sample-triggered update of the observer state whenever a new sample of the output arrives. The estimation error is analyzed via a discontinuous Lyapunov function, and an ε-independent observer gain is designed. It is shown that the resulting estimation error exponentially converges towards an ultimate bound of order O(ε). The theoretical results are successfully applied to state estimates of Chua’s circuit and a flexible link robot. The simulation results demonstrate that the proposed state estimation scheme can achieve a desirable estimation accuracy for small enough ε>0.