Estimation Error Of Observer Research Articles

An Improved ELOS Guidance Law for Path Following of Underactuated Unmanned Surface Vehicles.

In this paper, targeting the problem that it is difficult to deal with the time-varying sideslip angle of an underactuated unmanned surface vehicle (USV), a line-of-sight (LOS) guidance law based on an improved extended state observer (ESO) is proposed. A reduced-order ESO is introduced into the identification of the sideslip angle caused by the environmental disturbance, which ensures a fast and accurate estimation of the sideslip angle. This enables the USV to follow the reference path with high precision, despite external disturbances from wind, waves, and currents. These unknown disturbances are modeled as drift, which the modified ESO-based LOS guidance law compensates for using the ESO. In the guidance subsystem incorporating the reduced-order state observer, the observer estimation and track errors are proved uniformly ultimately bounded. Simulation and experimental results are presented to validate the effectiveness of the proposed method. The simulation and comparison results demonstrate that the proposed ELOS guidance can help a USV track different types of paths quickly and smoothly. Additionally, the experimental results confirm the feasibility of the method.

Designing a fixed-time observer-based adaptive non-singular sliding mode controller for flexible spacecraft

This paper investigates the stabilization problem with a fixed-time approach for a flexible spacecraft subject to vibrations of flexible modes, unknown bounded disturbance, and inherent uncertainty. To estimate the modal variables of a flexible spacecraft which are often unmeasurable in practice, an observer with guaranteed fixed-time convergence is designed. Using the estimated modal variables, a fixed-time non-singular sliding mode controller is designed so that the desired attitude can be reached before a pre-specified time threshold regardless of the spacecraft's initial attitude. By incorporating the estimated modal variables in the control design, significant reduction in the steady-state error of the system response is achieved. The proposed control system is further enhanced with an adaptive law to increase robustness against unknown external disturbances and uncertainties. Stability analysis based on Lyapunov theory guarantees the convergence of observer estimation error and spacecraft attitude error to a pre-determined set before a fixed threshold. Simulation results validate the promising performance of the proposed control system, highlighting its effectiveness in achieving accurate and robust attitude control for flexible spacecraft.

Distributed interval observer-based robust control for multirate systems under the FlexRay protocol

In this paper, an interval observer-based control problem under the FlexRay protocols is investigated for a class of multirate systems in which the noises are assumed to be unknown but bounded. The FlexRay protocol is employed to schedule the information transfer so as to reduce the communication burden. Based on the FlexRay protocol and the multirate sampling mechanism, a new measurement output representation is established with the help of the lifting technique and the augmentation technique, and then, a sufficient condition is proposed to guarantee the interval observer estimation error dynamics are bounded. In addition, the interval observer gain and the H∞ controller gain are obtained by solving the linear matrix inequalities, which further ensure the H∞ performance of the closed-loop system. Finally, a numerical simulation verifies the effectiveness of the FlexRay protocols and interval observer-based controllers.

Output Feedback for Nonlinear Systems With Nonlinear and Discontinuous Inputs

The paper aims to design a high-gain observer for nonlinear systems with nonlinear and discontinuous sensor signal. The ultimate boundedness and exponential stability of the estimation error of high-gain observer are presented. The performance recovery property of output feedback control using high-gain observer is demonstrated. Simulation examples are illustrated to validate the proposed results of this paper.

Position and Speed Estimation for a Surface-Mount PMSM using RBFNN Observer with Stability Guarantee

This paper proposes a radial basis function neural network (RBFNN) observer for surface-mount permanent magnet synchronous motor (SPMSM). The corresponding observer is used to estimate the rotor speed, and the rotor position. The convergence of the observer estimation error is analyzed using Lyapunov theory, and uniformly ultimate boundedness stability is guaranteed. Simulation results are shown to confirm the effectiveness of the proposed observer.

Integral barrier Lyapunov functions based sliding mode observer‐controller for nonlinear systems with performance constraints

AbstractThis article presents an observer‐controller structure for nonlinear systems with external disturbances, uncertainties and performance constraints. Firstly, considering the unmeasurable state issue, a sliding mode observer is designed to estimate the unknown state. Then an integral barrier Lyapunov function (iBLF) is established to ensure that the observer estimation errors are held within the performance constraints. With the objective of utilizing iBLF, an equivalent output injection technique is adopted. Combining with backstepping technique, an observer‐controller scheme is given. The controller can hold all signals in the closed‐loop system bounded with the help of iBLF, and the tracking error will converge to a bounded tight set without violating the corresponding constraints. The effectiveness of the proposed strategy is clarified via a vessel heading control example.

An Enhanced Feedback Adaptive Observer for Nonlinear Systems With Lack of Persistency of Excitation

The design of exponentially convergent adaptive observers is addressed for linear observable systems which are perturbed by linearly parameterized nonlinearities depending on measured signals (inputs and outputs). When there is a lack of persistency of excitation a new robust adaptive observer is presented which performs an additional feedback depending on the kernel of the Gramian of the regressor matrix, which is computed online, and generates state variables estimates whose estimation errors are exponentially convergent to zero, provided that a design parameter is chosen to be sufficiently small. The boundedness of the parameter and observer estimation errors is always guaranteed. Parameter estimates do not converge to their true values unless the regressor matrix is persistently exciting (i.e. the Gramian of the regressor matrix is nonsingular): in this case, a well-known exponentially convergent adaptive observer is reobtained, since the additional feedback is zero.

Asymptotically Tracking Control of Structural Balance for Discrete-Time Links System Associated with External Stimulations and State Observer

Considering that the link states of some practical networks are not measurable, it is impossible to control the links system directly to achieve structural balance. In order to handle this problem, the state observer design and the structural balance tracking control for the links system with complex dynamical networks are investigated. The dynamical model of the links system is molded as the Riccati matrix difference equation, which contains a coupling term associated with external stimulations. For the discrete-time model, the pole assignment algorithm is adopted to calculate the gain matrix for the observer of the links system. It could guarantee that the estimation error of observer for links system is globally asymptotically stable. Further, combining the effective estimation information of observer and external stimulations, an asymptotically tracking controller is proposed, which could achieve the asymptotic tracking of the reference structure balance network to the links system. Finally, the validity of the proposed method is verified by the simulation example.

An Improved Adaptive Dynamic Programming Algorithm Based on Fuzzy Extended State Observer for Dissolved Oxygen Concentration Control

To solve the anti-disturbance control problem of dissolved oxygen concentration in the wastewater treatment plant (WWTP), an anti-disturbance control scheme based on reinforcement learning (RL) is proposed. An extended state observer (ESO) based on the Takagi–Sugeno (T-S) fuzzy model is first designed to estimate the the system state and total disturbance. The anti-disturbance controller compensates for the total disturbance based on the output of the observer in real time, online searches the optimal control policy using a neural-network-based adaptive dynamic programming (ADP) controller. For reducing the computational complexity and avoiding local optimal solutions, the echo state network (ESN) is used to approximate the optimal control policy and optimal value function in the ADP controller. Further analysis demonstrates the observer estimation errors for system state and total disturbance are bounded, and the weights of ESNs in the ADP controller are convergent. Finally, the effectiveness of the proposed ESO-based ADP control scheme is evaluated on a benchmark simulation model of the WWTP.

Adaptive multi symptoms control of Parkinson's disease by deep reinforcement learning

Parkinson's disease (PD) is one of the really frequent disorders, with hand and head tremors and rigidity being the most common sequelae. Deep brain stimulation (DBS) is a common treatment used to alleviate the symptoms of this disease. This work investigates an ultra-local model (ULM) based on a sliding mode observer (SMO) to simultaneously reduce hand tremor and rigidity. specifically, a deep deterministic policy gradient (DDPG) controller is adaptively designed in the current study to reduce observer estimation error and improve the nonlinear dynamic features of a central neural network (CNN). The DDPG is designed with an actor that produces policy demands and a critic that measures the effectiveness of the actor’s policy orders. The offered methodology employs a DDPG-based mechanism to compensate for the shortcomings of the ULM-based SMO. In the present mechanism, training of the weight values of both networks (actor and critic) is by the gradient descent way that relies on the tremor fault's reward return. Finally, the following methodology is analyses by computer simulation in a variety of contexts (robustness and controller performance) and compared to current practices to prove the benefits and adaptability of the procedure with varied models and patients. Additionally, the controllers are implemented in the hardware-in-the-loop (HiL) simulations testbed to validate the performance of the developed scheme's profitability from a realistic perspective.

A Simplified Algorithm for Setting the Observer Parameters for Second-Order Systems with Persistent Disturbances Using a Robust Observer.

The properties of the convergence region of the estimation error of a robust observer for second-order systems are determined, and a new algorithm is proposed for setting the observer parameters, considering persistent but bounded disturbances in the two observation error dynamics. The main contributions over closely related studies of the stability of state observers are: (i) the width of the convergence region of the observer error for the unknown state is expressed in terms of the interaction between the observer parameters and the disturbance terms of the observer error dynamics; (ii) it was found that this width has a minimum point and a vertical asymptote with respect to one of the observer parameters, and their coordinates were determined. In addition, the main advantages of the proposed algorithm over closely related algorithms are: (i) the definition of observer parameters is significantly simpler, as the fulfillment of Riccati equation conditions, solution of LMI constraints, and fulfillment of eigenvalue conditions are not required; (ii) unknown bounded terms are considered in the dynamics of the observer error for the known state. Finally, the algorithm is applied to a model of microalgae culture in a photobioreactor for the estimation of biomass growth rate and substrate uptake rate based on known concentrations of biomass and substrate.

Comprehensive Engineering Frequency Domain Analysis and Vibration Suppression of Flexible Aircraft Based on Active Disturbance Rejection Controller.

The crash of an aircraft with an almost vertical attitude in Wuzhou, Guangxi, China, on 21 March 2022, has caused a robust discussion in the civil aviation community. We propose an active disturbance rejection controller (ADRC) for suppressing aeroelastic vibrations of a flexible aircraft at the simulation level. The ADRC has a relatively simple structure and it has been proved in several fields to provide better control than the classical proportional-integral-derivative (PID) control theory and is easier to translate from theory to practice compared with other modern control theories. In this paper, the vibration model of the flexible aircraft was built, based on the first elastic vibration mode of the aircraft. In addition, the principle of ADRC is explained in detail, a second-order ADRC was designed to control the vibration model, and the system’s closed-loop frequency domain characteristics, tracking effect and sensitivity were comprehensively analyzed. The estimation error of the extended state observer (ESO) and the anti-disturbance effect were analyzed, while the robustness of the closed-loop system was verified using the Monte Carlo method, which was used for the first time in this field. Simulation results showed that the ADRC suppressed aircraft elastic vibration better than PID controllers and that the closed-loop system was robust in the face of dynamic parameters.

Nonlinear motor-mechanism coupling tank gun control system based on adaptive radial basis function neural network optimised computed torque control

This study investigates the spatial pointing control of a motor-mechanism coupling tank gun. The tank gun control system (TGCS) is driven and stabilised by the motor servo system. However, complicated nonlinearities in the TGCS are inevitable, such as friction, parameter uncertainty, and modelling errors. To solve this problem, the TGCS is regarded as a coupling system composed of mechanical, motor, and control systems. Accordingly, the mechanical and motor models of the marching tank gun are developed first in this paper. The motor-mechanism coupling dynamics model is established based on the principle of equivalent torque. On this basis, a computed torque controller, whose uncertainty was estimated using a radial basis function neural network (RBFNN), is constructed. A modified adaptive algorithm is used to estimate the weights of the RBFNN, and the estimation error of the uncertain observer is compensated by a compensation controller. Simulation results under different conditions validated the effectiveness of the proposed control system, revealing that the proposed control system has good tracking accuracy, strong adaptability, and robustness.

Observer-Based Adaptive Synchronization Control of Unknown Discrete-Time Nonlinear Heterogeneous Systems.

This article is concerned with the optimal synchronization problem for discrete-time nonlinear heterogeneous multiagent systems (MASs) with an active leader. To overcome the difficulty in the derivation of the optimal control protocols for these systems, we develop an observer-based adaptive synchronization control approach, including the designs of a distributed observer and a distributed model reference adaptive controller with no prior knowledge of all agents' dynamics. To begin with, for the purpose of estimating the state of a nonlinear active leader for each follower, an adaptive neural network distributed observer is designed. Such an observer serves as a reference model in the distributed model reference adaptive control (MRAC). Then, a reinforcement learning-based distributed MRAC algorithm is presented to make every follower track its corresponding reference model on behavior in real time. In this algorithm, a distributed actor-critic network is employed to approximate the optimal distributed control protocols and the cost function. Through convergence analysis, the overall observer estimation error, the model reference tracking error, and the weight estimation errors are proved to be uniformly ultimately bounded. The developed approach further achieves the synchronization by means of synthesizing these results. The effectiveness of the developed approach is verified through a numerical example.

Observer‐based adaptive controller design for chaos synchronization using Bernstein‐type operators

AbstractThis article uses the Bernstein‐type operators as the universal approximator to present an observer‐based robust adaptive controller for chaos synchronization. The lumped uncertainties including, un‐modeled dynamics and external disturbances, are modeled with this potent mathematic tool. It is shown that using the Bernstein‐type operators as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniform ultimate boundedness of the observer estimation error and synchronization error can be assured. To analyze the performance of the proposed controller scheme in terms of transient response behavior and robustness, the Duffing–Holmes oscillator is considered as the simulation testbed. A set of two different experiments are conducted to evaluate the efficiency of the introduced control approach. The performance of the proposed approach is also compared with RBFNN as a powerful approximation method. Unlike neural network/fuzzy methods, which require system states as inputs to estimate functions and construct a regressor vector, the proposed method is not dependent on the system states. Furthermore, there are more adjustable parameters in the regressor vector of the RBFNN (such as the width and center of the Gaussian units), and assigning the best values for these parameters is tedious and time‐consuming work due to the repeated trial and error.

Distributed interval state estimation with [formula omitted]-gain optimization for cyber–physical systems subject to bounded disturbance and random stealthy attacks

This paper studies the distributed interval state estimation problem for cyber–physical systems with bounded disturbance and random stealthy attacks. Since conventional interval observers cannot complete the task of real-time monitoring system under random attacks, an attack-resistant distributed interval observer is designed by using attack frequency and interval attack estimation. Using the designed observer, upper- and lower-bounding estimation error systems are modeled by positive interconnected systems with hybrid deterministic and random bounded inputs. To explicitly attenuate the effect of disturbance and attacks, the resulting deterministic positive error system between upper- and lower-bounding estimates is formulated. By linear programming, the results of interval observer design and l∞-gain optimization are proposed. The remote monitoring of vehicle lateral dynamic is given for numerical verification of the results.

A Networked Competitive Multi-Virus SIR Model: Analysis and Observability

This paper proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be locally observable. We propose a Luenberger observer for the system state estimation and show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.

A Novel Guidance Law for Intercepting a Highly Maneuvering Target

Given the resolution of the guidance for intercepting highly maneuvering targets, a novel finite-time convergent guidance law is proposed, which takes the following conditions into consideration, including the impact angle constraint, the guidance command input saturation constraint, and the autopilot second-order dynamic characteristics. Firstly, based on the nonsingular terminal sliding mode control theory, a finite-time convergent nonsingular terminal sliding mode surface is designed. On the back of the backstepping control method, the virtual control law appears. A nonlinear first-order filter is constructed so as to address the “differential expansion” problem in traditional backstepping control. By designing an adaptive auxiliary system, the guidance command input saturation problem is dealt with. The RBF neural network disturbance observer is used for estimating the unknown boundary external disturbances of the guidance system caused by the target acceleration. The parameters of the RBF neural network are adjusted online in real time, for the purpose of improving the estimation accuracy of the RBF neural network disturbance observer and accelerating its convergence characteristics. At the same time, an adaptive law is designed to compensate the estimation error of the RBF neural network disturbance observer. Then, the Lyapunov stability theory is used to prove the finite-time stability of the guidance law. Finally, numerical simulations verify the effectiveness and superiority of the proposed guidance law.

Charge-Based Capacitive Self-Sensing With Continuous State Observation for Resonant Electrostatic MEMS Mirrors

This contribution presents charge-based capacitive self-sensing with a continuous full state observer for a parametrically driven resonant electrostatic 1D MEMS mirror considering precise and seamless estimation. Based on current integrators, series capacitances or a capacitance network the direct charge self-sensing principles are investigated and compared considering leakage currents, precision and a minimum implementation effort. In comparison to the other charge sensing methods, the proposed methods directly measure the charge changes while the drive voltage is switched on. Since resonant MEMS mirrors are driven by a rectangular signal, the direct self-sensing implies a lack of data when the drive voltage is switched off. A nonlinear observer is also proposed to estimate the full mirror state continuously based on an identified MEMS mirror model. The capacitive charge self-sensing methods achieve overall a high sensing precision of less than 0.14 % RMSE and the observer estimation error of the full state is below 1 % peak-to-peak error regardless of the availability of the charge self-sensing measurements, demonstrates accurate continuous full state estimation. [2021-0130]

Motion Control of Autonomous Underwater Vehicle Based on Fractional Calculus Active Disturbance Rejection

An active disturbance rejection control based on fractional calculus is proposed to improve the motion performance and robustness of autonomous underwater vehicle (AUV). The active disturbance rejection control (ADRC) method can estimate and compensate the total disturbance of AUV automatically. The fractional-order PID (proportional integral derivative) has fast dynamic response, which can eliminate the estimation error of extended state observer. The fractional calculus active disturbance rejection strategy combines the advantages of the above two algorithms, and it is designed for AUV heading and pitch subsystems. In addition, the stability of fractional calculus ADRC heading subsystem is proven by Lyapunov stability theorem. The numerical simulations and experimental results document that the superior performance has been achieved. The fractional calculus ADRC strategy has more excellent abilities for disturbance rejection, performs better than ADRC and PID, and has important theoretical and practical value.