An extended state observer with adjustable bandwidth for measurement noise

In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.

Backstepping Sliding Mode Control Based on Extended State Observer for Hydraulic Servo System

Hydraulic servo system plays an important role in industrial fields due to the advantages of high response,small size-to-power ratio and large driving force.However,inherent nonlinear behaviors and modeling uncertainties are the main obstacles for hydraulic servo system to achieve high tracking perfor-mance.To deal with these difficulties,this paper presents a backstepping sliding mode controller to improve the dynamic tracking performance and anti-interfer-ence ability.For this purpose,the nonlinear dynamic model is firstly established,where the nonlinear behaviors and modeling uncertainties are lumped as one term.Then,the extended state observer is introduced to estimate the lumped distur-bance.The system stability is proved by using the Lyapunov stability theorem.Finally,comparative simulation and experimental are conducted on a hydraulic servo system platform to verify the efficiency of the proposed control scheme.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Event-triggered model-free adaptive control for a class of surface vessels with time-delay and external disturbance via state observer

This paper provides an improved model-free adaptive control(IMFAC)strategy for solving the surface vessel trajectory tracking issue with time delay and restricted disturbance.Firstly,the original nonlinear time-delay system is transformed into a structure consisting of an unknown residual term and a parameter term with control inputs using a local compact form dynamic linearization(local-CFDL).To take advantage of the resulting structure,use a discrete-time extended state observer(DESO)to estimate the unknown residual factor.Then,according to the study,the inclusion of a time delay has no effect on the linearization structure,and an improved control approach is provided,in which DESO is used to adjust for uncertainties.Furthermore,a DESO-based event-triggered model-free adaptive control(ET-DESO-MFAC)is established by designing event-triggered conditions to assure Lyapunov stability.Only when the system’s indicator fulfills the provided event-triggered condition will the control input signal be updated;otherwise,the control input will stay the same as it is at the last trigger moment.A coordinate compensation approach is developed to reduce the steady-state inaccuracy of trajectory tracking.Finally,simulation experiments are used to assess the effectiveness of the proposed technique for trajectory tracking.

Observability and estimability of passive radar with unknown illuminator states using different observations

Most existing studies about passive radar systems are based on the already known illuminator of opportunity(IO)states.However,in practice,the receiver generally has little knowledge about the IO states.Little research has studied this problem.This paper analyzes the observability and estimability for passive radar systems with unknown IO states under three typical scenarios.Besides,the directions of high and low estimability with respect to various states are given.Moreover,two types of observations are taken into account.The effects of different observations on both observability and estimability are well analyzed.For the observability test,linear and nonlinear methods are considered,which proves that both tests are applicable to the system.Numerical simulations confirm the correctness of the theoretical analysis.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

A State Estimation Method for Sound Environment System with Unknown Observation Mechanism by Introducing Fuzzy Inference

The observed phenomena in real sound environment system often contain uncertainty such as the additional external noise with unknown statistics. Furthermore, there is complex nonlinear relationship between the specific signal and the observations, and it cannot be exactly expressed in any definite functional form. In these situations, it is one of reasonable analysis methods to treat the objective sound environment system as a fuzzy system. In this study, a state estimation method for a specific signal under the existence of an unknown observation mechanism and external noise of unknown statistics is proposed by introducing fuzzy inference. The effectiveness of the proposed theoretical method is experimentally confirmed by applying it to the actually observed data in the sound environment.

IMPULSIVE EXPONENTIAL SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX DYNAMICAL NETWORKS WITH DERIVATIVE COUPLINGS VIA FEEDBACK CONTROL BASED ON DISCRETE TIME STATE OBSERVATIONS

This article aims to address the global exponential synchronization problem for fractional-order complex dynamical networks(FCDNs)with derivative couplings and impulse effects via designing an appropriate feedback control based on discrete time state observations.In contrast to the existing works on integer-order derivative couplings,fractional derivative couplings are introduced into FCDNs.First,a useful lemma with respect to the relationship between the discrete time observations term and a continuous term is developed.Second,by utilizing an inequality technique and auxiliary functions,the rigorous global exponential synchronization analysis is given and synchronization criterions are achieved in terms of linear matrix inequalities(LMIs).Finally,two examples are provided to illustrate the correctness of the obtained results.

Parallelizable Calculation of Observables Values on Analog Quantum Computer

The superiority of hypothetical quantum computers is not due to faster calculations but due to different schemes of calculations running on special hardware. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In conventional approach it is implemented through tensor product of qubits. In the geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on three-dimensional sphere.

Retraction control of motorized seat belt system with linear state observer

A design and verification of linear state observers which estimate state information such as angular velocity and load torque for retraction control of the motorized seat belt (MSB) system were described. The motorized seat belt system provides functions to protect passengers and improve passenger's convenience. Each MSB function has its own required belt tension which is determined by the function's purpose. To realize the MSB functions, state information, such as seat belt winding velocity and seat belt tension are required. Using a linear state observer, the state information for MSB operations can be estimated without sensors. To design the linear state observer, the motorized seat belt system is analyzed and represented as a state space model which contains load torque as an augmented state. Based on the state space model, a linear state observer was designed and verified by experiments. Also, the retraction control of the MSB algorithm using linear state observer was designed and verified on the test bench. With the designed retraction control algorithm using the linear state observer, it is possible to realize various types of MSB functions.

Optimal observation configuration of UAVs based on angle and range measurements and cooperative target tracking in three-dimensional space

This article investigates the optimal observation configuration of unmanned aerial vehicles(UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimensions. The relative geometry of the UAVs-target will significantly affect the state estimation performance of the target, the cost function based on the Fisher information matrix(FIM) is used to derive the FIM determinant of UAVs' observation in three-dimensional space, and the optimal observation geometric configuration that maximizes the determinant of the FIM is obtained. It is shown that the optimal observation configuration of the UAVs-target is usually not unique, and the optimal observation configuration is proved for two UAVs and three UAVs in three-dimension. The long-range over-the-horizon target tracking is simulated and analyzed based on the analysis of optimal observation configuration for two UAVs. The simulation results show that the theoretical analysis and control algorithm can effectively improve the positioning accuracy of the target. It can provide a helpful reference for the design of over-the-horizon target localization based on UAVs.

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.

Differential geometric guidance command with finite time convergence using extended state observer

For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to zero or its neighborhood against maneuvering targets in three-dimensional(3D) space. The extended state observer(ESO) is employed to estimate the target acceleration, which makes the new DGGC more applicable to practical interception scenarios. Finally, the effectiveness of this newly proposed guidance command is demonstrated by the numerical simulation results.

An observer based asymptotic trajectory control using a scalar state for chaotic systems

A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.

Fault detection based on H_∞ states observer for networked control systems

The influence of random short time-delay to networked control systems （NCS） is changed into an unknown bounded uncertain part. Without changing the structure of the system, an Hoo states observer is designed for NCS with short time-delay. Based on the designed states observer, a robust fault detection approach is proposed for NCS. In addition, an optimization method for the selection of the detection threshold is introduced for better tradeoff between the robustness and the sensitivity. Finally, some simulation results demonstrate that the presented states observer is robust and the fault detection for NCS is effective.

Generalized projective synchronization via the state observer and its application in secure communication

Based on the improved state observer and the pole placement technique, by adding a constant which extends the scope of use of the original system, a new design method of generalized projective synchronization is proposed. With this method, by changing the projective synchronization scale factor, one can achieve not only complete synchronization, but also anti-synchronization, as well as arbitrary percentage of projective synchronization, so that the system may attain arbitrary synchronization in a relatively short period of time, which makes this study more meaningful. By numerical simulation, and choosing appropriate scale factor, the results of repeated experiments verify that this method is highly effective and satisfactory. Finally, based on this method and the relevant feedback concept, a novel secure communication project is designed. Numerical simulation verifies that this secure communication project is very valid, and moreover, the experimental result has been greatly improved in decryption time.

Online Detection of State Estimator Performance Degradation via Efficient Numerical Observability Analysis

An efficient observability analysis method is proposed to enable online detection of performance degradation of an optimization-based sliding window visual-inertial state estimation framework.The proposed methodology leverages numerical techniques in nonlinear observability analysis to enable online evaluation of the system observability and indication of the state estimation performance.Specifically,an empirical observability Gramian based approach is introduced to efficiently measure the observability condition of the windowed nonlinear system,and a scalar index is proposed to quantify the average system observability.The proposed approach is specialized to a challenging optimizationbased sliding window monocular visual-inertial state estimation formulation and evaluated through simulation and experiments to assess the efficacy of the methodology.The analysis result shows that the proposed approach can correctly indicate degradation of the state estimation accuracy with real-time performance.

PMSM speed control using adaptive sliding mode control based on an extended state observer

In this study,a composite strategy based on sliding-mode control( SMC) is employed in a permanent-magnet synchronous motor vector control system to improve the system robustness performance against parameter variations and load disturbances. To handle the intrinsic chattering of SMC,an adaptive law and an extended state observer( ESO) are utilized in the speed SMC controller design. The adaptive law is used to estimate the internal parameter variations and compensate for the disturbances caused by model uncertainty. In addition,the ESO is introduced to estimate the load disturbance in real time. The estimated value is used as a feed-forward compensator for the speed adaptive sliding-mode controller to further increase the system's ability to resist disturbances. The proposed composite method,which combines adaptive SMC( ASMC) and ESO,is compared with PI control and ASMC. Both the simulation and experimental results demonstrate that the proposed method alleviates the chattering of SMC systems and improves the dynamic response and robustness of the speed control system against disturbances.

Extended state observer-based control with an adjustable parameter for a large ground-based telescope

The high-precision requirements will always be constrained due to the complicated operating conditions of the ground-based telescope. Owing to various internal and external disturbances, it is necessary to study a control method, which should have a good ability on disturbance rejection and a good adaptability on system parameter variation. The traditional proportional-integral(PI) controller has the advantage of simple and easy adjustment, but it cannot deal with the disturbances well in different situations. This paper proposes a simplified active disturbance rejection control law, whose debugging is as simple as the PI controller, and with better disturbance rejection ability and parameter adaptability. It adopts a simplified second-order extended state observer(ESO) with an adjustable parameter to accommodate the significant variation of the inertia during the different design stages of the telescope. The gain parameter of the ESO can be adjusted online with a recursive least square estimating method once the system parameter has changed significantly. Thus, the ESO can estimate the total disturbances timely and the controller will compensate them accordingly. With the adjustable parameter of the ESO, the controller can always achieve better performance in different applications of the telescope. The simulation and experimental verification of the control law was conducted on a 1.2-meter ground based telescope. The results verify the necessity of adjusting the parameter of the ESO, and demonstrate better disturbance rejection ability in a large range of speed variations during the design stages of the telescope.