Stability Of Estimation Error Dynamics Research Articles

A Linear Variable Parameter Observer-Based Road Profile Height Estimation for Suspension Nonlinear Dynamics Improvements

The accuracy of road profile height estimation has a significant impact on suspension control quality, which in turn influences handling, stability of vehicle motion and occupants' comfort. Based on our previous published work, this article designs and proposes a novel method for road profile estimation that is based on suspension nonlinear dynamics. The proposed approach first establishes the road profile height estimation model considering a real suspension design, including nonlinear characteristics of the shock absorber, bushing stiffness and damping, actual geometry of the control arms, and positioning of absorber. Unlike the conventional sprung-unsprung mass model, the real nonlinear suspension model provides much higher output prediction accuracy as computational and experimental results demonstrated. Moreover, the established estimation method and model require only two easily measurable parameters, which are the acceleration of the sprung mass and the travel of the shock absorber. While considering nonlinearity and hysteretic characteristics of the damping force, the proposed approach is based on the estimation framework of linear parameter-varying systems and establishes a sliding mode observer for estimating the road profile height. The stability of estimation error dynamics of the observer is guaranteed by the Lyapunov stability analysis. As bench-test experiments of a hardware implementation of the suspension-wheel unit validated the computational results. The tests demonstrated that the proposed method allows for real-time estimating of the road profile height in different road conditions and electric currents of the suspension damper and is robust to uncertainty of the payload.

Adaptive State Observers for Incrementally Quadratic Nonlinear Systems with Application to Chaos Synchronization

This paper is concerned with the problem of adaptive state observer design for a class of incrementally quadratic nonlinear systems with parameter uncertainty. Its nonlinearity satisfies the condition of incremental quadratic constraints which contains many commonly encountered nonlinearities in existing literature as some special cases. A circle criterion-based adaptive observer is first designed to expand the freedom of observer design. Based on the incremental quadratic constraint condition, sufficient conditions ensuring asymptotic stability of estimation error dynamics are established in terms of linear matrix inequalities. Finally, the adaptive observer is applied to the synchronization design of chaotic systems with parameter uncertainty, which fully demonstrates the effectiveness of the proposed observer.

Multiple-mode adaptive state estimator for nonlinear switched systems

This paper deals with the issue of state estimator design for nonlinear switched systems. A multiplemode adaptive estimator is proposed under mode-dependent average dwell time (MDADT) switching, and the switching signal with MDADT constraint is also obtained to guarantee the exponential stability of estimation error dynamics, where the Lipschitz constant may be unknown since it is adaptively adjusted by designing an adaptation law. Based on both Lyapunov stable theory and the feasible solution of an optimization problem with linear matrix inequality constraint, the gain matrices and switching signals are provided, respectively. The sufficient conditions of the existence of multiple-mode adaptive switched estimator are also derived. Meanwhile, the above methods are also extended to the case of the average dwell time (ADT) switching, and an algorithm is given to summarize the implementation of the proposed estimators. Finally, the effectiveness of the designed methods is illustrated by simulation examples.

Robust L∞-induced filtering and deconvolution of a wide class of linear discrete-time stochastic systems

The problems of stationary robust L∞-induced filtering and deconvolution are addressed for discrete-time linear systems with deterministic and stochastic uncertainties in the state–space model. Stochastic uncertainties are in the form of state- and input-dependent multiplicative white noises which appear in both state and the measurement equations. The deterministic part of the system matrices and covariance matrices of the stochastic parameters is unknown and resides in a given polytopic-type domain. For this system a new lemma is derived which characterizes the induced L∞ norm disturbance attenuation performance by linear matrix inequalities (LMIs). According to this lemma, the problem of estimator design is solved for stochastic uncertain systems based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent design procedure, which is much less conservative than the quadratic approach. The proposed estimators guarantee the mean-square exponential stability of estimation error dynamics and satisfy the prescribed induced L∞ performance index. Two examples are used to demonstrate the proposed methods and their effectiveness.

Output Feedback Passivity-Based Controller for Microalgae Cultivation

Microalgae are microscopic plants existing in aquatic environment. They can be used in the production of high value compounds and they have promising opportunities in energy production, wastewater treatment and fixation of carbon dioxide. In this context, the control of the cultivation requires a special attention in order to obtain high amounts of biomass. The control of microalgae cultivation is approached from passivity-based control perspectives. The proposed controller solves set point tracking and stabilizes the control loop by the passivity properties. Moreover, in order to obtain the process state variables from the measurement output, which are used in the control law, a nonlinear observer with guaranteed stability of estimation error dynamics is proposed. The design of the nonlinear controller and the observer is based on the Droop model, describing the dynamic behaviour of the microalgae process in a practical way. Finally, the performance of the nonlinear observer-based controller is shown by simulation.

Gain-Scheduled Observers Using Inexact Scheduling Parameters

This note addresses the design problem of Gain-Scheduled (GS) observers for discrete-time Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). We give a sufficient condition for our problem in terms of Parameter-Dependent Linear Matrix Inequalities (PDLMIs). Our method not only guarantees the stability of estimation error dynamics but also optimizes the estimation errors under exogenous disturbances to LPV systems. A numerical example is included to illustrate our results.

Multiple sliding mode observers and unknown input estimations for Lipschitz nonlinear systems

AbstractMultiple sliding mode observers for state and unknown input estimations of a class of MIMO nonlinear systems are systematically developed in this paper. A new nonlinear transformation is formulated to divide the original system into two interconnected subsystems. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. Under structural assumptions for the unknown input distribution matrix, the sliding mode terms of the nonlinear observer are designed to track their respective unknown inputs. Also, the unknown inputs can be reconstructed from the multiple sliding mode structurally. The conditions for asymptotic stability of estimation error dynamics are derived. Finally, simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

Observer-Based Fault Diagnosis of Satellite Systems Subject to Time-Varying Thruster Faults

This paper presents a novel fault diagnosis approach in satellite systems for identifying time-varying thruster faults. To overcome the difficulty in identifying time-varying thruster faults by adaptive observers, an iterative learning observer (ILO) is designed to achieve estimation of time-varying faults. The proposed ILO-based fault-identification strategy uses a learning mechanism to perform fault estimation instead of using integrators that are commonly used in classical adaptive observers. The stability of estimation-error dynamics is established and proved. An illustrative example clearly shows that time-varying thruster faults can be accurately identified.

SIMULTANEOUS IDENTIFICATION OF TIME-VARYING PARAMETERS AND ESTIMATION OF SYSTEM STATES USING ITERATIVE LEARNING OBSERVER

This paper presents the design of an Iterative Learning Observer (ILO) for the purpose of estimating system states while simultaneously identifying time-varying parameters. The proposed ILO uses a novel updating mechanism to identify time-varying parameters instead of using integrators which are commonly used in classical adaptive observers to identify constant parameters while estimating system states. The main idea behind the design of the ILO is the use of learning, i.e. previous information is combined into the ILO for identifying online time-varying parameters. Stability of estimation error dynamics and convergence of parameter estimation error are established and proven. An illustrative example exhibits the effectiveness of the ILO.