Partial state estimation for linear systems with output and input time delays.

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.

Reduced order functional observers with application to partial state estimation of linear systems with input delay

Reduced order multi-functional observer design for multi-input multi-utput (MIMO) linear time-invariant (LTI) systems with constant delayed inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptoticobserver in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

Partial state estimation: a new design approach

© 2014 IEEE. There are three different approaches for functional observer design for Linear Time-Invariant (LTI) systems within the literature. One of the most common methods has been proposed by Aldeen [1] and further developed by others. We found several examples in which the necessary and sufficient conditions for the existence of a functional observer are actually not sufficient for this methodology. This finding motivated us to develop a new methodology for designing functional observers. Our new method provides enough degrees of freedom for the observer design parameter and it improves the weakness within the Aldeen's method in solving the observer coupled matrix equations. In this paper, we present the reason and an example to show the insufficiency of the former method. Furthermore, we present our new developed methodology. An illustrative algorithm also describes the design procedure step by step. A numerical example and simulation results support our findings and performance of the proposed method.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Designing delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.

Partial state estimation of time-delay systems.

This thesis broadly studies three crucial and rigorous inter-related control theoretical subjects: (i) Partial state estimation of linear systems; (ii) Stability analysis of time-delay systems with interval time-varying delays; and (iii) Functional observer design for time-delay systems.

Partial state and unknown input estimation for time-delay systems

This article considers the problem of estimating a partial set of the state vector and/or unknown input vector of linear systems driven by unknown inputs and time-varying delay in the state variables. Three types of reduced-order observers, namely, observers with delays, observers without internal delays and delay-free observers are proposed in this article. Existence conditions and design procedures are presented for the determination of parameters for each case of observers. Numerical examples are presented to illustrate the design procedures.

Partial-state observers for nonlinear systems

This note deals with the design of reduced-order observers for a class of nonlinear systems. The order reduction of the observer is achieved by only estimating a required partial set of the state vector. Necessary and sufficient conditions are derived for the existence of reduced-order observers. An observer design procedure based on linear matrix inequalities is given. A numerical example is given to illustrate the design method.

Traffic state estimation from partial Bluetooth and volume observations : case study in the Brisbane metropolitan area

The application of the Bluetooth (BT) technology to transportation has been enabling researchers to make accurate travel time observations, in freeway and arterial roads. The Bluetooth traffic data are generally incomplete, for they only relate to those vehicles that are equipped with Bluetooth devices, and that are detected by the Bluetooth sensors of the road network. The fraction of detected vehicles versus the total number of transiting vehicles is often referred to as Bluetooth Penetration Rate (BTPR). The aim of this study is to precisely define the spatio-temporal relationship between the quantities that become available through the partial, noisy BT observations; and the hidden variables that describe the actual dynamics of vehicular traffic. To do so, we propose to incorporate a multi- class traffic model into a Sequential Montecarlo Estimation algorithm. Our framework has been applied for the empirical travel time investigations into the Brisbane Metropolitan region.

Real-time traffic state estimation in urban corridors from heterogeneous data

In recent years, rapid advances in information technology have led to various data collection systems which are enriching the sources of empirical data for use in transport systems. Currently, traffic data are collected through various sensors including loop detectors, probe vehicles, cell-phones, Bluetooth, video cameras, remote sensing and public transport smart cards. It has been argued that combining the complementary information from multiple sources will generally result in better accuracy, increased robustness and reduced ambiguity. Despite the fact that there have been substantial advances in data assimilation techniques to reconstruct and predict the traffic state from multiple data sources, such methods are generally data-driven and do not fully utilize the power of traffic models. Furthermore, the existing methods are still limited to freeway networks and are not yet applicable in the urban context due to the enhanced complexity of the flow behavior. The main traffic phenomena on urban links are generally caused by the boundary conditions at intersections, un-signalized or signalized, at which the switching of the traffic lights and the turning maneuvers of the road users lead to shock-wave phenomena that propagate upstream of the intersections. This paper develops a new model-based methodology to build up a real-time traffic prediction model for arterial corridors using data from multiple sources, particularly from loop detectors and partial observations from Bluetooth and GPS devices.

Prognosis of bearing failure based on health state estimation

This paper proposes a new prognosis model based on the technique for health state estimation of machines for accurate assessment of the remnant life. For the evaluation of health stages of machines, the Support Vector Machine (SVM) classifier was employed to obtain the probability of each health state. Two case studies involving bearing failures were used to validate the proposed model. Simulated bearing failure data and experimental data from an accelerated bearing test rig were used to train and test the model. The result obtained is very encouraging and shows that the proposed prognostic model produces promising results and has the potential to be used as an estimation tool for machine remnant life prediction.

Dynamic equivalent state estimation for multi-area power systems with synchronized phasor measurement units

This paper proposes a new approach for state estimation of angles and frequencies of equivalent areas in large power systems with synchronized phasor measurement units. Defining coherent generators and their correspondent areas, generators are aggregated and system reduction is performed in each area of inter-connected power systems. The structure of the reduced system is obtained based on the characteristics of the reduced linear model and measurement data to form the non-linear model of the reduced system. Then a Kalman estimator is designed for the reduced system to provide an equivalent dynamic system state estimation using the synchronized phasor measurement data. The method is simulated on two test systems to evaluate the feasibility of the proposed method.

Machine prognostics based on health state estimation using SVM

The ability to accurately predict the remaining useful life of machine components is critical for machine continuous operation, and can also improve productivity and enhance system safety. In condition-based maintenance (CBM), maintenance is performed based on information collected through condition monitoring and an assessment of the machine health. Effective diagnostics and prognostics are important aspects of CBM for maintenance engineers to schedule a repair and to acquire replacement components before the components actually fail. All machine components are subjected to degradation processes in real environments and they have certain failure characteristics which can be related to the operating conditions. This paper describes a technique for accurate assessment of the remnant life of machines based on health state probability estimation and involving historical knowledge embedded in the closed loop diagnostics and prognostics systems. The technique uses a Support Vector Machine (SVM) classifier as a tool for estimating health state probability of machine degradation, which can affect the accuracy of prediction. To validate the feasibility of the proposed model, real life historical data from bearings of High Pressure Liquefied Natural Gas (HP-LNG) pumps were analysed and used to obtain the optimal prediction of remaining useful life. The results obtained were very encouraging and showed that the proposed prognostic system based on health state probability estimation has the potential to be used as an estimation tool for remnant life prediction in industrial machinery.

100Hz onboard vision for quadrotor state estimation

This paper introduces a high-speed, 100Hz, visionbased state estimator that is suitable for quadrotor control in close quarters manoeuvring applications. We describe the hardware and algorithms for estimating the state of the quadrotor. Experimental results for position, velocity and yaw angle estimators are presented and compared with motion capture data. Quantitative performance comparison with state-of-the-art achievements are also presented.