Further results on "Reduced order disturbance observer for discrete-time linear systems"

Reduced order Disturbance OBservers (DOB) have been proposed in Kim et al (2010) and Kim and Rew (2013) for continuous-time and discrete-time linear systems, respectively. The existence condition of the promising algorithm has been established but is not straightforward to check. This work further improves the reduced order DOB design by formulating it as a functional observer design problem. By carefully designing the state functional matrix, a generic DOB is resulted with an easily-checked necessary and sufficient existence condition and an easily-adjusted convergence rate. It is also shown that both the reduced order DOB in Kim and Rew (2013) and the full order DOB in Chang (2006) are special cases of this new DOB

Fault diagnosis for vehicle lateral dynamics with robust threshold

This paper investigates the robust fault diagnosis problem for vehicle lateral dynamics, which play a key role in vehicle stability and driving safety. The proposed fault diagnosis system consists of two sub-systems: fault diagnosis observer and robust threshold. By treating faults as disturbances, Disturbance/Uncertainty Estimation technique is used as fault diagnosis observer to generate residuals. Considering that residuals of model-based fault diagnosis are subject to the effect of uncertainties and consequently large false alarm rate may be resulted in, a novel robust threshold is then proposed based on reachability analysis technique for uncertain systems. The proposed fault diagnosis system is finally applied to the accelerometer and gyrometer sensor fault diagnosis problem of vehicle lateral dynamics, where initial states and velocity are considered to be uncertain. Simulation study verifies the effectiveness of the proposed fault diagnosis system

Model based fault diagnosis system verification using reachability analysis

In model-based Fault Detection and Isolation (FDI) systems, Fault Indicating Signals (FIS) such as residuals and fault estimates are corrupted by various noises, uncertainties and variations. It becomes challenging to verify whether a FDI system still works or not in real life applications. It is also challenging to select a threshold so that false alarm rate and missed detection rate are kept low depending on real operation conditions. This paper proposes solutions to the aforementioned problems by quantitatively analyzing the effect of uncertainties on FIS. The problems are formulated into reachability analysis problem for uncertain systems. The reachable sets of FIS are calculated under normal and selected faulty cases respectively. From these reachable sets, the effectiveness of a FDI system can be qualitatively verified under described uncertainties. A dedicated threshold can be further chosen to be robust to all possible described uncertainties. As a by-product, the minimum detectable fault can also be quantitatively determined by checking the intersection of the computed reachable sets. The proposed approach is demonstrated by evaluating a FDI algorithm of a motor in the presence of parameter uncertainties, unknown load and sensor noises, where a fault estimation based approach is adopted to diagnose amplifier, velocity and current sensor faults

Simultaneous state and input estimation with partial information on the inputs

This paper investigates the problem of simultaneous state and input estimation for discrete-time linear stochastic systems when the information on the inputs is partially available. To incorporate the partial information on the inputs, matrix manipulation is used to obtain an equivalent system with reduced-order in puts. Then Bayesian inference is drawn to obtain a recursive filter for both state and input variables. The proposed filter is an extension of the recently developed state filter with partially observed inputs to the case where the input filter is also of in terest, and an extension of the Simultaneous State and Input Estimation (SSIE) to the case where the information on the inputs is partially available. A numerical example is given to illustrate the proposed method. It is shown that, due to the additional information on the inputs being incorporated in the filter design, the performances of both state and input estimation are substantially improved in comparison with the conventional SSIE without partial input information

High order disturbance observer design for linear and nonlinear systems

© 2015 IEEE. In this paper, a disturbance observer is proposed for nonlinear systems with high order disturbance, where not only disturbance but also its high order derivatives are estimated. The relationship of the proposed observer with the existing results is discussed. Then, the result is further extended to the case of minimal-order output-based disturbance observer design for linear systems subject to high order disturbances. Two practical examples about actuator fault diagnosis for a nonlinear missile system and disturbance estimation for a double-effect pilot plant evaporator system with unobservable states are provided to illustrate the effectiveness of the proposed approaches

On relationship between time-domain and frequency-domain disturbance observers and its applications

This paper provides a generic analysis of the relationship between time/frequency-domain DOB design methodology. It is discovered that the traditional frequency-domain DOBs using a low pass filter with unity gain can only handle disturbances satisfying matching condition, while the traditional time-domain DOBs always generate an observer with a high order. A Functional Disturbance OBserver (FDOB) is proposed to improve the existing results together with its design guideline, frequency analysis and existence condition. Compared with the existing frequency-domain DOBs, the proposed FDOB can handle more classes of disturbances, while compared with the existing time-domain DOBs the proposed FDOB can generate an observer with a lower order. Numerical examples are presented to illustrate the main findings of this paper including a rotary mechanical system of nonminimum phase

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Reduced-order disturbance observer design for discrete-time linear stochastic systems

The conventional disturbance observers for discrete-time linear stochastic systems assume that the system states are fully estimable and the disturbance estimate is dependent on the estimated system states, hereafter termed Full-Order Disturbance Observers (FODOs). This paper investigates the design of Reduced-Order Disturbance Observers (RODOs) when the system state variables are not fully estimable. An existence condition of RODO is established, which is shown to be more easily satisfied than that of the conventional FODOs and consequently it has substantially extended the scope of applications of disturbance observer theory. Then a set of recursive formulae for the RODO is developed for on-line applications. Finally, it is furth er shown that the conventional FODOs are a special case of the proposed RODO in the sense that the former reduces to the RODO when the states become fully estimable in the presence of disturbances. Examples are given to demonstrate the effectiveness and advantages of the proposed approach

Dynamic decision making in lane change: game theory with receding horizon

Decision making for lane change manoeuvre is of practical importance to guarantee a smooth, efficient and safe operation for autonomous driving. It is, however, challenging. On one hand, the behaviours of ego vehicle and adjacent vehicles are dependent and interactive. On the other hand, the decision should strictly guarantee safety during the whole process of lane change with uncertain and incomplete information in a dynamic and cluttered environment. To this end, the concept of Receding Horizon Control (RHC) is integrated into game theory in conjunction with reachability analysis tool, resulting in RHC based game theory. Specifically, the decision of each game relies on not only uncertain information at current step but also the future information calculated by reachability analysis. The decision is repeatedly made with the advent of new information using the concept of RHC. As a result, safety can be guaranteed during the whole process of lane change in a dynamic environment. Case study is conducted to demonstrate the advantages of the proposed approach. It is shown that the proposed RHC based game theory approach incorporating uncertain information can provide a safer and real-time decision

Personalized driver workload inference by learning from vehicle related measurements

Adapting in-vehicle systems (e.g. Advanced Driver Assistance Systems, In-Vehicle Information Systems) to individual drivers’ workload can enhance safety and convenience. To make this possible, it is a prerequisite to infer driver workload so that adaptive aiding can be provided to the driver at the right time and in a proper manner. Rather than developing an average model for all drivers, a Personalized Driver Workload Inference (PDWI) system considering individual drivers’ driving characteristics is developed using machine learning techniques via easily accessed Vehicle Related Measurements (VRMs). The proposed PDWI system comprises two stages. In offline training, individual drivers’ workload is first automatically splitted into different categories according to its inherent data characteristics using Fuzzy C means clustering. Then an implicit mapping between VRMs and different levels of workload is constructed via classification algorithms. In online implementation, VRMs samples are classified into different clusters, consequently driver workload can be successfully inferred. A recently collected dataset from real-world naturalistic driving experiments is drawn to validate the proposed PDWI system. Comparative experimental results indicate that the proposed framework integrating Fuzzy C-means clustering and Support Vector Machine classifier provides a promising workload recognition performance in terms of accuracy, precision, recall, F1-score and prediction time. The inter-individual differences in term of workload are also identified and can be accommodated by the proposed framework due to its adaptiveness