Nonlinear actuator fault detection for small-scale UAS

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating corresponding velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on is less restrictive than earlier criteria.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

An exponential stability criterion for certain nonlinear systems

Improved sufficient conditions are derived for the exponential stability of a nonlinear time varying feedback system having a time invariant blockG in the forward path and a nonlinear time varying gain ϕ(.)k(t) in the feedback path. φ(.) being an odd monotone nondecreasing function. The resulting bound on $$\left( {{{\frac{{dk}}{{dt}}} \mathord{\left/ {\vphantom {{\frac{{dk}}{{dt}}} k}} \right. \kern-\nulldelimiterspace} k}} \right)$$ is less restrictive than earlier criteria.

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Theory of radar imaging using time-frequency distribution

The concept of radar was developed for the estimation of the distance (range) and velocity of a target from a receiver. The distance measurement is obtained by measuring the time taken for the transmitted signal to propagate to the target and return to the receiver. The target's velocity is determined by measuring the Doppler induced frequency shift of the returned signal caused by the rate of change of the time- delay from the target. As researchers further developed conventional radar systems it become apparent that additional information was contained in the backscattered signal and that this information could in fact be used to describe the shape of the target itself. It is due to the fact that a target can be considered to be a collection of individual point scatterers, each of which has its own velocity and time- delay. DelayDoppler parameter estimation of each of these point scatterers thus corresponds to a mapping of the target's range and cross range, thus producing an image of the target. Much research has been done in this area since the early radar imaging work of the 1960s. At present there are two main categories into which radar imaging falls. The first of these is related to the case where the backscattered signal is considered to be deterministic. The second is related to the case where the backscattered signal is of a stochastic nature. In both cases the information which describes the target's scattering function is extracted by the use of the ambiguity function, a function which correlates the backscattered signal in time and frequency with the transmitted signal. In practical situations, it is often necessary to have the transmitter and the receiver of the radar system sited at different locations. The problem in these situations is 'that a reference signal must then be present in order to calculate the ambiguity function. This causes an additional problem in that detailed phase information about the transmitted signal is then required at the receiver. It is this latter problem which has led to the investigation of radar imaging using time- frequency distributions. As will be shown in this thesis, the phase information about the transmitted signal can be extracted from the backscattered signal using time- frequency distributions. The principle aim of this thesis was in the development, and subsequent discussion into the theory of radar imaging, using time- frequency distributions. Consideration is first given to the case where the target is diffuse, ie. where the backscattered signal has temporal stationarity and a spatially white power spectral density. The complementary situation is also investigated, ie. where the target is no longer diffuse, but some degree of correlation exists between the time- frequency points. Computer simulations are presented to demonstrate the concepts and theories developed in the thesis. For the proposed radar system to be practically realisable, both the time- frequency distributions and the associated algorithms developed must be able to be implemented in a timely manner. For this reason an optical architecture is proposed. This architecture is specifically designed to obtain the required time and frequency resolution when using laser radar imaging. The complex light amplitude distributions produced by this architecture have been computer simulated using an optical compiler.

Markov modelling of the IEEE 802.11 DCF for real-time applications with periodic traffic

Popular wireless network standards, such as IEEE 802.11/15/16, are increasingly adopted in real-time control systems. However, they are not designed for real-time applications. Therefore, the performance of such wireless networks needs to be carefully evaluated before the systems are implemented and deployed. While efforts have been made to model general wireless networks with completely random traffic generation, there is a lack of theoretical investigations into the modelling of wireless networks with periodic real-time traffic. Considering the widely used IEEE 802.11 standard, with the focus on its distributed coordination function (DCF), for soft-real-time control applications, this paper develops an analytical Markov model to quantitatively evaluate the network quality-of-service (QoS) performance in periodic real-time traffic environments. Performance indices to be evaluated include throughput capacity, transmission delay and packet loss ratio, which are crucial for real-time QoS guarantee in real-time control applications. They are derived under the critical real-time traffic condition, which is formally defined in this paper to characterize the marginal satisfaction of real-time performance constraints.

Local adjustment and global adaptation of control periods for QoC management of control systems

Linking real-time schedulability directly to the Quality of Control (QoC), the ultimate goal of a control system, a hierarchical feedback QoC management framework with the Fixed Priority (FP) and the Earliest-Deadline-First (EDF) policies as plug-ins is proposed in this paper for real-time control systems with multiple control tasks. It uses a task decomposition model for continuous QoC evaluation even in overload conditions, and then employs heuristic rules to adjust the period of each of the control tasks for QoC improvement. If the total requested workload exceeds the desired value, global adaptation of control periods is triggered for workload maintenance. A sufficient stability condition is derived for a class of control systems with delay and period switching of the heuristic rules. Examples are given to demonstrate the proposed approach.

Modelling and performance evaluation of the IEEE 802.11 DCF for real-time control

Popular wireless networks, such as IEEE 802.11/15/16, are not designed for real-time applications. Thus, supporting real-time quality of service (QoS) in wireless real-time control is challenging. This paper adopts the widely used IEEE 802.11, with the focus on its distributed coordination function (DCF), for soft-real-time control systems. The concept of the critical real-time traffic condition is introduced to characterize the marginal satisfaction of real-time requirements. Then, mathematical models are developed to describe the dynamics of DCF based real-time control networks with periodic traffic, a unique feature of control systems. Performance indices such as throughput and packet delay are evaluated using the developed models, particularly under the critical real-time traffic condition. Finally, the proposed modelling is applied to traffic rate control for cross-layer networked control system design.

Benefits and issues of urban network travel time prediction

This paper presents the benefits and issues related to travel time prediction on urban network. Travel time information quantifies congestion and is perhaps the most important network performance measure. Travel time prediction has been an active area of research for the last five decades. The activities related to ITS have increased the attention of researchers for better and accurate real-time prediction of travel time. Majority of the literature on travel time prediction is applicable to freeways where, under non-incident conditions, traffic flow is not affected by external factors such as traffic control signals and opposing traffic flows. On urban environment the problem is more complicated due to conflicting areas (intersections), mid-link sources and sinks etc. and needs to be addressed.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.