Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.

Some properties of finite-time stable stochastic nonlinear systems

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

An explicit criterion for finite-time stability of linear nonautonomous systems with delays

In this paper, the problem of finite-time stability of linear nonautonomous systems with time-varying delays is considered. Using a novel approach based on some techniques developed for linear positive systems, we derive new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval. These conditions are shown to be relaxed for the Lyapunov asymptotic stability. A numerical example is given to illustrate the effectiveness of the obtained result.

DSP-based sliding-mode control for electromagnetic-levitation precise position system

This paper investigates the robust tracking control problem for a bipolar electromagnetic-levitation precise-position system. The dynamic model of the precise-position device is derived by conducting a thorough analysis on the nonlinear electromagnetic forces. Conventional sliding-mode control and terminal sliding-mode control strategies are developed to guarantee asymptotic and finite-time tracking capabilities of the closed-loop system. A lumped uncertainty estimator is proposed to estimate the system uncertainties. The estimated information is then used to construct a smooth uniformly ultimately bounded sliding-mode control. An exact estimator is also proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding-mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic-levitation system to validate the analysis.

Integral terminal sliding mode cooperative control of multi-robot networks

This paper studies the integral terminal sliding mode cooperative control of multi-robot networks. Here, we first propose an integral terminal sliding mode surface for a class of first order systems. Then, we prove that finite time consensus tracking of multi-robot networks can be achieved on this integral terminal sliding mode surface. Simulation results are presented to validate the analysis.

Robust fault-tolerant leader-follower control of four-wheel-steering mobile robots using terminal sliding mode

This paper addresses the actuator failure compensation problem of non-linear fourwheel-steering mobile robots based on vehicle kinematics, undergoing both known and unknown failures causing degenerated steering performance or wheels stuck at some observable angles. Terminal sliding mode control technique is used to guarantee the tracking stability infinite time with the presence of actuator fault. Simulation results are given to illustrate the effectiveness of the proposed control scheme. © Institution of Engineers Australia 2012.

Exact-estimator-based terminal sliding mode control system design

This paper investigates an estimator-based terminal sliding mode control system. An exact estimator is proposed to exactly estimate the unknown uncertainties in finite time. The output of the exact estimator is used to design a continuous chattering free terminal sliding mode control. The time taken for the closed-loop system to reach zero tracking error is proven to be finite. Experiment results are presented, using a real time digital-signal-processor (DSP) based electromagnetic levitation system to implement the control performance.

Placing sensors for area coverage in a complex environment by a team of robots

Existing solutions to carrier-based sensor placement by a single robot in a bounded unknown Region of Interest (ROI) do not guarantee full area coverage or termination. We propose a novel localized algorithm, named Back-Tracking Deployment (BTD). To construct a full coverage solution over the ROI, mobile robots (carriers) carry static sensors as payloads and drop them at the visited empty vertices of a virtual square, triangular, or hexagonal grid. A single robot will move in a predefined order of directional preference until a dead end is reached. Then it back-tracks to the nearest sensor adjacent to an empty vertex (an "entrance" to an unexplored/uncovered area) and resumes regular forward movement and sensor dropping from there. To save movement steps, the back-tracking is carried out along a locally identified shortcut. We extend the algorithm to support multiple robots that move independently and asynchronously. Once a robot reaches a dead end, it will back-track, giving preference to its own path. Otherwise, it will take over the back-track path of another robot by consulting with neighboring sensors. We prove that BTD terminates within finite time and produces full coverage when no (sensor or robot) failures occur. We also describe an approach to tolerate failures and an approach to balance workload among robots. We then evaluate BTD in comparison with the only competing algorithms SLD [Chang et al. 2009a] and LRV [Batalin and Sukhatme 2004] through simulation. In a specific failure-free scenario, SLD covers only 40-50% of the ROI, whereas BTD covers it in full. BTD involves significantly (80%) less robot moves and messages than LRV.

Real-time measurement of radiocarpal joint angle during dart-thrower's movement

Recently, a renewed attention has been drawn into the dart-thrower's motion as the radiocarpal joint is unique to humans and this is believed to have played a pivotal role in human evolution. Considering the importance of the motion and the complexity of the wrist joint, there have been many articles discussing the kinematics behind this movement. CT scan techniques have been used in a number of these research activities. Due to limitations in the speed of the image acquisition, the positions of the wrist were recorded in static postures. To our knowledge, a data acquisition for the motion with realtime capturing has not been reported. This paper presents the use of a 3D vision-based motion capture device. Leap Motion Controller (LMC), for measuring the radiocarpal joint angles during the dart-thrower's motion in a real-time analysis. The practical capability of the LMC in measuring dart-thrower's motion was examined in a trial involving four subjects and the angles were compared to the angles acquired from an inertial measurement unit (IMU). The results confirmed the LMC can successfully be used in the application of measuring radiocarpal kinematics" of dart-thrower's motion.

Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.

A new sliding mode-based learning control scheme

 A new sliding mode-based learning control scheme for a class of SISO dynamic systems is developed in this paper. It is seen that, based on the most recent information on the closed-loop stability, a recursive learning chattering-free sliding mode controller can be designed to drive the closed-loop dynamics to reach the sliding mode surface in a finite time, on which the desired closed-loop dynamics with the zero-error convergence can be achieved.

A new design of sliding mode control systems

A new sliding mode control technique for a class of SISO dynamic systems is presented in this chapter. It is seen that the stability status of the closed-loop system is first checked, based on the approximation of the most recent information of the first-order derivative of the Lyapunov function of the closed-loop system, an intelligent sliding mode controller can then be designed with the following intelligent features: (i) If the closed-loop system is stable, the correction term in the controller will continuously adjust control signal to drive the closed-loop trajectory to reach the sliding mode surface in a finite time and the desired closed-loop dynamics with the zero-error convergence can then be achieved on the sliding mode surface. (ii) If, however, the closed-loop system is unstable, the correction term is capable of modifying the control signal to continuously reduce the value of the derivative of the Lyapunov function from the positive to the negative and then drives the closed-loop trajectory to reach the sliding mode surface and ensures that the desired closed-loop dynamics can be obtained on the sliding mode surface. The main advantages of this new sliding mode control technique over the conventional one are that no chattering occurs in the sliding mode control system because of the recursive learning control structure; the system uncertainties are embedded in the Lipschitz-like condition and thus, no priori information on the upper and/or the lower bounds of the unknown system parameters and uncertain system dynamics is required for the controller design; the zero-error convergence can be achieved after the closed-loop dynamics reaches the sliding mode surface and remains on it. The performance for controlling a third-order linear system is evaluated in the simulation section to show the effectiveness and efficiency of the new sliding mode control technique.

Being a ‘wog’ in Melbourne – young people's self-fashioning through discourses of racism

The Greek community in Melbourne, Australia, is large and has a long history in the city. It is diverse and associated with a range of cultural, social and political structures. It has strong transnational links and in many ways exemplifies ‘diasporic’ in contradistinction to ‘migrant’. This paper focuses on young people from this community, particularly those who attend schools established to promote Greek language and cultural maintenance. In this paper, we examine such students’ explorations of their cultural identifications, most specifically how they adopt the term ‘wog’. This term is complex and its place in Australian discourse has shifted over time. Tracking these shifts and considering them as a context for these young people's use of the term allows us to consider the processes involved in their self-fashioning. We argue that their uptake of ‘wog’ involves the deployment of irony, given their awareness of its strong association with racism. We are also interested in the potential for women's experience to be silenced through the common association between ‘wog’ and protest masculinities. We argue that these students’ use of the term illustrates self-fashioning that provides insights into the complexities that surround cultural identification at the micro level, including schooling, but also in the broader context of globalisation.

Rock slope stability analyses using extreme learning neural network and terminal steepest descent algorithm

The analysis of rock slope stability is a classical problem for geotechnical engineers. However, for practicing engineers, proper software is not usually user friendly, and additional resources capable of providing information useful for decision-making are required. This study developed a convenient tool that can provide a prompt assessment of rock slope stability. A nonlinear input-output mapping of the rock slope system was constructed using a neural network trained by an extreme learning algorithm. The training data was obtained by using finite element upper and lower bound limit analysis methods. The newly developed techniques in this study can either estimate the factor of safety for a rock slope or obtain the implicit parameters through back analyses. Back analysis parameter identification was performed using a terminal steepest descent algorithm based on the finite-time stability theory. This algorithm not only guarantees finite-time error convergence but also achieves exact zero convergence, unlike the conventional steepest descent algorithm in which the training error never reaches zero.