Stability and Equilibrium Analysis of Laneless Traffic with Local Control Laws

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis representing the direction of motion and the X-axis representing the lateral or the direction perpendicular to the direction of motion. Different influence graphs are used to model the interaction between the vehicles in these two directions. The instantaneous accelerations of each car, in both X and Y directions, are functions of the measurements from the neighbouring cars according to these influence graphs. The stability and equilibrium spacings of the car formation is analyzed for usual traffic situations such as steady flow, obstacles, lane changing and rogue drivers arbitrarily changing positions inside the formation. Conditions are derived under which the formation maintains stability and the desired intercar spacing for each of these traffic events. Simulations for some of these scenarios are included.Comment: 8 page

High power modelocking using a nonlinear mirror

This thesis presents work on the high average power operation of pulsed diode-pumped solid-state lasers by using a laser configuration known as the bounce geometry. The bounce geometry has previously produced efficient, high power and high spatial quality laser outputs in continuous-wave, Q-switched and modelocked regimes. This thesis explores the capabilities of the bounce geometry for power scaling, shown using Nd:YVO4 and Nd:GdVO4 in both a passively Q-switched laser system and a variety of nonlinear mirror modelocked systems. The high gain experienced by Nd-doped gain media pumped at 808 nm has traditionally posed difficulties in producing stable passive Q-switching with Cr4+:YAG. By using a novel stigmatic design of the bounce geometry that experiences lower gain, but highly circular output, passive Q-switching with > 11 W of average power is produced, at a pulse repetition rate of 190 kHz. This is the highest output power ever achieved from a passively Q-switched Nd-doped vanadate laser to date. Nonlinear mirror modelocking is a passive modelocking technique that employs a χ(2) nonlinear medium in combination with a dichroic output coupler. The first nonlinear mirror modelocking of a bounce geometry laser is presented, obtaining 11.3 W of average power and 57 ps pulse duration using a type-II phase-matched KTP nonlinear crystal. Using type-I phase-matched BiBO, shorter pulses of 5.7 ps in duration are obtained at an average power of 6.1 W. The nonlinear mirror modelocking technique is then applied to the stigmatic bounce geometry laser, obtaining a highly stable train of modelocked pulses with pulse duration 14 ps and an average power of 12 W, with high spatial quality output. Mixed vanadate lasers offer customisation of the laser fluorescence spectrum, but tend to experience lower gain than single vanadates. Using the mixed vanadate combination Nd:Gd0.6Y0.4YVO4 in the bounce geometry, 27.5 W of average power in continuous-wave operation is shown. This is the highest power of any mixed vanadate laser ever reported. By then applying the nonlinear mirror modelocking technique to the mixed vanadate system, 16.8 W of average modelocked output power and a pulse duration of 12.7 ps is obtained. This is simultaneously the first time that the nonlinear mirror technique has been applied to mixed vanadate gain media and the highest power of any modelocked mixed vanadate laser to date. Finally, power scaling of a nonlinear mirror modelocked Nd:GdVO4 laser in the bounce geometry is achieved through use of the double bounce geometry design and through use of a high power pump diode. The system employing the high power pumping produced > 30 W of average power — world record power using the nonlinear mirror technique

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page

Switched Convergence of Second-Order Switched Homogeneous Systems

This paper studies the stabilization of second-order switched homogeneous systems. We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured. Moreover, given an initial condition, our method determines if there exists a switching law under which the solution converges to the origin and, if there exists this switching law, how it is constructed. Finally, two numerical examples are presented in order to illustrate the results

Bias analysis in mode-based Kalman filters for stochastic hybrid systems

Doctor of PhilosophyDepartment of Electrical and Computer EngineeringBalasubramaniam NatarajanStochastic hybrid system (SHS) is a class of dynamical systems that experience interaction of both discrete mode and continuous dynamics with uncertainty. State estimation for SHS has attracted research interests for decades with Kalman filter based solutions dominating the area. Mode-based Kalman filter is an extended version of the traditional Kalman filter for SHS. In general, as Kalman filter is unbiased for non-hybrid system estimation, prior research efforts primarily focus on the behavior of error covariance. In SHS state estimate, mode mismatch errors could result in a bias in the mode-based Kalman filter and have impacts on the continuous state estimation quality. The relationship between mode mismatch errors and estimation stability is an open problem that this dissertation attempts to address. Specifically, the probabilistic model of mode mismatch errors can be independent and identically distributed (i.i.d.), correlated across different modes and correlated across time. The proposed approach builds on the idea of modeling the bias evolution as a transformed system. The statistical convergence of the bias dynamics is then mapped to the stability of the transformed system. For each specific model of the mode mismatch error, the system matrix of the transformed system varies which results in challenges for the stability analysis. For the first time, the dissertation derives convergence conditions that provide tolerance regions for the mode mismatch error for three mode mismatch situations. The convergence conditions are derived based on generalized spectral radius theorem, Lyapunov theorem, Schur stability of a matrix polytope and interval matrix method. This research is fundamental in nature and its application is widespread. For example, the spatially and timely correlated mode mismatch errors can effectively capture cyber-attacks and communication link impairments in a cyber-physical system. Therefore, the theory and techniques developed in this dissertation can be used to analyze topology errors in any networked system such as smart grid, smart home, transportation, flight management system etc. The main results provide new insights on the fidelity in discrete state knowledge needed to maintain the performance of a mode-based Kalman filter and provide guidance on design of estimation strategies for SHS

A hybrid switched reactive-based visual servo control of 5-DOF robot manipulators for pick-and-place tasks

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