Blocking Former Sex Offenders from Online Social Networks: Is this a Due Process Violation?

Extremum seeking control (ESC) is a classical adaptive control method aimed at locating and tracking optimal operating conditions in complex non-linear plants. Early results on ESC were restricted to plants that could bedescribed by Wiener or Hammerstein models. However, recent results haveshown that ESC will possess a stationary solution close to the optimum also for more general dynamical systems, provided the gradient estimation and feedback is sufficiently slow relative to the process dynamics. This thesis addresses the uniqueness of this solution and the achievable rate of convergence.The motivation for the work stems from the need to optimize a complex biofilm reactor, the CANON process, which if operated near a narrow optimum may significantly lower the cost of ammonium removal in wastewater treatment. Simulations of ESC applied to the CANON process reveal that, depending on initial conditions and tuning parameters, the ESC loop may converge to stationary solutions far removed from the optimum and that multiple stationary solutions may exist. Analysis of a general model for the ESC loop shows that the stationary solutions are characterized either by a gain condition or a phase lag condition on the locally linearized system, the latter indicating that the ESC loop can act as a phase-lock loop. The phase lag condition is shown to be satisfied close to the optimum, but can be fulfilled also at operating points with no relation to the optimality criterion whatsoever and this serves to explain the observed solution multiplicity. Bifurcation theory is employed to further analyze the stationary solutions of the ESC loop and conditions for existence of saddle-node bifurcations are derived. A saddle node bifurcation implies a hard loss of stability and the existence of multiple stationary solutions. It is also demonstrated, using examples, that the ESC loop may undergo other types of bifurcations, including period doubling bifurcations into chaos. For the considered example, the resulting chaotic solution is significantly closer to optimum than the underlying nominal limit cycle. Previous results on ESC applied to general dynamic systems have relied on the use of asymptotic methods, such as singular perturbations and averaging. This has resulted in a three time-scale separation of the problem, in which the gradient estimation and control have been forced to be significantly slower than the open-loop process dynamics. For most processes, including the CANON process studied in this thesis, this renders ESC of little practical use and we therefore consider relaxing some of the restrictive assumptions. Inparticular, we allow for any gradient estimation rate and significantly faster gradient feedback as compared to previous studies. Using a linear parameter varying (LPV) description of the plant, quantitative expressions for the convergence rate in terms of the ESC tuning parameters and plant properties are derived.QC 20141106</p

Towards 'smart lasers': self-optimisation of an ultrafast pulse source using a genetic algorithm

Short-pulse fibre lasers are a complex dynamical system possessing a broad space of operating states that can be accessed through control of cavity parameters. Determination of target regimes is a multi-parameter global optimisation problem. Here, we report the implementation of a genetic algorithm to intelligently locate optimum parameters for stable single-pulse mode-locking in a Figure-8 fibre laser, and fully automate the system turn-on procedure. Stable ultrashort pulses are repeatably achieved by employing a compound fitness function that monitors both temporal and spectral output properties of the laser. Our method of encoding photonics expertise into an algorithm and applying machine-learning principles paves the way to self-optimising `smart' optical technologies

Formation Shape Control Based on Distance Measurements Using Lie Bracket Approximations

We study the problem of distance-based formation control in autonomous multi-agent systems in which only distance measurements are available. This means that the target formations as well as the sensed variables are both determined by distances. We propose a fully distributed distance-only control law, which requires neither a time synchronization of the agents nor storage of measured data. The approach is applicable to point agents in the Euclidean space of arbitrary dimension. Under the assumption of infinitesimal rigidity of the target formations, we show that the proposed control law induces local uniform asymptotic stability. Our approach involves sinusoidal perturbations in order to extract information about the negative gradient direction of each agent's local potential function. An averaging analysis reveals that the gradient information originates from an approximation of Lie brackets of certain vector fields. The method is based on a recently introduced approach to the problem of extremum seeking control. We discuss the relation in the paper

Exponential and Prescribed-Time Extremum Seeking with Unbiased Convergence

We present multivariable extremum seeking (ES) designs that achieve unbiased convergence to the optimum. Two designs are introduced: one with exponential unbiased convergence (unbiased extremum seeker, uES) and the other with user-assignable prescribed-time unbiased convergence (unbiased PT extremum seeker, uPT-ES). In contrast to the conventional ES, which uses persistent sinusoids and results in steady-state oscillations around the optimum, the exponential uES employs an exponentially decaying amplitude in the perturbation signal (for achieving convergence) and an exponentially growing demodulation signal (for making the convergence unbiased). The achievement of unbiased convergence also entails employing an adaptation gain that is sufficiently large in relation to the decay rate of the perturbation amplitude. Stated concisely, the bias is eliminated by having the learning process outpace the waning of the perturbation. The other algorithm, uPT-ES, employs prescribed-time convergent/blow-up functions in place of constant amplitudes of sinusoids, and it also replaces constant-frequency sinusoids with chirp signals whose frequency grows over time. Among the convergence results in the ES literature, uPT-ES may be the strongest yet in terms of the convergence rate (prescribed-time) and accuracy (unbiased). To enhance the robustness of uES to a time-varying optimum, exponential functions are modified to keep oscillations at steady state. Stability analysis of the designs is based on a state transformation, averaging, local exponential/PT stability of the averaged system, local stability of the transformed system, and local exponential/PT stability of the original system. For numerical implementation of the developed ES schemes and comparison with previous ES designs, the problem of source seeking by a two-dimensional velocity-actuated point mass is considered.Comment: 16 pages, 7 figure

Particle Swarm Optimization Based Source Seeking

Signal source seeking using autonomous vehicles is a complex problem. The complexity increases manifold when signal intensities captured by physical sensors onboard are noisy and unreliable. Added to the fact that signal strength decays with distance, noisy environments make it extremely difficult to describe and model a decay function. This paper addresses our work with seeking maximum signal strength in a continuous electromagnetic signal source with mobile robots, using Particle Swarm Optimization (PSO). A one to one correspondence with swarm members in a PSO and physical Mobile robots is established and the positions of the robots are iteratively updated as the PSO algorithm proceeds forward. Since physical robots are responsive to swarm position updates, modifications were required to implement the interaction between real robots and the PSO algorithm. The development of modifications necessary to implement PSO on mobile robots, and strategies to adapt to real life environments such as obstacles and collision objects are presented in this paper. Our findings are also validated using experimental testbeds.Comment: 13 pages, 12 figure

Piezoelectric units with self-tuning multi-resonant shunts for vibration absorption

This thesis is focused on a lightweight and modular control system formed by a piezoelectric patch connected to either a single-resonant or a multi-resonant self-tuning shunt, which can be used to mitigate the resonant response of one or multiple low-order flexural modes of a hosting structure. The aim of the study is to develop a self-contained unit, which can be bonded in batches on thin structures to decrease the low frequency flexural response generated by stationary stochastic disturbances. To this end, the study investigates the optimal tuning of both single-resonant and multi-resonant shunts with reference to a global and a local cost function. Two configurations of the single-resonant shunt are considered, which are formed by a resistance-inductance (RL) connected respectively in series and in parallel. Instead, a single configuration of the multi-resonant shunt is investigated, which is formed by an array of parallel branches encompassing a resistance-inductance-capacitance (RLC) connected in series. The global cost function, given by the minimisation of the hosting structure time-averaged total flexural kinetic energy, is used as a reference metric to assess the optimal tuning of the shunt. Instead, the local cost function, given by the maximisation of the time-averaged electric power absorbed either by the RL single-resonant shunt or by each RLC branch of the multi-resonant shunt, is employed for the practical implementation of the self-tuning shunt. The study shows that, with respect to the resistance and inductance shunt parameters, the two cost functions are characterised by mirror bell surfaces. Hence, the optimal shunt resistance and inductance values that would minimise the global cost function coincide with those that would maximise the local cost functions. As a result, both the single-resonant and multi-resonant shunts can be suitably tuned within the shunt itself by maximising the time-average electric power absorbed by the single-resonant shunt or by each branch of the multi-resonant shunt. The study also shows that, the tuning can be effectively implemented with a recursive two-paths tuning approach, whereby the inductance is first tuned along a constant-resistance path characterised by a bell shaped curve of the cost function and then the resistance is tuned along a constant-inductance path characterised by a bell shaped curve of the cost function too. This two-paths tuning sequence can be run recursively online such that the shunt can be adapted to variations of the electro-mechanical response of the hosting structure and piezoelectric transducer as well as to variations of the electric response of the shunt components, which can both occur in presence of temperature variations or other exogenous physical effects. Since the optimisations along the constant resistance and constant inductance paths are characterised by non-convex cost functions, the study proposes to employ the extremum seeking algorithm to find the optimal shunt parameters that would maximise the electric power absorption. This is a model-free gradient driven search algorithm, which asymptotically leads to the maximum of the non-convex bell-shaped paths. The algorithm is based on a periodic dithering signal that perturbs the inductance and resistance tuning signals such that the resulting electric power absorbed by the shunt equally shows such a periodic signal, which is either in phase or out-of-phase with the dithering signal depending the tuning is under or over estimating the shunt parameter with respect to the optimal one that maximises the power absorption. The study shows that this algorithm suitably leads to the optimal shunt values regardless the structure is excited by a stochastic disturbance such that the power cost function undergoes significant variations over time