BP-RRT: Barrier Pair Synthesis for Temporal Logic Motion Planning

For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex optimization problem. We devise a new algorithm to solve this type of non-convex problems by formulating a rapidly-exploring random tree of barrier pairs, with each barrier pair composed of a quadratic barrier function and a full state feedback controller. The proposed method employs a rapid-exploring random tree to deal with the non-convex constraints and uses barrier pairs to fulfill the local convex constraints. As such, the method solves control problems fulfilling the required transitions of an automaton in order to satisfy given linear temporal logic constraints. At the same time it synthesizes locally optimal controllers in order to transition between the regions corresponding to the alphabet of the automaton. We demonstrate this new algorithm on a simulation of a two linkage manipulator robot.Comment: 6 pages, 5 figures. Accepted for publication in IEEE Conference on Decision and Control (CDC) copyright 2020 IEE

Decentralized Abstractions and Timed Constrained Planning of a General Class of Coupled Multi-Agent Systems

This paper presents a fully automated procedure for controller synthesis for a general class of multi-agent systems under coupling constraints. Each agent is modeled with dynamics consisting of two terms: the first one models the coupling constraints and the other one is an additional bounded control input. We aim to design these inputs so that each agent meets an individual high-level specification given as a Metric Interval Temporal Logic (MITL). Furthermore, the connectivity of the initially connected agents, is required to be maintained. First, assuming a polyhedral partition of the workspace, a novel decentralized abstraction that provides controllers for each agent that guarantee the transition between different regions is designed. The controllers are the solution of a Robust Optimal Control Problem (ROCP) for each agent. Second, by utilizing techniques from formal verification, an algorithm that computes the individual runs which provably satisfy the high-level tasks is provided. Finally, simulation results conducted in MATLAB environment verify the performance of the proposed framework

Linear Time Logic Control of Discrete-Time Linear Systems

The control of complex systems poses new challenges that fall beyond the traditional methods of control theory. One of these challenges is given by the need to control, coordinate and synchronize the operation of several interacting submodules within a system. The desired objectives are no longer captured by usual control specifications such as stabilization or output regulation. Instead, we consider specifications given by linear temporal logic (LTL) formulas. We show that existence of controllers for discrete-time controllable linear systems and LTL specifications can be decided and that such controllers can be effectively computed. The closed-loop system is of hybrid nature, combining the original continuous dynamics with the automatically synthesized switching logic required to enforce the specification

Reissner-Nordström black holes and mass inflation

The existence and structure of black holes are derived from Einstein’s general theory of relativity. Mass inflation (an increase in mass) is found when the internal structure of black holes is studied. The objective of the present study is two-fold: (i) to obtain an understanding of the nature of Reissner-Nordström black holes and (ii) examine the mass inflation phenomenon. To do so, spherical symmetric solutions to Einstein’s field equations are analyzed.The Schwarzschild solution is analyzed to show the most basic result of general relativity. The analytical (Kruskal) continuation of the Schwarzschild solution and the mechanism of gravitational collapse are also discussed. The Reissner-Nordström metric is then examined in detail analyzing both the general characteristics and the most generic field equations for a body with spherical symmetry. Moreover two important applications are considered: the Vaidya solutions and the Dray-’t Hooft-Redmount (DTR) relation. The mass inflation phenomenon is then formulated by formally integrating Einstein’s field equations considering continuous infalling and outgoing radial fluxes of gravitational radiation. To evaluate the growth rate of the gravitational mass, a formal perturbation expansion in terms of the product of the flux luminosities is developed. Finally, the possibility that the asymmetries occurring during a realistic collapse could change the conclusions obtained for spherical symmetry is considered. The most striking features of the physics behind black holes and the mass inflation phenomenon are shown

Investigations of transesterification of canola oil with methanol and ethanol for a new efficient method of biodiesel production

Transesterification of vegetable oil to biodiesel is a multistep process affected by mass transfer, mixing and chemical reaction equilibrium. Attempts have been made in this study to overcome these limitations by gradually feeding oil into a pool of alcohol. This approach provided large excess of alcohol to allow reaction to proceed further as well as allowed easy dispersion of oil into the alcohol. As a result improved conversion of feed, higher yield and better product quality were achieved. Comparisons have been made with other methods to show the differences and highlight improvements. Reactions were conducted at various reaction conditions for transesterification of canola oil with both methanol and ethanol using potassium hydroxide as a base catalyst. Reaction progress was followed by analysing samples collected at regular intervals from one liter reactor using Gas Chromatography Technique. The quality and yield of biodiesel obtained with the gradually fed method (G-Fed Method) were significantly improved ¸¸compared to conventional method. Detailed comparison studies are included for methanolysis and ethanolysis in G-Fed method. Methanolysis gives better yield over ethanolysis in G-Fed method. In addition kinetic studies have been conducted in detail and a kinetic model is developed to predict reaction rate constants of the transesterification reaction in batch as well as G-Fed method. The kinetic model following second order was used to determine the kinetics of canola oil in ethanolysis reaction at different temperature in batch runs. For the kinetic study of G-Fed method appropriate reaction rate equations are formulated including the mass transfer effects for different cases of order of reaction. Methanolysis and ethanolysis in G-fed method follow pseudo first order with higher rate constant with methanol

Formal methods paradigms for estimation and machine learning in dynamical systems

Formal methods are widely used in engineering to determine whether a system exhibits a certain property (verification) or to design controllers that are guaranteed to drive the system to achieve a certain property (synthesis). Most existing techniques require a large amount of accurate information about the system in order to be successful. The methods presented in this work can operate with significantly less prior information. In the domain of formal synthesis for robotics, the assumptions of perfect sensing and perfect knowledge of system dynamics are unrealistic. To address this issue, we present control algorithms that use active estimation and reinforcement learning to mitigate the effects of uncertainty. In the domain of cyber-physical system analysis, we relax the assumption that the system model is known and identify system properties automatically from execution data. First, we address the problem of planning the path of a robot under temporal logic constraints (e.g. "avoid obstacles and periodically visit a recharging station") while simultaneously minimizing the uncertainty about the state of an unknown feature of the environment (e.g. locations of fires after a natural disaster). We present synthesis algorithms and evaluate them via simulation and experiments with aerial robots. Second, we develop a new specification language for tasks that require gathering information about and interacting with a partially observable environment, e.g. "Maintain localization error below a certain level while also avoiding obstacles.'' Third, we consider learning temporal logic properties of a dynamical system from a finite set of system outputs. For example, given maritime surveillance data we wish to find the specification that corresponds only to those vessels that are deemed law-abiding. Algorithms for performing off-line supervised and unsupervised learning and on-line supervised learning are presented. Finally, we consider the case in which we want to steer a system with unknown dynamics to satisfy a given temporal logic specification. We present a novel reinforcement learning paradigm to solve this problem. Our procedure gives "partial credit'' for executions that almost satisfy the specification, which can lead to faster convergence rates and produce better solutions when the specification is not satisfiable

Biopharmaceutical studies of slow release, subcutaneous polymeric drug delivery systems

Subcutaneously injected polymeric dosage forms have been used successfully to achieve sustained release of various drugs and peptides. A complex interplay of factors affect drug release rates from such dosage forms, such as nature of dosage form, drug and polymer properties, formulation variables etc. making the prediction of release characteristics challenging. In this thesis, the effect of drug lipophilicity on absorption rates from PLGA microspheres and in situ-forming depots was investigated. The beta-blockers were chosen as model drug compounds, being a homologous group of drugs having similar molecular weights and pKa values, yet widely differing lipophilicities. Alprenolol, metoprolol and atenolol were selected to represent the series based on their experimentally determined octanol-buffer partition coefficients. The first part of the study focused on formulation and characterisation of beta-blocker loaded microspheres with suitable in vitro release profiles. Microspheres were prepared by spray drying, and characterised in terms of particle size, surface morphology, drug loading and release. The beta-blockers represented a considerable challenge owing to their surface-active nature and tendency to suffer a large burst release from microspheres. Efforts were therefore directed towards modifying the formulation to improve the drug release profiles, including emulsion spray drying, addition of competing surfactants and hydrophobic ion pairing. The latter was successful in reducing burst and prolonging release, and microspheres were deemed suitable for in vivo investigation. In situ-forming depot preparations were also formulated with the aim of comparing release profiles and tissue compatibility with the preformed microspheres. Following initial experiments to ascertain intravenous clearance kinetics, the polymeric dosage forms were injected subcutaneously in rats. Drug plasma concentrations were analysed and absorption profiles were determined by deconvolution. It was found that the nature of the dosage form had a significantly greater impact on the rate and extent of absorption than the lipophilicity of the encapsulated drugs

In-vitro Anti-cercarial activity of extracts and steroidal alkaloids from the stem bark of Holarrhena floribunda (G. Don) Dur. & Schinz

Context: Schistosomiasis continues to be the leading cause of morbidity and mortality among the neglected tropical diseases. Apart from the high cost of chemotherapy, concerns over drug resistance and tolerance have been raised in the past decade. Objective: The aim of the study was to evaluate the anticercarial activity of extracts and compounds from the stem bark of Holarrhena floribunda on cercaria of Schistosoma haematobium. Methods: Hydroethanolic and alkaloidal extracts from the stem bark of H. floribunda were tested on cercaria at concentrations between 500.00 and 15.625 μg/mL for 180 minutes and assessing the percentage viability at time intervals of 0, 15, 30, 60, 120 and 180 minutes. Praziquantel, used as reference drug, and the isolated compounds were tested at similar concentrations. The cercaria mortalities and IC50 of extracts and compounds were estimated after 30 minutes of incubation. Results: The 70 %v/v ethanol extract showed the highest activity (IC50=20.09±1.11 μg/mL) with praziquantel giving IC50 of 695.50±1.12. The alkaloids holonamine, holadienine and conessine, isolated from the stem bark, showed considerable cercaricidal activity with the latter recording an IC50 of 33.28±1.04. Conclusion: The study gives first-hand knowledge of the anti-cercarial activity of H. floribunda and its steroidal alkaloids. This gives credence to the traditional uses of the plant as an anti-parasitic agent

EVALUATION OF WATER QUALITY MODELLING PARAMETERS: TOWARDS THE EVOLVEMENT OF RE-AERATION COEFFICIENT FOR RIVERS IN THE NIGERIAN ENVIRONMENT

This study was carried out on River Atuwara in Ota, Ogun State, Nigeria with the aim of developing a coefficient of re-aeration model applicable to River Atuwara and other rivers in the Nigerian environment. This was achieved by sourcing for data once every month from 22 sampling locations of interest within a pre-selected segment of the river over a period covering the dry and wet seasons. The data collected include hydraulic data (depth, width, velocity and time of travel) and water quality data such as Dissolved Oxygen (DO) and Biochemical Oxygen Demand (BOD). Excel Spreadsheet and MATLAB were used for data processing. Regression analysis was carried out where stream velocity and depth were the regressors and the re-aeration constant k2 (as a function of BOD, DO and Temperature) was the dependent variable. A coefficient of re-aeration, k2, (Atuwara re-aeration model) was developed and validated statistically. Its performance was also verified by comparing the model with 10 other internationally recognized models. It was found that even though Atuwara model performed better than Agunwamba model and most of the other well cited models, both Atuwara model and Agunwamba model could be safely adopted for future water quality modelling researches in the Nigerian environment. Results of detailed water analysis of samples from River Atuwara shows high level of pollution hence it is unfit for human consumption without adequate treatment. It is recommended that River Atuwara and similar rivers in the country should be regularly monitored for quality contro