Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics

Soliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with environments. Beginning with links of contextuality to non-Kolmogorovity we introduce the general formalism of soliton rate equations and work out explicit examples of subsystems interacting with environments. Of particular interest is the case of a soliton autocatalytic rate equation coupled to a linear conservative environment, a formal way of expressing seasonal changes. Depending on strength of the system-environment coupling we observe phenomena analogous to hibernation or even complete blocking of decay of a population.Comment: 51 pages, 15 eps figure

A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models

In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but much less comprehensively.Comment: 20 pages + 9 pages references + 1 page figures. Submitted to the International Journal of Wildland Fir

A Human Driver Model for Autonomous Lane Changing in Highways: Predictive Fuzzy Markov Game Driving Strategy

This study presents an integrated hybrid solution to mandatory lane changing problem to deal with accident avoidance by choosing a safe gap in highway driving. To manage this, a comprehensive treatment to a lane change active safety design is proposed from dynamics, control, and decision making aspects. My effort first goes on driver behaviors and relating human reasoning of threat in driving for modeling a decision making strategy. It consists of two main parts; threat assessment in traffic participants, (TV s) states, and decision making. The first part utilizes an complementary threat assessment of TV s, relative to the subject vehicle, SV , by evaluating the traffic quantities. Then I propose a decision strategy, which is based on Markov decision processes (MDPs) that abstract the traffic environment with a set of actions, transition probabilities, and corresponding utility rewards. Further, the interactions of the TV s are employed to set up a real traffic condition by using game theoretic approach. The question to be addressed here is that how an autonomous vehicle optimally interacts with the surrounding vehicles for a gap selection so that more effective performance of the overall traffic flow can be captured. Finding a safe gap is performed via maximizing an objective function among several candidates. A future prediction engine thus is embedded in the design, which simulates and seeks for a solution such that the objective function is maximized at each time step over a horizon. The combined system therefore forms a predictive fuzzy Markov game (FMG) since it is to perform a predictive interactive driving strategy to avoid accidents for a given traffic environment. I show the effect of interactions in decision making process by proposing both cooperative and non-cooperative Markov game strategies for enhanced traffic safety and mobility. This level is called the higher level controller. I further focus on generating a driver controller to complement the automated car’s safe driving. To compute this, model predictive controller (MPC) is utilized. The success of the combined decision process and trajectory generation is evaluated with a set of different traffic scenarios in dSPACE virtual driving environment. Next, I consider designing an active front steering (AFS) and direct yaw moment control (DYC) as the lower level controller that performs a lane change task with enhanced handling performance in the presence of varying front and rear cornering stiffnesses. I propose a new control scheme that integrates active front steering and the direct yaw moment control to enhance the vehicle handling and stability. I obtain the nonlinear tire forces with Pacejka model, and convert the nonlinear tire stiffnesses to parameter space to design a linear parameter varying controller (LPV) for combined AFS and DYC to perform a commanded lane change task. Further, the nonlinear vehicle lateral dynamics is modeled with Takagi-Sugeno (T-S) framework. A state-feedback fuzzy H∞ controller is designed for both stability and tracking reference. Simulation study confirms that the performance of the proposed methods is quite satisfactory