Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Aton- sistema automatizado de aquisição e tratamento de dados para radiometria solar

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Active Visual Features Based on Events to Guide Robot Manipulators in Tracking Tasks

Traditional visual servoing systems do not deal with the topic of moving objects tracking. When these systems are employed to track a moving object, depending on the object velocity, visual features can go out of the image, causing the fail of the tracking task. This occurs specially when the object and the robot are both stopped and then the object starts the movement. In this work, we have employed a retina camera based on Address Event Representation (AER) in order to use events as input in the visual servoing system. The events launched by the camera indicate a pixel movement. Event visual information is processed only at the moment it occurs, reducing the response time of visual servoing systems when they are used to track moving objects.

An event-based traffic flow model for traffic control at railway junctions

This paper introduces an event-based traffic model for railway systems adopting fixed-block signalling schemes. In this model, the events of trains' arrival at and departure from signalling blocks constitute the states of the traffic flow. A state transition is equivalent to the progress of the trains by one signalling block and it is realised by referring to past and present states, as well as a number of pre-calculated look-up tables of run-times in the signalling block under various signalling conditions. Simulation results are compared with those from a time-based multi-train simulator to study the improvement of processing time and accuracy.

Event-related brain potentials dissociate the developmental time-course of automatic numerical magnitude analysis and cognitive control functions during the first three years of primary school

In this study we set out to dissociate the developmental time course of automatic symbolic number processing and cognitive control functions in grade 1-3 British primary school children. Event-related potential (ERP) and behavioral data were collected in a physical size discrimination numerical Stroop task. Task-irrelevant numerical information was processed automatically already in grade 1. Weakening interference and strengthening facilitation indicated the parallel development of general cognitive control and automatic number processing. Relationships among ERP and behavioral effects suggest that control functions play a larger role in younger children and that automaticity of number processing increases from grade 1 to 3.

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

Single event molecular signalling for estimation and control

Cell biology is characterised by low molecule numbers and coupled stochastic chemical reactions with intrinsic noise permeating and dominating the interactions between molecules. Recent work [9] has shown that in such environments there are hard limits on the accuracy with which molecular populations can be controlled and estimated. These limits are predicated on a continuous diffusion approximation of the target molecule (although the remainder of the system is non-linear and discrete). The principal result of [9] assumes that the birth rate of the signalling species is linearly dependent on the target molecule population size. In this paper, we investigate the situation when the entire system is kept discrete, and arbitrary non-linear coupling is allowed between the target molecule and downstream signalling molecules. In this case it is possible, by relying solely on the event triggered nature of control and signalling reactions, to define non-linear reaction rate modulation schemes that achieve improved performance in certain parameter regimes. These schemes would not appear to be biologically relevant, raising the question of what are an appropriate set of assumptions for obtaining biologically meaningful results. © 2013 EUCA.

Event-driven implicit authentication for mobile access control

In order to protect user privacy on mobile devices, an event-driven implicit authentication scheme is proposed in this paper. Several methods of utilizing the scheme for recognizing legitimate user behavior are investigated. The investigated methods compute an aggregate score and a threshold in real-time to determine the trust level of the current user using real data derived from user interaction with the device. The proposed scheme is designed to: operate completely in the background, require minimal training period, enable high user recognition rate for implicit authentication, and prompt detection of abnormal activity that can be used to trigger explicitly authenticated access control. In this paper, we investigate threshold computation through standard deviation and EWMA (exponentially weighted moving average) based algorithms. The result of extensive experiments on user data collected over a period of several weeks from an Android phone indicates that our proposed approach is feasible and effective for lightweight real-time implicit authentication on mobile smartphones.

Adaptive control of event integration

Identifying 2 target stimuli in a rapid stream of visual symbols is much easier if the 2nd target appears immediately after the 1st target (i.e., at Lag 1) than if distractor stimuli intervene. As this phenomenon comes with a strong tendency to confuse the order of the targets, it seems to be due to the integration of both targets into the same attentional episode or object file. The authors investigated the degree to which people can control the temporal extension of their (episodic) integration windows by manipulating the expectations participants had with regard to the time available for target processing. As predicted, expecting more time to process increased the number of order confusions at Lag 1. This was true for between-subjects and within-subjects (trial-to-trial) manipulations, suggesting that integration windows can be adapted actively and rather quickly.

Adaptive control of event integration: evidence from event-related potentials

We investigated whether it is possible to control the temporal window of attention used to rapidly integrate visual information. To study the underlying neural mechanisms, we recorded ERPs in an attentional blink task, known to elicit Lag-1 sparing. Lag-1 sparing fosters joint integration of the two targets, evidenced by increased order errors. Short versus long integration windows were induced by showing participants mostly fast or slow stimuli. Participants expecting slow speed used a longer integration window, increasing joint integration. Difference waves showed an early (200 ms post-T2) negative and a late positive modulation (390 ms) in the fast group, but not in the slow group. The modulations suggest the creation of a separate event for T2, which is not needed in the slow group, where targets were often jointly integrated. This suggests that attention can be guided by global expectations of presentation speed within tens of milliseconds.