Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System

Pole and zero assignment and observer design

Imperial Users onl

Duality for nonlinear filtering

This thesis is concerned with the stochastic filtering problem for a hidden Markov model (HMM) with the white noise observation model. For this filtering problem, we make three types of original contributions: (1) dual controllability characterization of stochastic observability, (2) dual minimum variance optimal control formulation of the stochastic filtering problem, and (3) filter stability analysis using the dual optimal control formulation. For the first contribution of this thesis, a backward stochastic differential equation (BSDE) is proposed as the dual control system. The observability (detectability) of the HMM is shown to be equivalent to the controllability (stabilizability) of the dual control system. For the linear-Gaussian model, the dual relationship reduces to classical duality in linear systems theory. The second contribution is to transform the minimum variance estimation problem into an optimal control problem. The constraint is given by the dual control system. The optimal solution is obtained via two approaches: (1) by an application of maximum principle and (2) by the martingale characterization of the optimal value. The optimal solution is used to derive the nonlinear filter. The third contribution is to carry out filter stability analysis by studying the dual optimal control problem. Two approaches are presented through Chapters 7 and 8. In Chapter 7, conditional Poincar\'e inequality (PI) is introduced. Based on conditional PI, various convergence rates are obtained and related to literature. In Chapter 8, the stabilizability of the dual control system is shown to be a necessary and sufficient condition for filter stability on certain finite state space model.Comment: Ph.D. Thesis of the autho

The development and evaluation of computer vision algorithms for the control of an autonomous horticultural vehicle

Economic and environmental pressures have led to a demand for reduced chemical use in crop production. In response to this, precision agriculture techniques have been developed that aim to increase the efficiency of farming operations by more targeted application of chemical treatment. The concept of plant scale husbandry (PSH) has emerged as the logical extreme of precision techniques, where crop and weed plants are treated on an individual basis. To investigate the feasibility of PSH, an autonomous horticultural vehicle has been developed at the Silsoe Research Institute. This thesis describes the development of computer vision algorithms for the experimental vehicle which aim to aid navigation in the field and also allow differential treatment of crop and weed. The algorithm, based upon an extended Kalman filter, exploits the semi-structured nature of the field environment in which the vehicle operates, namely the grid pattern formed by the crop planting. By tracking this grid pattern in the images captured by the vehicles camera as it traverses the field, it is possible to extract information to aid vehicle navigation, such as bearing and offset from the grid of plants. The grid structure can also act as a cue for crop/weed discrimination on the basis of plant position on the ground plane. In addition to tracking the grid pattern, the Kalman filter also estimates the mean distances between the rows of lines and plants in the grid, to cater for variations in the planting procedure. Experiments are described which test the localisation accuracy of the algorithms in offline trials with data captured from the vehicle's camera, and on-line in both a simplified testbed environment and the field. It is found that the algorithms allow safe navigation along the rows of crop. Further experiments demonstrate the crop/weed discrimination performance of the algorithm, both off-line and on-line in a crop treatment experiment performed in the field where all of the crop plants are correctly targeted and no weeds are mistakenly treated

Detection of hard faults in combinational logic circuits

ABSTRACT: Previous Work in identifying hard to test faults (HFs) -- The effect of reconvergent fanout and redundancy -- Testability measures (TMs)Using of ATPGs to detect HFs -- Previous use of cost in Testability analysis -- Review of automatic test pattern generation (ATPG) -- Fault modelling -- Single versus multiple path sensitization -- The four ATPG phases of deterministic gate level test generation -- Random test pattern generation and hybrid methods -- Review of the fan algorithm -- Backtrack reduction methods and the importance of heuristics -- Mixed graph -- binary decision diagram (GBDD) circuit model -- A review of graph techniques -- A review of binary decisions diagrams (BDDs) techniques -- gBDD -- graph binary decision diagrams -- Detection of hard faults using HUB -- Introduction to budgetary constraints -- The HUB algorithm -- Important HUB attributes -- Circuits characteristics of used for results -- Comparison of gBDD -- ATPG related results -- Fault simulation related results -- Hard fault detection

A note on Riccati matrix difference equations

International audienceDiscrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a self-contained study of discrete time Riccati matrix difference equations. In particular, we provide a novel Riccati semigroup duality formula and a new Floquet-type representation for these equations. Due to the aperiodicity of the underlying flow of the solution matrix, conventional Floquet theory does not apply in this setting and thus further analysis is required. We illustrate the impact of these formulae with an explicit description of the solution of time-varying Riccati difference equations and its fundamental-type solution in terms of the fixed point of the equation and an invertible linear matrix map, as well as uniform upper and lower bounds on the Riccati maps. These are the first results of this type for time varying Riccati matrix difference equations

Spacecraft trajectory tracking and parameter estimation in the presence of a splitting contact binary asteroid

Increasing interest in asteroid mining and in-situ resource utilization will lead to an increase in asteroid surface operations. The composition of asteroids is often unknown and potentially unstable, many of which are bound together predominantly by gravitational forces. Surface operations such as mining may significantly alter the asteroid’s structure or, in the case of contact binary asteroids, cause the asteroid to split. Conditions on the evolution of the contact binary system after splitting are derived. Observability issues causing inconclusive results in the previous work were addressed here by identifying an observable set of constant parameters which describes the splitting system. The coupled problem of estimating unknown parameters of a newly-formed binary system and controlling a spacecraft’s trajectory in the system’s vicinity is investigated. An indirect adaptive control scheme is utilized to simultaneously and accurately meet both objectives. Finally, a simpler control scheme, based only on 2-body dynamics is derived to show significant improvement in performance when using the proposed adaptive control scheme over using the simple 2-body controller. For larger contact binary asteroids, the adaptive control scheme has shown up to a 20% reduction in control cost over the 2-body controller