Browsing by Author "Dadone, Paolo"

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    Design Optimization of Fuzzy Logic Systems
    Dadone, Paolo (Virginia Tech, 2001-05-18)
    Fuzzy logic systems are widely used for control, system identification, and pattern recognition problems. In order to maximize their performance, it is often necessary to undertake a design optimization process in which the adjustable parameters defining a particular fuzzy system are tuned to maximize a given performance criterion. Some data to approximate are commonly available and yield what is called the supervised learning problem. In this problem we typically wish to minimize the sum of the squares of errors in approximating the data. We first introduce fuzzy logic systems and the supervised learning problem that, in effect, is a nonlinear optimization problem that at times can be non-differentiable. We review the existing approaches and discuss their weaknesses and the issues involved. We then focus on one of these problems, i.e., non-differentiability of the objective function, and show how current approaches that do not account for non-differentiability can diverge. Moreover, we also show that non-differentiability may also have an adverse practical impact on algorithmic performances. We reformulate both the supervised learning problem and piecewise linear membership functions in order to obtain a polynomial or factorable optimization problem. We propose the application of a global nonconvex optimization approach, namely, a reformulation and linearization technique. The expanded problem dimensionality does not make this approach feasible at this time, even though this reformulation along with the proposed technique still bears a theoretical interest. Moreover, some future research directions are identified. We propose a novel approach to step-size selection in batch training. This approach uses a limited memory quadratic fit on past convergence data. Thus, it is similar to response surface methodologies, but it differs from them in the type of data that are used to fit the model, that is, already available data from the history of the algorithm are used instead of data obtained according to an experimental design. The step-size along the update direction (e.g., negative gradient or deflected negative gradient) is chosen according to a criterion of minimum distance from the vertex of the quadratic model. This approach rescales the complexity in the step-size selection from the order of the (large) number of training data, as in the case of exact line searches, to the order of the number of parameters (generally lower than the number of training data). The quadratic fit approach and a reduced variant are tested on some function approximation examples yielding distributions of the final mean square errors that are improved (i.e., skewed toward lower errors) with respect to the ones in the commonly used pattern-by-pattern approach. Moreover, the quadratic fit is also competitive and sometimes better than the batch training with optimal step-sizes, thus showing an improved performance of this approach. The quadratic fit approach is also tested in conjunction with gradient deflection strategies and memoryless variable metric methods, showing errors smaller by 1 to 7 orders of magnitude. Moreover, the convergence speed by using either the negative gradient direction or a deflected direction is higher than that of the pattern-by-pattern approach, although the computational cost of the algorithm per iteration is moderately higher than the one of the pattern-by-pattern method. Finally, some directions for future research are identified.
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    Fuzzy Control of Flexible Manufacturing Systems
    Dadone, Paolo (Virginia Tech, 1997-12-05)
    Flexible manufacturing systems (FMS) are production systems consisting of identical multipurpose numerically controlled machines (workstations), automated material handling system, tools, load and unload stations, inspection stations, storage areas and a hierarchical control system. The latter has the task of coordinating and integrating all the components of the whole system for automatic operations. A particular characteristic of FMSs is their complexity along with the difficulties in building analytical models that capture the system in all its important aspects. Thus optimal control strategies, or at least good ones, are hard to find and the full potential of manufacturing systems is not completely exploited. The complexity of these systems induces a division of the control approaches based on the time frame they are referred to: long, medium and short term. This thesis addresses the short-term control of a FMS. The objective is to define control strategies, based on system state feedback, that fully exploit the flexibility built into those systems. Difficulties arise since the metrics that have to be minimized are often conflicting and some kind of trade-offs must be made using "common sense". The problem constraints are often expressed in a rigid and "crisp" way while their nature is more "fuzzy" and the search for an analytical optimum does not always reflect production needs. Indeed, practical and production oriented approaches are more geared toward a good and robust solution. This thesis addresses the above mentioned problems proposing a fuzzy scheduler and a reinforcement-learning approach to tune its parameters. The learning procedure is based on evolutionary programming techniques and uses a performance index that contains the degree of satisfaction of multiple and possibly conflicting objectives. This approach addresses the design of the controller by means of language directives coming from the management, thus not requiring any particular interface between management and designers. The performances of the fuzzy scheduler are then compared to those of commonly used heuristic rules. The results show some improvement offered by fuzzy techniques in scheduling that, along with ease of design, make their applicability promising. Moreover, fuzzy techniques are effective in reducing system congestion as is also shown by slower performance degradation than heuristics for decreasing inter- arrival time of orders. Finally, the proposed paradigm could be extended for on-line adaptation of the scheduler, thus fully responding to the flexibility needs of FMSs.