Complexity analysis of binary nonlinear feedforward sequences through minimum polynomials of compound matrices

AbstractThe problem of finding the complexity of the Nonlinear feedforward sequences has been analysed and a unified method has been developed for finding the complexity of such sequences for the cases when feedback is 1.(i) an irreducible polynomial;2.(ii) product of two irreducible polynomials;3.(iii) power of an irreducible polynomial. The method is based on the minimum polynomial of the compound matrix formed from the companion matrix of the feedback polynomial. Apart from being a unified method, this approach has the advantage that it can be applied to any level of logic and one can get the minimal generator of all possible non-linear feedforward sequences

Parametrized maneuvers for autonomous vehicles

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 197-209).This thesis presents a method for creating continuously parametrized maneuver classes for autonomous vehicles. These classes provide useful tools for motion planners, bundling sets of related vehicle motions based on a low-dimensional parameter vector that describes the fundamental high-level variations within the trajectory set. The method follows from a relaxation of nonlinear parametric programming necessary conditions that discards the objective function, leaving a simple coordinatized feasible space including all dynamically admissible vehicle motions. A trajectory interpolation algorithm uses projection and integration methods to create the classes, starting from arbitrary user-provided maneuver examples, including those obtained from standard nonlinear optimization or motion capture of human-piloted vehicle flights. The interpolation process, which can be employed for real-time trajectory generation, efficiently creates entire maneuver sets satisfying nonlinear equations of motion and nonlinear state and control constraints without resorting to iterative optimization. Experimental application to a three degree-of-freedom rotorcraft testbed and the design of a stable feedforward control framework demonstrates the essential features of the method on actual hardware. Integration of the trajectory classes into an existing hybrid system motion planning framework illustrates the use of parametrized maneuvers for solving vehicle guidance problems. The earlier relaxation of strict optimality conditions makes possible the imposition of affine state transformation constraints, allowing maneuver sets to fit easily into a mixed integer-linear programming path planner.(cont.) The combined scheme generalizes previous planning techniques based on fixed, invariant representations of vehicle equilibrium states and maneuver elements. The method therefore increases the richness of available guidance solutions while maintaining problem tractability associated with hierarchical system models. Application of the framework to one and two-dimensional path planning examples demonstrates its usefulness in practical autonomous vehicle guidance scenarios.by Christopher Walden Dever.Ph.D

Applied and Computational Statistics

Research without statistics is like water in the sand; the latter is necessary to reap the benefits of the former. This collection of articles is designed to bring together different approaches to applied statistics. The studies presented in this book are a tiny piece of what applied statistics means and how statistical methods find their usefulness in different fields of research from theoretical frames to practical applications such as genetics, computational chemistry, and experimental design. This book presents several applications of the statistics: A new continuous distribution with five parameters—the modified beta Gompertz distribution; A method to calculate the p-value associated with the Anderson–Darling statistic; An approach of repeated measurement designs; A validated model to predict statement mutations score; A new family of structural descriptors, called the extending characteristic polynomial (EChP) family, used to express the link between the structure of a compound and its properties. This collection brings together authors from Europe and Asia with a specific contribution to the knowledge in regards to theoretical and applied statistics