Multi-learner based recursive supervised training

In this paper, we propose the Multi-Learner Based Recursive Supervised Training (MLRT) algorithm which uses the existing framework of recursive task decomposition, by training the entire dataset, picking out the best learnt patterns, and then repeating the process with the remaining patterns. Instead of having a single learner to classify all datasets during each recursion, an appropriate learner is chosen from a set of three learners, based on the subset of data being trained, thereby avoiding the time overhead associated with the genetic algorithm learner utilized in previous approaches. In this way MLRT seeks to identify the inherent characteristics of the dataset, and utilize it to train the data accurately and efficiently. We observed that empirically, MLRT performs considerably well as compared to RPHP and other systems on benchmark data with 11% improvement in accuracy on the SPAM dataset and comparable performances on the VOWEL and the TWO-SPIRAL problems. In addition, for most datasets, the time taken by MLRT is considerably lower than the other systems with comparable accuracy. Two heuristic versions, MLRT-2 and MLRT-3 are also introduced to improve the efficiency in the system, and to make it more scalable for future updates. The performance in these versions is similar to the original MLRT system

Observability for two dimensional systems

Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model