During the development of floating-point signal processing systems, an efficient error analysis method is needed to guarantee the output quality. We present a novel approach to floating-point error bound analysis based on affine arithmetic. The proposed method not only provides a tighter bound than the conventional approach, but also is applicable to any arithmetic operation. The error estimati...

A series of systems of nonlinear equations with affine Weyl group symmetry of type A (1) l is studied. This series gives a generalization of Painlevé equations P IV and PV to higher orders. Introduction In this paper we propose a series of systems of nonlinear differential equations which have symmetry under the affine Weyl groups of type A (1) l (l ≥ 2). These systems are thought of as higher ...

In this letter, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving sequence of linear programs, resulting affine upper and lower hyperplanes with expanding operating regions. Although the problem can be solved using single program, existing approaches suffer from computation space complexity that grows exponentially s...

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximat...

A singular control system SG on G is defined by a pair E, D of.type for a single-input, control affine, nonlinear system in small dimension. Has on the optimality of singular controls when the control is replaced with.ABSTRACT A normal form for open loop control systems is provided, based on their interpretation as skew product flows and on normal forms for.Introduction. In this paper, the foll...

This paper presents a nonlinear extension of the affine transform as used in the iterated function systems (IFS) to compress signals and data. Compared with ∅ien and Nårstad’s orthogonal transform with compression ratio of 6.0:1 for the electrocardiogram (ECG) signal, the nonlinear approach produces higher compression ratios of 10.2:1, and is more flexible in finding the corresponding strange a...

In this paper, we propose an observer-based fuzzy adaptive control scheme for a class of multiple-input-multiple-output (MIMO) nonlinear non-affine systems with uncertainty and unknown state derivative. The proposed approach combines the recurrent-type fuzzy logic system (RFLS) and nonlinear observer to deal with the tracking control problem. It adopts the RFLS to approximate nonlinear unknown ...