Using the differential geometric control theory, we present the necessary and sufficient conditions under which an analytic affine nonlinear system with multiple inputs is equivalent to, via state ...transformation without feedback, a kind of extended Brunovsky canonical form. The proof is based on a new technique for applying the Frobenius Theorem in a more convenient way by converting a set of quasilinear partial differential equations with the same main portion to a set of homogeneous linear partial differential equations.
The observability of nonlinear systems was considered in this note. First, we reviewed the definitions and relations of observable, locally observable, weakly observable, locally weakly observable, ...uniformly locally weakly observable and completely uniformly locally weakly observable. Then, a sufficient condition under which a multi-output nonlinear system is completely uniformly locally weakly observable was given. The sufficient condition becomes necessary and sufficient condition when the system is single-output. We also gave a canonical form of these multi-output systems. In the end, an example illustrated how to use the given sufficient conditions to determine whether a nonlinear system is completely uniformly locally weakly observable
Two criteria for converting a chaotic system to a normal form via coordinate transformation are presented. Firstly, it was proved that a chaotic system can be converted to a normal form if and only ...if there exists a single-input control system which treats the vector field of the chaotic system as drift vector field and can be fully linearized by state feedback. Secondly, near the non-singular point, there always exist some coordinate transformation to perform the converting; and near the singular point, the converting can be found if and only if, at this point, the eigenpolynomial of the Jacobian matrix of the vector field is equal to the minimal polynomial of the same matrix. Moreover, the condition, under which the synchronization between the normal form of the drive system and the Brunovsky canonical form of the response system implies the synchronization between the drive system and the response system, was discussed. Finally, synchronizing two Rossler chaotic systems with difference in two parameters was taken as a concrete example to illustrate the new method.
In waste printed circuit boards (PCBs) recycling fields, how to recycle and reuse nonmetals is a challenging problem, and there is no preferable solutions up to now. This paper presents new methods ...for reusing nonmetals reclaimed from waste PCBs. Nonmetals are used to make formative models, compound boards or related products. When compared with traditional materials, such as talc and silica powder, PCB nonmetals improve the mechanical features of these products greatly with comparable tensile and shearing strength and 30 percent larger flexural strength, which indicates good application prospect for its undoubted potential.
There exists combination explosion during the course of modeling of AND/OR graph for disassembly planning for recycling, which makes it nearly impossible to handle a product with numerous parts. To ...conquer the difficulty, set AND/OR graph (SAOG) is defined, and with the mapping from SAOG to product, complete disassembly AND/OR graph (DAOG) is presented. In order to ensure the validity and applicability of DAOG, several sieves are designed to delete most of the vertexes and edges. These sieves are successively applied to DAOG, and finally the complete DAOG becomes sieved DAOG which is the model used for disassembly planning. DAOG contains all possible disassembly actions, thus it provides a suitable basis for generation and evaluation of all possible disassembly sequences of an end-of-life product.
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