Analysis and Design of Multiscale Neurodynamic Systems with Their Applications for Robust Control, Data Processing, and Supervised Learning

Project: ResearchGRF

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Optimization is omnipresent in science, engineering, and business. Many optimization problems consist of nonconvex objective functions or constraints. These global optimization problems post great challenges due to the presence of local optima and lack of efficacious solution methods to find global optima. In the era of big data, effective and efficient global optimization methods are deemed to be much needed or desirable. The past three decades witnessed the birth and growth of neurodynamic optimization which has emerged and matured as a viable optimization approach due to its inherent nature of parallel and distributed information processing and the hardware realizability. Despite the success, almost all existing neurodynamic approaches work well only for convex and generalized-convex optimization problems with unimodal objective functions. Effective neurodynamic approaches to constrained global optimization with multimodal objective functions are rarely available. Further investigations of neurodynamic approaches to global optimization is imperative. It is known that human brains operate on multiple scales of time and space. For example, the timescale of perception is supposed to be much smaller than that of cognition. In addition, brain modeling on multiple spatial scales is more effective. The existence of different temporal and spatial scales in neurodynamics is essential for the brains to function and be modelled properly. As multiscale modeling and analysis are better for brain dynamics and more heads are better than one in social dynamics, neurodynamic systems on multiple temporal and spatial scales are both biologically and socially plausible. The recent results of related research also indicate that multiscale neurodynamic systems would be more suitable for global optimization. In this proposed research, multiscale neurodynamic systems will be developed for constrained global optimization. The research will consist of three coherent parts. In the first two parts, the research will focus on the analysis and design of neurodynamic systems operating on multiple temporal and spatial scales for solving optimization problems with special and general nonconvex objective functions and constraints. The solvability scope and convergence properties of conceived multiscale neurodynamic systems will be thoroughly investigated. In the third part of the research, the proposed approaches will be applied to several interested topics in intelligent control, information processing, and machine learning. In particular, neurodynamics-based approaches to robust control, data analysis, and supervised learning will be developed. It is expected that the accomplishments of the proposed project will significantly advance the frontiers of global optimization research from both theoretical and practical points of view. ?


Effective start/end date1/01/18 → …