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

Description

Optimization is omnipresent in science, engineering, and business. Many optimizationproblems consist of nonconvex objective functions or constraints. These globaloptimization problems post great challenges due to the presence of local optima andlack 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 ordesirable.The past three decades witnessed the birth and growth of neurodynamic optimizationwhich has emerged and matured as a viable optimization approach due to its inherentnature of parallel and distributed information processing and the hardwarerealizability. Despite the success, almost all existing neurodynamic approaches workwell only for convex and generalized-convex optimization problems with unimodalobjective functions. Effective neurodynamic approaches to constrained globaloptimization with multimodal objective functions are rarely available. Furtherinvestigations of neurodynamic approaches to global optimization is imperative.It is known that human brains operate on multiple scales of time and space. Forexample, the timescale of perception is supposed to be much smaller than that ofcognition. In addition, brain modeling on multiple spatial scales is more effective. Theexistence of different temporal and spatial scales in neurodynamics is essential for thebrains to function and be modelled properly. As multiscale modeling and analysis arebetter for brain dynamics and more heads are better than one in social dynamics,neurodynamic systems on multiple temporal and spatial scales are both biologicallyand socially plausible. The recent results of related research also indicate thatmultiscale neurodynamic systems would be more suitable for global optimization.In this proposed research, multiscale neurodynamic systems will be developed forconstrained global optimization. The research will consist of three coherent parts. Inthe first two parts, the research will focus on the analysis and design of neurodynamicsystems operating on multiple temporal and spatial scales for solving optimizationproblems with special and general nonconvex objective functions and constraints. Thesolvability scope and convergence properties of conceived multiscale neurodynamicsystems will be thoroughly investigated. In the third part of the research, the proposedapproaches will be applied to several interested topics in intelligent control,information processing, and machine learning. In particular, neurodynamics-basedapproaches to robust control, data analysis, and supervised learning will be developed.It is expected that the accomplishments of the proposed project will significantlyadvance the frontiers of global optimization research from both theoretical andpractical points of view.?