Network-Centric Stochastic Hybrid Dynamic Time-Event Process Modeling, Methods and Analysis
Abstract
The overall objective of the proposal is to develop and to study an analytic interconnected network-centric stochastic hybrid dynamic technique (INSHDT) for at least four interacting nonlinear and non-stationary stochastic dynamic processes. First, the proposal will develop a prototype stochastic model for interconnected stochastic hybrid dynamic process, and analytically validate the feasibility of the model. Furthermore, the proposal will also investigate stochastic network dynamic state and structural parameter estimation techniques, and will provide a means of validating the correctness of analytic assumptions, results, and conclusions utilizing. the recently developed innovative computational/simulation and statistical dynamic technique referred(LLGM1vI). Based on the proposal objective, the analytic interconnected network-centric stochastic hybrid dynamic technique(INSHDT) is composed of at least four existing interacting techniques, namely: (i) upper and lower solution technique, (ii) comparison technique (iii) nonlinear variation of constants technique in the context single/vector Lyapunov Function and differential inequalities, (iv) dynamic survival analysis. The most feasible nonlinear and non-stationary rate functions in interconnected stochastic hybrid dynamic models are locally Lipschitz continuous in state variables. Therefore, the Khasminskii-type of approach plays an important role for establishing the analytic stochastic dynamic model validation (existence and uniqueness theorem) in the frame-work ofLypunove-type function, Dynkin-type stopped stochastic process, differential inequality and comparison technique. This proposal would generate a new research area in survival analysis, namely, network dynamic survival state models (NDSSM) that interacts with INSHDT. The interaction between INSHDT and NDSSM sheds a light on (a) developing statistical network dynamic state and structural parameter estimation techniques; and (b) to validate the correctness of analytic assumptions, results and conclusions under the innovative numerical/simulation techniques. The Moreover, the proposal will investigate the qualitative and quantitative properties, namely, adaptability, sustainability and survivability of systems encountered both in civilian life and national defense arena. This proposal will also provide mechanisms to characterize safe and unsafe zones of operations, operations on multiple time-scale, discrete and continuous time behavior, layers of complexity, sustaionable-unsustaionable threats, tool for planning, policy and decision making processes or common cause objectives depending on network dynamic process. The methods of comparison and upper and lower solutions will be playing the significant role in exhibiting these characterizations. Moreover, these techniques are algebraically simple, computationaly attractive and easily verifiable. Moreover, it further sheds a light on the classical issues, complexity versus sustaionability, stochastic versus deterministic, in unified way.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510182
Entities
People
- Gangaram Ladde
Organizations
- Army Contracting Command
- United States Army
- University of South Florida