Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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DyNARUM

logo_dynarum The goal of the RUM Program is to develop new mathematical tools that enable the design of large federated nonlinear systems with guaranteed performance in the presence of epistemic, aleatory, a priori, and a posteriori errors.

The Robust Uncertainty Management (RUM) Program will emphasize the development of mathematics and algorithms that guarantees performance by design for complex large-scale nonlinear federated systems. The Department of Defense will often integrate a number of large, nonlinear subsystems to form a single system whose purpose is to perform a specific function. The total system is composed of subsystems that are highly interconnected, simultaneously feature weak and strong nonlinear couplings, and are subject to resource constraints.

Typically the subsystems exploit different physical properties and mechanisms, and the subsystems are governed by their own nonlinear dynamics across multiple temporal and spatial scales. By its nature, the system is federated, distributed, and subject to uncertainty arising from incomplete knowledge of initial conditions, reducible errors arising from sensors, irreducible errors derived from modeling the physical system, as well as exogenous disturbances with an unknown distribution.

The primary issue is then to guarantee performance of the overall system and provide bounds on the performance of the system in the presence of epistemic and aleatory errors by design where guaranteeing performance is understood to mean that in the presence of partial or incomplete knowledge of the parameters or model describing the system that the values of specific state variables of the federated system can be predicted and maintained within a specified bound.

The goal of the RUM Program is to develop new mathematical tools that enable the design of large federated nonlinear systems with guaranteed performance in the presence of epistemic, aleatory, a priori, and a posteriori errors. In addition, RUM will address computational strategies that will minimize the computational costs associated with the evaluation of a nonlinear model while maintaining an appropriate precision in control or optimization applications, as well as analysis methods and computational techniques that enable the propagation of non-Gaussian distributed uncertainties through coupled nonlinear systems.

Several new methods have been developed based on a principled graph theoretical method that enable a system to be broken apart across multiple spatial and temporal scales. These methods are being tested and have been used to design interactions between particles to form lattices that cover the plane. Several anisotropic potentials have been found that enable honeycomb and Kagome lattices that are robust to perturbations. The methods are also being applied to calculate phase diagrams as a precursor to solving a large-scale surveillance problem.

Last Updated on Wednesday, 08 April 2009 19:07  

Acknowledgements