Design, Optimization, and Control for Multiscale Systems Murat Arcak, John Wen Electrical, Computer, and Systems Engineering Prabhat Hajela, Achille Messac Mechanical, Aerospace, and Nuclear Engineering Roger Ghanem Civil Engineering Johns Hopkins University

Attributes of Multiscale System Design Complex dynamics (large # of DOF, nonlinear) with multiple descriptions for different system behaviors and properties Intensive computation requirement for high fidelity simulation Identification/calibration requirement for model parameters Multiple design objectives and constraints Static and dynamically adjustable design parameters

Example Integrated control/structure design for electronic manufacturing: objective: rapid motion with minimal vibration model: FEM structural model static design parameters: head inertia/geometry, sensor/actuator type and location, motion profile dynamically adjustable parameters: actuator output constraints: torque, velocity, acceleration, temperature, and cost Current practice/limitation: FEM guided mechanical design, heuristic sensor/actuator selection and placement, control design based on empirical model

Example Nanocomposite: objective: produce materials with specified mechanical, electrical, optical properties model: multibody model with many polymer chains interacting with nanospheres and one another. static design parameters: binding material on nanosphere dynamically adjustable parameters: temperature, pressure, mixing rate constraints: types of material, actuator limitation Current practice/limitation: trial and error recipe, intensive model computation (decoupled from design)

MSERC Approach A design methodology integrating modeling, identification, optimization and control Modeling Identification Dynamical Process Optimization Control

Model Reduction/Identification Key technology in large scale system simulation and design, e.g., electromagnetics, structural systems, VLSI circuits, fluid dynamics etc. Motivation: wider and faster exploration of design space, lower order on-line estimator and controller, model validation/calibration Approximation of high order analytical model by a lower order model or fitting input/output data to parameterized model: an interpolation problem. key issues: parameterization, distance metric, error bound, property-preserving (gain, dissipativity, energy conservation), measurement noise. quantitative trade-off between model order, error bound, computation time not well developed, especially for nonlinear dynamical systems

probing to reduce uncertainty Modeling Engine modeling engine maintains, updates, and provides physics-based and data-driven models based on computation efficiency, accuracy, resolution, parameterization requirements. design optimization process optimization simulation real-time control analytical models modeling engine on-line diagnostics probing to reduce uncertainty physical data physical system

Multi-Disciplinary Optimization (MDO) Multiscale system design involves distinct but coupled subsystems with large number of design parameters, constraints, and performance metrics – multidisciplinary formulation with multiple objectives, constraints, models. In addition to system design and process optimization, optimization is also needed for model reduction and identification, and real-time controller and estimator design Key issues: surrogate model for efficient search, uncertainty modeling and management, imprecise problem formulation, machine learning Active research area: optimization in the presence of uncertainty – in underlying models, in performance objectives, in system constraints.

Optimization Engine Robust, simulation-based exploration of design space, batch and on-line optimization and diagnosis, based on models and error bounds provided by the modeling engine. incorporation of control objectives design optimization real-time control simulation simulation based design exploration model predictive control process optimization modeling engine optimization engine learning based optimal estimator on-line diagnostics processing parameters measurement data physical system

On-line Estimation and Control Multiscale systems are complex nonlinear dynamical systems with multiple inputs/outputs. Usual approach: linearization about operating point and treat linearization error as uncertainty -- most control design tools are for linear systems (robust control). Nonlinear estimation and control: exploit system structure rather than canceling or ignoring it. Broader consideration: system design including control objectives, actuator/sensor selection/placement low order models needed for real-time implementation trade-off between achievable performance and model uncertainty

Dynamic Control and Estimation Robust control and estimation algorithms that apply nonlinear model identification and reduction and incorporates model error estimates. optimization engine optimization with closed loop objectives real-time control modeling engine nonlinear model identification & reduction control & estimation on-line diagnostics actuator sensor physical system

Research Goals Developing on-demand model generation based on physical data, analytical models with tunable parameterization, error metric, error bound, size/order, communication overhead, and active probing to reduce model uncertainty Establishing integrated design methodology based on simulation driven multidisciplinary optimization, using gradient and evolutionary methods, taking into account imprecise problem formulation, model uncertainty, error management, computation cost, system dynamics, noise. Identifying fundamental limits on performance and robustness of multiscale systems based on static and dynamic optimization.

Linkage to Other Technology Components in MSERC fast simulation speeds up parameter space sampling in design iteration error estimate useful in optimization and control optimization tools applied to model reduction and identification data-driven model can be used to augment physics-based model physics based modeling provides parameterized model and computation tool develop common integrated tools and tailor them to specific applications