Design, Optimization, and Control for Multiscale Systems

1. 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

2. 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

3. 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

4. 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)

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

6. 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

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

8. 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.

9. simulation process optimization on-line diagnostics modeling engine optimization engine physical system design optimization real-time control 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 simulation based design exploration model predictive control learning based optimal estimator processing parameters measurement data

10. 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

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

12. 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.

13. 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