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
Optimization
Control

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. 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

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. 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

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. 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

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