Modeling and Control of Distributed Parameter Systems
This area of research focuses on modeling and control of dynamical systems/processes described by partial differential equations (pdes) and time delays. Such systems/processes are referred to as distributed parameter or infinitedimensional systems/processes. This terminology is intended to capture the significant complexity that distinguishes such systems/processes from their lumpedparameter or finitedimensional relatives. To date, most of the classical and modern control research has focused on systems/processes described by ordinary differential equations (odes); i.e. systems/processes described by lumpedparameter or finitedimensional models.
Application Area
Relevant application areas include:
 Aerothermoelasticity for flexible airbreathing hypersonic aircraft
 Servoelastic effects for aircraft
 Flexible spacecraft and space structures
 Semiconductor thermal processes; e.g. chemical vapor deposition (CVD), active cooling of advanced microprocessor units
 Time delay compensation within distributed communication systems
 Time delays within digital (sampleddata) control system implementations
Relevant Control Challenges
Relevant control challenges include:
 uncertain nonlinearities (e.g. variable constraints),
 uncertain high frequency dynamics (i.e. unmodeled differential equations),
 parametric uncertainty,
 uncertain actuator and sensor dynamics,
 centralized versus decentralized control architectures,
 multiple timescale dynamics; e.g. multiple measurement/actuation rates,
 selection of weighting function parameters for dynamical optimization,
 assessment of fundamental performance limitations and tradeoffs,
 stabilization,
 following of varying (typically low frequency) reference commands,
 attenuation of (stochastic, typically low frequency) disturbances,
 attenuation of (stochastic, typically high frequency) measurement noise,
 state estimation,
 parameter and uncertainty estimation (system identification).
Objectives and Goals
The main objective of this research is to develop systematic (finitedimensional) methods for designing robust control systems for parameter systems and processes operating in the presence of significant nonlinearities and uncertainty. One relevant goal of this work is the development of a priori performancedependent approximation/fidelity requirements.
Approaches
 Classical pdes, delay differential equations, inputoutput operator theory, semigroupbased state space theory
 First principles and empirical (system identification) modeling
 Approximation of distributed parameter (infinitedimensional) models by lumpedparameter (finitedimensional) models that maintain essential physical attributes (relative to the target bandwidth and design specifications) while keeping the associated control design computationally manageable.
Collaborators and Sponsors
This work has been sponsored by the following organizations:
 National Science Foundation (NSF), DARPA, AFOSR, Intel, Honeywell, Boeing, NASA.
