This monograph presents new model-based design methods for trajectory
planning, feedback stabilization, state estimation, and tracking control
of distributed-parameter systems governed by partial differential
equations (PDEs). Flatness and backstepping techniques and their
generalization to PDEs with higher-dimensional spatial domain lie at the
core of this treatise. This includes the development of systematic late
lumping design procedures and the deduction of semi-numerical approaches
using suitable approximation methods. Theoretical developments are
combined with both simulation examples and experimental results to
bridge the gap between mathematical theory and control engineering
practice in the rapidly evolving PDE control area.
The text is divided into five parts featuring:
- a literature survey of paradigms and control design methods for PDE
systems
- the first principle mathematical modeling of applications arising in
heat and mass transfer, interconnected multi-agent systems, and
piezo-actuated smart elastic structures
- the generalization of flatness-based trajectory planning and
feedforward control to parabolic and biharmonic PDE systems defined on
general higher-dimensional domains
- an extension of the backstepping approach to the feedback control and
observer design for parabolic PDEs with parallelepiped domain and
spatially and time varying parameters
- the development of design techniques to realize exponentially
stabilizing tracking control
- the evaluation in simulations and experiments
Control of Higher-Dimensional PDEs - Flatness and Backstepping Designs
is an advanced research monograph for graduate students in applied
mathematics, control theory, and related fields. The book may serve as a
reference to recent developments for researchers and control engineers
interested in the analysis and control of systems governed by PDEs.
