Arthur J Krener
Position: Distinguished Professor
Year joining UC Davis: 1971
Degree: Ph.D., 1971, University of California, Berkeley
Refereed publications: Via
Math Reviews
Recent publications: Via
math arXiv
Professor Arthur Krener's research interests are in control theory, more
specifically in developing methods in control and estimation of
non-linear dynamical systems and
stochastic processes.
With R. Hermann [1], he gave the definitive treatment of controllability and
observability for nonlinear systems.
The celebrated Pontryagin Maximum Principle gives the necessary
first-order conditions for a control to be optimal. Professor Krener [2]
developed the Higher Order Maximum Principle that can be used to obtain
optimality conditions that generalize the classical Legendre-Clebsch
conditions.
Along with Isidori, Gori-Giorgi and Monaco [3] he gave conditions for the
existence of decoupling and noninteracting control laws for nonlinear systems.
Most systems are causal, meaning that their current state
depends only past input and not on future input. But some systems, such as
those with boundary conditions, are acausal. In [4], Professor Krener gave the
realization theory for linear acausal systems, i.e., conditions for their
controllability, observability and minimality.
Another research interest of Professor Krener is stochastic processes,
particularly reciprocal processes. He has
developed the theory reciprocal diffusions, their representation by
stochastic differential equations of second order and their connection
with conservation laws [5]. Reciprocal diffusions can be used to develop
a stochastic model for quantum mechanics. This was the original
motivation for the introduction of reciprocal processes by E. Schrödinger in
1929.
Professor Krener is currently a co-PI on an AFOSR sponsored multicampus
research project to control surge, stall and flutter in compressors and
aeroengines. This is part of a new AFOSR Program for Research Excellence and
Transitions (PRET) which is designed to encourage academic researchers to more
closely couple their research efforts with those in industry while advancing
basic research. He is working with colleagues at UCSB, Cal Tech, MIT and United
Technologies Research Center, the basic research facility of Pratt and
Whitney.
The goal is to develop new techniques for robust nonlinear control of jet
engines. More specifically, the project is an investigation of the active
control of compression system rotating stall and surge, and blade flutter and
forced vibration. These complex physical phenomena bear heavily on engine
safety and performance and are among the most important considerations in
modern aeroengine design.
Selected publications
[1] Nonlinear controllability and observability (with R. Hermann),
IEEE Trans. Automat. Control 22 (1977), 728-740
[2] The high order maximal principle and its application to singular
extremals, SIAM J. Control Optim. 15 (1977) 256-293.
[3] Nonlinear decoupling via feedback: a differential-geometric approach,
(with A. Isidori, C. Gori-Giorgi, and S. Monaco), IEEE Trans. Automat.
Control 26 (1981) 331-345.
[4] Acausal realization theory, Part I: Linear deterministic systems. SIAM
SIAM J. Control Optim. 25 (1987) 499-525.
[5] Reciprocal diffusions in flat space. Probab. Theory Relat. Fields
107 (1997), 43-281.
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