Arthur J Krener

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

[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.

Last updated: unknown