1981 — 1984 
Shiflett, Geoffrey (coPI) [⬀] Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Analysis of Rigid Body Displacement Parameters From Imprecise Data @ University of Southern California 
0.976 
1984 — 1988 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Algorithms, Analysis, and Software For Riccati Equations @ University of CaliforniaSanta Barbara 
0.97 
1988 — 1992 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
LargeScale Scientific Computing in Control @ University of CaliforniaSanta Barbara
This proposal describes an interdisciplinary research project whose principal objective is to extend the computational frontiers of control and system theory. A hierarchy of computational considerations is outlined, ranging from smallorder problems to largeorder problems. Recent analytic techniques which demonstrate numerical limitations of standard algorithms for the former will be improved and extended. However, the principal research thrust will be towards highorder problems for which rather few dependable numerical techniques presently exist, particularly for problems arising from models in socalled secondorder matrix form. Such models arise naturally throughout most branches of engineering and the sciences. It is proposed to extend various control and system theory algorithms to exploit the special matrix structures available in the ubiquitous secondorder equations. Parallel algorithms and specialized computing architectures offer promising opportunities to meet the challenge of advanced control strategies for both online and offline computations. By examining problems of fundamental and generic interest (especially those generated by secondorder models), this project will contribute parallel algorithms and software to support computations arising in problems ranging from active control for high performance aircraft engines to vibration control for large space structures to control of interconnected power systems. Such applications will require at least an order of magnitude improvement in speed and the size of problems solvable. Close attention will be paid to basic numerical issues such as conditioning and stability; and implementation of algorithms into reliable and robust software will facilitate effective technology transfer to industry, government, and academia.

0.97 
1988 — 1990 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences: Numerical Solution of Control Problems @ University of CaliforniaSanta Barbara
The ability to accurately determine the sensitivity of Riccati problems leads to the possibility of improving the condition of the Riccati equation, thereby improving the closedloop response, by making changes in either the underlying system being controlled or by changing the weighing matrices for the state and input variables in the performance index. An immediate application of such a procedure involves the optimal positioning of sensors and actuators, particularly for structures with a large number of identical sensor/actuator mechanism, such as large space antennas. A related question is whether colocating actuators and sensors always leads to the best system performance. Aspects of a method for determining optimal changes, in either the underlying system or the weighing matrices of the performance index, are discussed, as well as extensions to infinite dimensional distributed parameter systems.

0.97 
1991 — 1992 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
International Travel Funds For the 30th Ieee Conference On Decision and Control (Cdc) to Be Held in Brighton, England; December 1113, 1991 @ University of CaliforniaSanta Barbara
This is a request for block international travel funds for the 30th IEEE Conference on Decision and Control (CDC) to be held in Brighton, England from December 1113, 1991. The CDC is one of the world's largest and most important conferences on control theory and applications. The Brighton location will be only the second time the CDC has been held outside the United States. The funds will be instrumental in improving the technical success of the conference by enabling participation of sufficient numbers of key U.S. authors.

0.97 
1992 — 1995 
Laub, Alan Kokotovic, Petar (coPI) [⬀] Seborg, Dale (coPI) [⬀] Paden, Brad (coPI) [⬀] Dahleh, Mohammed 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Intelligent Control of Systems With SetPartitioned Dynamics @ University of CaliforniaSanta Barbara
In this project, a new paradigmsystem with setpartitioned dynamics is introduced. This paradigm encompasses a broad class of control formulations motivated by applications to systems such as industrial process, energy systems, and transportation vehicles. In this new paradigm, continuous but often uncertain dynamics of the system interacts with logical, although usually fuzzy structure imposed by component limits and design constraints. The research effort is devoted through analysis, design and experimental case studies, the formulation of an overall problem of controlling a plant whose behavior is determined not only by dynamics, but also by sharp or fuzzy boundaries on which these dynamics abruptly change. Design methods are developed for sharp and fuzzy partitioned observers, and for interior and transitional controls. Estimation and control parts of the design are integrated into an overall numericallogical feedback control loop.***//

0.97 
1992 — 1996 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
LargeScale Computing in Control @ University of CaliforniaSanta Barbara
In this proposal we discuss algorithms for solving highorder numerical problems that arise in the design of control laws for systems modeled with large numbers of variables (parameters, inputs, outputs, states, etc.). Particular attention is focused on certain key matrix equations arising in state spacebased control engineering. The most common such equations are Lyapunov and Riccati equations, and their effective numerical solution is described in detail, although our techniques also apply more generally. Considerable discussion is focused on largescale matrix problems, including those in which the matrices are sparse or structured. In addition to continuing our research on algorithms for implementation on vector supercomputers such as the Cray YMP for which coarsegrained parallelism can also be exploited, we proposing now to extend our efforts to computers such as the Connection Machine with massive parallelism. Much of our proposed research is intended to lay the groundwork for the next generation of computeraided control system design and analysis software.

0.97 
1994 — 1997 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
U.S.France Cooperative Research (Inria): Advanced ComputerAided Design Tools For Robust Control Engineering @ University of CaliforniaSanta Barbara
9311965 Laub This threeyear award supports U.S.France cooperative research in advanced computeraided design tools for robust control engineering between Alan J. Laub of the University of California at Santa Barbara and Pascal Gahinet of the French National Institute for Research in Computer Science and Applied Mathematics (INRIA) at Rocquencourt. The objective of their research is to develop efficient, reliable, easy to use software for the design of the next generation of control systems. Specifically, the U.S. and French investigators will combine their complementary expertise to develop state of the art techniques and tools for robustness analysis and control design. Robust control theory addresses practical control engineering concerns with powerful statespace techniques and offers a variety of analysis and design tools. The current lack of reliable, easy to use computeraided design packages is an obstacle to wider diffusion of robust control techniques in industry. The proposed research addresses this issue and deals with problems of generic interest to control engineers. The results will have widespread applications in aeronautical, chemical, electrical, and optical systems, among others. ***

0.97 
1996 — 2000 
Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Numerical Algorithms For Sensitivity Estimation in Control @ University of CaliforniaDavis 
0.984 
2002 — 2006 
Bai, Zhaojun [⬀] Laub, Alan 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Itr: Computational Theory and Tools For ReducedOrder Modeling of Very Large Dynamical Systems and Applications @ University of CaliforniaDavis
The continual and compelling need for accurately and efficiently simulating dynamical behavior of physical systems arising from a wide variety of applications has led to increasingly large and complex models. Reducedorder modeling (ROM), also called model reduction, techniques play an indispensable role in providing efficient computational prototyping tools to replace such largescale models by approximate smaller models. Such reducedorder models must be capable of capturing critical dynamical behavior and faithfully preserving essential properties of the larger models they approximate. An accurate and effiective reducedorder model can be applied for steadystate analysis, transient analysis, or sensitivity analysis of largescale models and the physical systems they emulate. Consequently, scientists and engineers can significantly reduce design time and pursue more aggressive design strategies. Designers can try ``whatif" experiments in hours instead of days.
In this proposal, we propose a broad range of synergistic research activities on ROM relating to three interlinking strands: computational theory, reliable algorithms, and highperformance software tools. We will also be actively involved with promoting applications of ROM techniques and testing our methods through existing and new collaborations with researchers in circuit simulation, structural dynamics, control systems, and microelectromechanical systems (MEMS). Specifically, our proposed research activities on computational theory and algorithms include:
Accuracy estimation in both time and frequency domains.
Sensitivity analysis of linear systems using the techniques of ROM and statistical condition estimation.
Development of ROM techniques that directly exploit socalled secondorder model structures and generate a reducedorder model in secondorder form.
Exploration of a framework of ROM techniques for certain types of largescale nonlinear systems of technological importance.

0.984 
2006 — 2012 
Bertozzi, Andrea [⬀] Laub, Alan Anderson, Christopher (coPI) [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Research Training Group in Applied Differential Equations and Scientific Computing (Emsw21Rtg) @ University of CaliforniaLos Angeles
UCLA has a unique environment for advancing the careers of young researchers. State of the art research in applied mathematics, including image processing, materials science, and fluid dynamics is developed with full participation of a vibrant group of graduate students and postdocs. We propose to build on this program to provide an exceptional training and mentoring experience for younger students at the undergraduate and early graduate level. This program will support, over five years, up to 60 REU students from both UCLA and Harvey Mudd College. Proposed research projects include spatiotemporal pattern analysis in crime data, experimental and analysis of slurry flows, imaging processing, and cooperative control of robotic vehicles. An additional group of 15 PhD students, in the early stages of their career, will develop a research career in applied mathematics. These students will have the opportunity to participate in summer internship projects with faculty from other departments and with industry and national laboratories. Students will receive additional training in computation as well as mathematical analysis skills necessary to succeed in a top PhD program.
The investigators propose a research training program to enhance the workforce of US citizens and permanent residents entering research study applied and computational differential equations. This program is designed for undergraduate students and graduate students in the early part of a research career. They will work both oneonone and in small research groups with faculty mentors on cutting edge research problems in an immersive research environment. This program will support, over five years, up to 60 REU students from both UCLA and Harvey Mudd College. These students will have the opportunity to be part of a research team in a large research university. Proposed research projects include modeling of crime in Los Angeles, laboratory and mathematical studies of mud slides, medical imaging, and coordination and tracking of autonomous vehicles. In addition, up to 15 PhD students, in the early part of their careers, will participate in this program, which includes summer graduate internship projects with faculty from other departments and with industry and national laboratories. All students in the program will have the opportunity to participate in new curricular activities aimed at developing the mathematical and computational background necessary to succeed in a top PhD program in computational and applied mathematics.

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