This project is centered around the idea of incorporating general implementation constraints and requirements in the theory of robust controller design. One aspect is the design of sampled-data controllers with continuous-time performance objectives (hybrid systems), specifically, the design and analysis of single- and multirate control systems in the l ;s1 and H ^;in norms. Among the issues considered are design algorithms and nonconservative conditions for robustness in time-invariant, time-varying, and/or nonlinear unmodeled dynamics. The second aspect is to develop systematic and computable methods for the design of low-order controllers, through various types of model reduction in conjunction with robust stability and closed-loop performance analysis.

Optimal and Robust Control Theory and Applications
B. Bamieh, J. Sreedhar, S. Landry
National Science Foundation, ECS-96-24152
(Conducted in the Coordinated Science Laboratory)

This project deals with mixed continuous/discrete-time systems and systems with switching nonlinearities systems. We concentrate on developing a framework in which intersample behavior as well as quantization and round off error effects can be analyzed, and when possible, controllers designed. We are also investigating model reduction and identification of linear parameter varying (LPV) systems. This identification scheme alleviates the need to perform many identification experiments for processes whose dynamics may change with set-point changes.

This project seeks a new approach to designing complex systems in which advanced techniques are integrated to produce ``intelligent'' systems of superior performance in the presence of large uncertainties and stringent specifications. The goal is to translate high-level commands or specifications automatically into lower level actions on the environment or plant, while fully utilizing any prior information as well as information contained in the real-time environmental responses. Multilayer decision models for control of subsystems with conflicting objectives, decentralized control, and robust and adaptive control approaches will be developed.

This project involves fundamental research on the modeling, control, and optimization of large-scale systems. It encompasses both linear and nonlinear models, deterministic and stochastic systems with external and internal uncertainty, systems with weak spatial and weak or strong informational links, and dynamic decision models with multiple criteria. The overall goal is the development of new and effective methodologies for robust control, stabilization and optimization of large-scale systems in the presence of static as well as dynamic uncertainty, and the analysis of such systems using concepts of multimodeling, decomposition, and aggregation.

This project is aimed at developing a comprehensive time-domain-based theory for the analysis and synthesis of performance-robust minimax controllers and identifiers for nonlinear systems subject to deterministic and/or partially stochastic disturbances. The general approach adopted is that of dynamic or differential game theory, and in this regard part of the current research is devoted to obtaining fundamental results on zero-sum and nonzero-sum differential games. Part of the research activity is also devoted to exploration of the relationship with stochastic control problems with exponentiated cost, again from a performance-robustness point of view.

This research addresses the problem of designing efficient scheduling policies to reduce the mean and variance of cycle-time. Comprehensive comparative testing of policies on realistic fabrication models is planned. We also address the problem of performance evaluation of queueing networks, which arise not only in semiconductor manufacturing systems, but also in communication networks and computer systems. Questions of the following type are addressed: Given a system description, in terms of the number of servers, their up and down time statistics, the description of the various flows, and parameters such as throughput rates, routes, and processing times at each server, how does one predict the performance of the system?

The goal of this project is to develop an applicable theory for analysis and control of manufacturing systems. Manufacturing systems are composed of a complex interaction of machines and parts. The systems are typically large scale and subject to disruptions such as machine failures. The goal is to control or schedule these systems efficiently to achieve optimal performance in terms of mean manufacturing lead time, variance, ability to meet due dates, cost of work in process, and shortfall costs. The issues are: How does a specific scheduling policy perform? and How does one synthesize good scheduling policies?

This research is concerned with the development of new methods for performance evaluation of broadband net works and multihop radio networks. The key performance issues are the study of delay and throughput. The new methodology is based on linear programming and optimization theory. Also studied is the design of wireless networks in volatile environments.

In this project we consider scheduling policies for large manufacturing systems and the dynamics of these systems under the influence of random breakdowns, fluctuations in demand and yield, and changes in operating conditions.

We consider generalizations of the least squares algorithm for identifying time-varying systems and the performance of adaptive control schemes based upon these estimation algorithms. These controllers are currently being implemented on an arc welder at the U.S. Army Construction Engineering Research Laboratory.