His future research plans fall into three broad areas and are outlined below. I. Parallel Algorithms. His principal objective here is to develop efficient multiprocessor algorithms for the solution of large, sparse Lyapunov and Riccati equations. Such equations typically arise in the control, stability analysis and model reduction of large flexible structures for which high order, banded, sparse finite element models are often available. The development of efficient Lyapunov and Riccati solvers would facilitate obtaining low order approximations to these complex models. These simplified models would play a key role in the context of simulation and feedback control of flexible structures. II. Adaptive Robust Control. Physical plant models are inherently inaccurate and incorporate both parametric and dynamic modelling uncertainty, often involving a large number of parameters. In many circumstances it may be possible to fragment the set of possible plant models into smaller, more manageable "operating points" for which locally robust LTI controllers may be readily designed using, for instance, H -optimal control methods. The entire problems of controlling the plant then reduces to adaptively "gain-scheduling" between these robust controllers. In this connection he has provided an adaptation scheme that uniformly input-output stabilizes the uncertain plant. Much work, however, remains, especially in the context of obtaining acceptable transient responses and disturbance rejection. III. Nonlinear Feedback. The research here is motivated by fundamental questions such as: What can and cannot be accomplished by the use of (arbitrary) nonlinear feedback? When are nonlinear controllers significantly better than linear ones? Answers to these questions are vitally important because they would allow control system engineers to select or eliminate broad classes of design methodologies for specific design problems. His principal research goals are to develop quantitative techniques that offer guidelines on actuator-sensor reconfiguration and the choice of an appropriate feedback synthesis methodology.
