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Nonlinear, Stochastic and Hybrid Control

 

Control systems are used in a diverse range of engineering systems including those found in aerospace, manufacturing and telecommunications, as well as in emerging applications such as quantum physics, quantum information and computing, and quantum chemistry. Control systems are a key enabling technology, though often invisible to the public. Modern control engineering relies heavily on a mathematical model for the system to be controlled. The majority of this theory has been for models which are linear, since such models are more easily analysed and problems can be generally be solved either explicitly or via efficient numerical methods. Control theory for systems with nonlinear models has also undergone substantial development over the years, but because of the wide range of nonlinear phenonema which can occur and the nature of the nonlinearities, explicit solutions are rarely available and numerical algorithms can be computationally expensive. Because models may not be known exactly, and also because systems are often subject to disturbances and other uncertainty, methods have been developed for robust control design. Robust controllers are designed to achieve good performance under nominal conditions, and acceptable performance in other than nominal conditions.

Feedback is the most important concept in control engineering, and has a long history. Feedback is used to compensate for disturbances and uncertainty. In the absence of disturbances and uncertainty, feedback is completely unnecessary and control can be achieved by a prescribed open loop controller. However, in reality the systems to be controlled are subject to disturbances and uncertainty, e.g. (i) the influence of an environment, (ii) model error due to approximation (e.g. linearisation) and unknown or poorly known parameters, and (iii) imprecise or noisy measurements. A crucial issue for feedback control system design is what measurement information is available to the controller, and how this information should be represented and used. Since the real world is generally nonlinear, it is very important to develop design methodologies for nonlinear systems. Research in nonlinear control theory is important not only because of the fundamental insights that are obtained but because of its potential future application.

These considerations underscore the importance of measurement feedback control for nonlinear systems and the need for robustness. Research in this project considers fundamental issues concerning measurement feedback robust control. Current topics include:

• H-infinity control
• L-infinity control
• Input to state stability (ISS) analysis and synthesis
• H-infinity model reduction
• Cheap sensor problems
• Optimal robust control of hybrid systems

People

• Zhang Huan Nonlinear Robust Control (FEIT/NICTA PhD, commenced July 2003)
• Shaudong Huang Nonlinear Robust Control (ARC Research Assistant, now at UTS Sydney)
• Bill Helton (Math, UCSD)
• Bill McEneaney (Math/AME, UCSD)
• Ian Petersen (EE, ADFA)
• Dragan Nesic (EE, Melbourne)
• Peter Dower (EE, Melbourne)
• Z.P. Jiang (EE, BPI)

Papers

 

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