Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analy ....Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications. We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.Read moreRead less
Advances in the Verification of Communication Protocols. Australia's economy is becoming increasingly dependent on many complex distributed systems. Some important examples are the Internet, electronic commerce, financial networks, transportation systems, health care networks, telecommunication networks, defence systems, intelligent manufacturing systems and organisational workflow management systems. Failure in these systems can result in serious financial loss (in banking applications) and los ....Advances in the Verification of Communication Protocols. Australia's economy is becoming increasingly dependent on many complex distributed systems. Some important examples are the Internet, electronic commerce, financial networks, transportation systems, health care networks, telecommunication networks, defence systems, intelligent manufacturing systems and organisational workflow management systems. Failure in these systems can result in serious financial loss (in banking applications) and loss of life or serious accidents in safety critical areas (medical, transport and defence applications). It is thus of utmost importance that distributed systems are designed correctly. This project aims to advance the state of the art in verifying that distributed systems will work correctly.Read moreRead less