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Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's st ....Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis. The proposed research will significantly advance knowledge by creating new analytical and numerical methods for tackling complex nonlinear control problems arising in many applications. The study's outputs will lead to a deeper understanding of fundamental issues in mathematical modelling. Collaboration with renowned researchers will further improve Australia's standing in the international research community. Also their visits may further promote research both within and outside the host institution. In particular, lectures and seminars that they will deliver will be transmitted to Australian universities participating in the Access Grid Room Project.Read moreRead less
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