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Optimal Control of Functional Differential Systems

This presentation by Mr. Iyai Davies and Dr. Olivier Haas at the UKACC PhD Showcase delves into the complexities of neutral functional differential systems, characterized by dependencies on past and present states. The challenge of maintaining stability in such systems highlights the need for innovative control strategies. This work introduces a new theoretical framework based on the Razumikhin method, demonstrating conditions for total asymptotic stability. Practical applications spanning population ecology and distributed networks will also be explored, alongside future directions for developing optimal control laws.

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Optimal Control of Functional Differential Systems

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  1. Optimal Control of Functional Differential Systems Mr IyaiDavies Dr Olivier Haas UKACC PhD Presentation Showcase

  2. Introduction • A neutral system has derivatives of the past history as well as the present states • Stability and control of neutral system is a challenge • Objectives • Develop new theoretical findings on stability and control using neutral functional differential (using maximum principle) • Apply new result to practical systems UKACC PhD Presentation Showcase

  3. Example of Neutral System A cascade connection of two mixers

  4. In State Space Form Derivation of asymptotic stability using Razumikhin method A cascade connection involving two mixers can be expressed as : Assumptions: arematrices, continuous function which satisfies , where is uniformly stable, , u, , .

  5. New Theorem (Razumikhin method) • If there exists constant ,continuousfunction for , , and for such that all condition on the assumptions are satisfied then for all satisfying . Then the zero solution of the system is totally asymptotically stable • Proof: UKACC PhD Presentation Showcase

  6. Conclusions • Neutral systems: Population ecology, controllability, distributed networks containing lossless transmission lines, heat exchangers and robots in contact with rigid environments • Main result: (Using Razumikhinmethod) • The zero solution of the system (1) is Totally Asymptotically Stable • Other methods to demonstrate stability includes Lyapunov functional, Comparison • Future work: • Develop optimal control law • Apply to transmission lines UKACC PhD Presentation Showcase

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