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Optimal Control of Functional Differential Systems

Optimal Control of Functional Differential Systems. Mr Iyai Davies Dr Olivier Haas. 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

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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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