Mathematical Systems Theory Mathematical Analysis and Systems Theory Lassi Paunonen Assistant Professor, Mathematics Tampere University of Technology, Finland 27.8.2018 Funded by Academy of Finland project numbers 298182 and 310489. L. Paunonen
Mathematical Systems Theory Mathematical Systems Theory and Control u ( t ) y ( t ) P Mathematical control theory studies di ff erential equations d dtx ( t ) = Ax ( t ) + Bu ( t ) , x (0) = x 0 y ( t ) = Cx ( t ) where u ( t ) ∈ C is the control input y ( t ) ∈ C is the measured output. L. Paunonen
Mathematical Systems Theory Key Focus Areas: Control of temperature and fluid flows Control of vibrating and flexible systems Dynamics of large-scale systems Modern mathematical techniques in control L. Paunonen
Mathematical Systems Theory Example: Robust Trajectory Tracking for Heat Equations Objective: Control the system in such a way that the temperature measurements converge to reference trajectories. 1 0 4 − 1 2 0 1 1 0.8 − 2 0.6 0 − 4 z 0.4 7 6 5 0.2 4 3 − 1 2 1 0 0 t Figure: Controlled heat profile Figure: Measurements L. Paunonen
Mathematical Systems Theory Example: Optimal Disturbance Rejection Objective: Choose locations of active dampers so that the structural vibrations are suppressed as e ffi ciently as possible. Damper locations − → − → L. Paunonen
Mathematical Systems Theory Example: Dynamics of Large Vehicle Formations wireless communication radar v i +1 v i v i– 1 d i +1 i d i d i– 1 i +1 i– 1 Source: Ploeg et. al. , ’11. Source: TED/R. D’Andrea L. Paunonen
Mathematical Systems Theory Research Group at TUT Lassi Paunonen Assistant Professor Dmytro Baidiuk Postdoctoral Researcher Duy Phan-Duc Postdoctoral Researcher Jukka-Pekka Humaloja PhD Student Konsta Huhtala PhD Student Petteri Laakkonen University Teacher Find out more! sysgrouptampere.wordpress.com lassipaunonen.wordpress.com Youtube: Sysgroup Tampere L. Paunonen
Mathematical Systems Theory Research Group at TUT L. Paunonen
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