Mathematical Analysis and Systems Theory Lassi Paunonen Assistant - - PowerPoint PPT Presentation

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

P

u(t) y(t)

Mathematical control theory studies differential equations d dtx(t) = Ax(t) + Bu(t), x(0) = x0 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.

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 −4 −2 2 4

z t

Figure: Controlled heat profile

−1 1 −1 1

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 efficiently as possible. − →

Damper locations

− →

• L. Paunonen

Mathematical Systems Theory

Example: Dynamics of Large Vehicle Formations

di di–1 di+1 vi+1 i+1 vi vi–1 wireless communication radar i–1 i

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