Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

ABOUT ME

2013 - 2017
B. Sc. Mathematics

2017 - 2019
M. Sc. Scientific Computing

2019 - 2015
PhD Numerical Optimization (with Prof. Kostina)

Tennis

Mountains

Climbing
and
more

MOTIVATION FOR MY RESEARCH

Zeit Online, 10.01.25

Tagesschau, 10.01.25

Süddeutsche Zeitung, 10.01.25

Spiegel Online, 10.01.25

Frankfurter Allgemeine, 10.01.25

ZDF heute, 10.01.25

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

MOTIVATION FOR MY RESEARCH

Zeit Online, 10.01.25

Tagesschau, 10.01.25

Süddeutsche Zeitung, 10.01.25

Spiegel Online, 10.01.25

Frankfurter Allgemeine, 10.01.25

ZDF heute, 10.01.25

MSO

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

MOTIVATION

Zeit Online, 10.01.25

Tagesschau, 10.01.25

Süddeutsche Zeitung, 10.01.25

Spiegel Online, 10.01.25

Frankfurter Allgemeine, 10.01.25

ZDF heute, 10.01.25

MSO

Source: M.Minderhoud derivative work: Malyszkz, CC BY-SA 3.0 via Wikimedia Commons

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

MOTIVATION FOR MY RESEARCH

Zeit Online, 10.01.25

Tagesschau, 10.01.25

Süddeutsche Zeitung, 10.01.25

Spiegel Online, 10.01.25

Frankfurter Allgemeine, 10.01.25

ZDF heute, 10.01.25

MSO

Goal:

Develop efficient numerical methods for Nonlinear Model Predictive Control with applications in (Ecological) Adaptive Cruise Control systems

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

NONLINEAR MODEL PREDICTIVE CONTROL (NMPC)

At each sampling time:
 

1. Obtain current state

3. Use feedback value until next sampling time

2. Solve Optimal Control Problem (OCP) over

prediction horizon

Closed-loop control strategy

allows to react to disturbances

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

state
and
control

state
and
control

running and terminal costs

running and terminal costs

ODE model

ODE model

mixed state-control path constraints

+

boundary constraints

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}
\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{\Delta s\in\mathbb{R}^{n_s}\\\Delta q\in\mathbb{R}^{n_q}}} & &\frac{1}{2}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}^T\begin{pmatrix}B^{ss} & B^{sq} \\ B^{qs} & B^{qq}\end{pmatrix}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix} + \begin{pmatrix}b^s\\b^q\end{pmatrix}^T\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}\\ &\quad\text{s.\,t. }& 0 &= S_m^s\Delta s_m + S_m^q\Delta q_m - \Delta s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0 - \Delta s_0,&&\\ && 0 &\leq H_m^s\Delta s_m + H_m^q\Delta q_m + h_m,\quad m=0,\ldots,N-1,\\ && 0 &= R_{s_0}^\mathrm{e}\Delta s_0 + R_{s_M}^\mathrm{e}\Delta s_M + r^\mathrm{e},\\ && 0 &\leq R_{s_0}^\mathrm{i}\Delta s_0 + R_{s_M}^\mathrm{i}\Delta s_M + r^\mathrm{i}. \end{aligned}

tailored Sequential Quadratic Programming (SQP) method

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}
\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{\Delta s\in\mathbb{R}^{n_s}\\\Delta q\in\mathbb{R}^{n_q}}} & &\frac{1}{2}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}^T\begin{pmatrix}B^{ss} & B^{sq} \\ B^{qs} & B^{qq}\end{pmatrix}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix} + \begin{pmatrix}b^s\\b^q\end{pmatrix}^T\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}\\ &\quad\text{s.\,t. }& 0 &= S_m^s\Delta s_m + S_m^q\Delta q_m - \Delta s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0 - \Delta s_0,&&\\ && 0 &\leq H_m^s\Delta s_m + H_m^q\Delta q_m + h_m,\quad m=0,\ldots,N-1,\\ && 0 &= R_{s_0}^\mathrm{e}\Delta s_0 + R_{s_M}^\mathrm{e}\Delta s_M + r^\mathrm{e},\\ && 0 &\leq R_{s_0}^\mathrm{i}\Delta s_0 + R_{s_M}^\mathrm{i}\Delta s_M + r^\mathrm{i}. \end{aligned}

tailored  SQP method

Real-Time Iterations (RTI)

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}
\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{\Delta s\in\mathbb{R}^{n_s}\\\Delta q\in\mathbb{R}^{n_q}}} & &\frac{1}{2}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}^T\begin{pmatrix}B^{ss} & B^{sq} \\ B^{qs} & B^{qq}\end{pmatrix}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix} + \begin{pmatrix}b^s\\b^q\end{pmatrix}^T\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}\\ &\quad\text{s.\,t. }& 0 &= S_m^s\Delta s_m + S_m^q\Delta q_m - \Delta s_{m+1},\quad m=0,\ldots,M-1,\\ && 0 &= x^j - s_0 - \Delta s_0,&&\\ && 0 &\leq H_m^s\Delta s_m + H_m^q\Delta q_m + h_m,\quad m=0,\ldots,M-1,\\ && 0 &= R_{s_0}^\mathrm{e}\Delta s_0 + R_{s_M}^\mathrm{e}\Delta s_M + r^\mathrm{e},\\ && 0 &\leq R_{s_0}^\mathrm{i}\Delta s_0 + R_{s_M}^\mathrm{i}\Delta s_M + r^\mathrm{i}. \end{aligned}

Real-Time Iterations (RTI)

Multi-Level Iterations (MLI)

tailored  SQP method

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{x(\cdot),u(\cdot)} & \int_{t^j}^{t^j+T_\mathrm{hor}} &\Psi\left(x(t),u(t)\right) \ud t + \Phi\left(x(t^j+T_\mathrm{hor})\right)\\ &\quad\text{s.\,t. }& \dot{x}(t) &= f\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && x(t^j) &= x^j,&&\\ && 0 &\leq h\left(x(t),u(t)\right),\quad t\in[t^j,t^j+T_\mathrm{hor}],\\ && 0 &= r^{\mathrm{e}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right),\\ && 0 &\leq r^{\mathrm{i}} \left(x(t^j),x(t^j+T_\mathrm{hor})\right). \end{aligned}

modelling

Direct Multiple Shooting

\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{s\in\mathbb{R}^{n_s}\\q\in\mathbb{R}^{n_q}}} & \sum_{m=0}^{N-1} &\Psi_m\left(s_m,q_m\right) + \Phi\left(s_N\right)\\ &\quad\text{s.\,t. }& 0 &= x\left(\tau_{m+1};s_m,q_m\right)-s_{m+1},\quad m=0,\ldots,N-1,\\ && 0 &= x^j - s_0,&&\\ && 0 &\leq h\left(s_m,q_m\right),\quad m=0,\ldots,N-1,\\ && 0 &= r^{\mathrm{e}} \left(s_0,s_N\right),\\ && 0 &\leq r^{\mathrm{i}} \left(s_0,s_N\right). \end{aligned}
\newcommand{\ud}{\mathrm{d}} \begin{aligned} &\min_{\substack{\Delta s\in\mathbb{R}^{n_s}\\\Delta q\in\mathbb{R}^{n_q}}} & &\frac{1}{2}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}^T\begin{pmatrix}B^{ss} & B^{sq} \\ B^{qs} & B^{qq}\end{pmatrix}\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix} + \begin{pmatrix}b^s\\b^q\end{pmatrix}^T\begin{pmatrix}\Delta s \\ \Delta q\end{pmatrix}\\ &\quad\text{s.\,t. }& 0 &= S_m^s\Delta s_m + S_m^q\Delta q_m - \Delta s_{m+1},\quad m=0,\ldots,M-1,\\ && 0 &= x^j - s_0 - \Delta s_0,&&\\ && 0 &\leq H_m^s\Delta s_m + H_m^q\Delta q_m + h_m,\quad m=0,\ldots,M-1,\\ && 0 &= R_{s_0}^\mathrm{e}\Delta s_0 + R_{s_M}^\mathrm{e}\Delta s_M + r^\mathrm{e},\\ && 0 &\leq R_{s_0}^\mathrm{i}\Delta s_0 + R_{s_M}^\mathrm{i}\Delta s_M + r^\mathrm{i}. \end{aligned}

Real-Time Iterations (RTI)

Multi-Level Iterations (MLI)

our work

theoretical foundations

tailored  SQP method

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

OUR FRAMEWORK OF EFFICIENT NUMERICAL METHODS FOR NMPC

MY WORK

Smooth and shape preserving interpolation of multivariate look-up tables

Treating external inputs in Multiple Shooting, RTI and MLI

Sensitivity and external input scenario based (SensEIS) feedback

Leveraging our methods to realize an Adaptive Cruise Control System

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

Stability of inexact NMPC of semilinear parabolic PDEs

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

MY TIME AT THE SIAM CHAPTER

Chapter board in 2020

  • Board member from 2018 - 2022
  • President from 2019 - 2022
  • Helped organizing 12 events
  • Chapter representative at the SIAM conference in 2021

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

Talks

MY TIME AT THE SIAM CHAPTER

MY TIME AT THE SIAM CHAPTER

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

Bosch Center for AI

ZEISS

Deutscher Wetterdienst

Lufthansa Systems

Field
Trips

HOW THE SIAM CHAPTER HAS HELPED ME

Ihno Schrot — SIAM/GAMM Chapter Kick-Off — May 23rd 2025

As a chapter member:

INDUSTRY
INSIGHTS

NETWORK

RESEARCH
INSIGHTS

SOFT SKILLS

DEEPER
NETWORK

FRIENDS & FUN

As a board member:

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