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:
SIAM/GAMM Chapter Kick-Off
By Ihno Schrot
