Ihno Schrot — The Story Behind the Professional — December 16th 2025

MY CV

2013 - 2017
Bachelor
Mathematics

Internship
2016

Consultant
2017

Student Assistant
2017

2017 - 2019
Master Scientific
Computing

2019 - 2025
PhD
Numerical
Optimization

Scientist for Optimization Algorithm Development
since 2025

Ihno Schrot — The Story Behind the Professional — December 16th 2025

BACHELOR STUDIES

2013 - 2017 Bachelor Mathematics

PDEs and Cellular Automata for Modelling Inflammatory Processes

Thesis

Integer and Linear Programming 

Focus

Physics

Minor

Ihno Schrot — The Story Behind the Professional — December 16th 2025

DEUTSCHES ZENTRUM FÜR LUFT- UND RAUMFAHRT

2016/2017 Internship and Student Assistant

Integer
(and a bit Dynamic) Programming

Focus

Algorithms for Dial-a-Ride Problems for the "Reallabor Schorndorf"

Student Assistant

Traffic Light Algorithms

Internship

Ihno Schrot — The Story Behind the Professional — December 16th 2025

SIDEWALK LABS

2017 Consultant

Evaluation and Presentation

Focus

 Improving Urban Infrastructure Through Technological Solutions

Purpose

Traffic Light Algorithms
V2X-Communication
Platooning

Traffic Simulations

Ihno Schrot — The Story Behind the Professional — December 16th 2025

PHD STUDIES

2019 - 2025 PhD Numerical Optimization

Application

Algorithms

Theory

Teaching

Ihno Schrot — The Story Behind the Professional — December 16th 2025

MOTIVATION FOR MY PHD PROJECT

Bildquellen: jcomp, bzw. rawpixel.com, auf Freepik

Adaptive Cruise Control (ACC)

  • Driving Assistance System
  • Cruise Control + Distance Control

Ecological ACC (EACC)

  • Vary distance to preceding vehicle (PP0)
  • Leverage traffic and route data \(\rightarrow\) Save energy

\(\rightarrow\) Nonlinear Model Predictive Control (NMPC)

  • Handling tabulated data and external inputs
  • Limited computational power of onboard hardware  

Challenges for Numerical NMPC Methods

NONLINEAR MODEL PREDICTIVE CONTROL (NMPC)

At each sampling time point:

1. Get current state

3. Use feedback value until next

sampling time point

2. Solve optimal control problem (OCP) over

prediction horizon

Closed-loop Control Strategy \(\rightarrow\) allows to react to disturbances

Ihno Schrot — The Story Behind the Professional — December 16th 2025

FRAMEWORK TO EFFICIENTLY SOLVE PARAMETRIZED OCPS

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

State
and
Control

Running and terminal costs

ODE model

Mixed state and control constraints
+
boundary conditions

Modelling

Ihno Schrot — The Story Behind the Professional — December 16th 2025

State
and
Control

Running and terminal costs

ODE model

FRAMEWORK TO EFFICIENTLY SOLVE PARAMETRIZED OCPS

\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}

\(\infty\) - dimensional OCP

Modelling

Multi-Level Iterations (MLI)
[Wirsching, 2018]

Real-Time Iterations (RTI)
[Diehl et. al, 2002]

\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}

Nonlinear Program (NLP)

Direct Multiple Shooting (DMS)
[Bock, Plitt 1984]

  • [Bock, Plitt, 1984] H. G. Bock and K. J. Plitt. “A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems”. In: IFAC Proceedings Volumes 17.2 (1984). 9th IFAC World Congress: A Bridge Between Control Science and Technology, Budapest, Hungary, 2-6 July 1984, pp. 1603–1608
  • [Diehl et. al., 2002] M. Diehl, H. G. Bock, J. P. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer. “Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations”. In: Journal of Process Control 12.4 (2002), pp. 577–585
  • [Wirsching, 2018] L. Wirsching. “Multi-level iteration schemes with adaptive level choice for nonlinear model predictive control”. PhD thesis. Heidelberg University, 2018
\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}

Quadratic Program (QP)

Tailored
SQP-Method

Ihno Schrot — The Story Behind the Professional — December 16th 2025

MULTIPLE SHOOTING DISCRETIZATION

  • [Bock, Plitt, 1984] H. G. Bock and K. J. Plitt. “A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems”. In: IFAC Proceedings Volumes 17.2 (1984). 9th IFAC World Congress: A Bridge Between Control Science and Technology, Budapest, Hungary, 2-6 July 1984, pp. 1603–1608

Ihno Schrot — The Story Behind the Professional — December 16th 2025

  1. Introduce Shooting Grid
     
  2. Replace state trajectory by points
     
  3. Replace control trajectory by, e.g., piecewise constant controls
     
  4. Introduce Matching Conditions
     
  5. Constraints  and objective functions are evaluated only at shooting nodes

Control $$u(\cdot)$$

s_0
s_1
s_2
s_N
q_0
q_1
q_2
q_{N-1}
\underbrace{x(\tau_{i+1};s_i,q_i)} - s_{i+1} = 0

Infinite-Dimensional

\tau_0
\tau_1
\tau_N

State $$x(\cdot)$$

SEQUENTIAL QUADRATIC PROGRAMMING

Ihno Schrot — The Story Behind the Professional — December 16th 2025

\begin{aligned} &\min_x & & f(x)\\ & ~~\text{s.t.} & & g(x) = 0 \end{aligned}
F(x)=0

Nonlinear System of Equations

SQP Method

Step of Newton's Method

Optimality Conditions

Quadratic Approximation

Quadratic Program

\begin{aligned} &\min_{\Delta x} & &\frac{1}{2}\Delta x ^T \nabla_{xx}^2\mathcal{L}\left(x_k,\lambda_k\right)\Delta x + \nabla_x f(x_k)^T\Delta x\\ & ~~\text{s.t.} & & g(x_k) + \nabla_x g(x_k)^T \Delta x_k = 0 \end{aligned}

Step $$\Delta x$$

Current Guess $$x_k$$

Solving the QP

Update

FOCUS OF MY THESIS

Ihno Schrot — The Story Behind the Professional — December 16th 2025

Application:
EACC

  • Realistic test problem with
    real look-up tables and driving data

  • Numerical tests

Stability
of
Inexact NMPC

  • OCP semilinear parabolic PDEs

  • Proof of asymptotic stability
    of system-optimizer-dynamics

Shape-
Preserving
Interpolation

  • Classification for multivariate case

  • Method for multivariate, shape-preserving, smooth interpolation

Incorporate external inputs in
- DMS
- RTI
- MLI

External
Inputs

  • Scenario-based online feedback

  • Online effort: matrix-vector-product or QP-solve

SensEIS
FEEDBACK

OUTSIDE OF WORK

Mountains

More Sports

Tennis

Ihno Schrot — The Story Behind the Professional — December 16th 2025

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