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07:15, 9 October 2025 RobertLampel talk contribs created page File:Compartmental OED.png
07:15, 9 October 2025 RobertLampel talk contribs uploaded File:Compartmental OED.png
07:12, 9 October 2025 RobertLampel talk contribs created page Compartmental OED (Created page with "{{Dimensions |nd = 1 |nx = 12 |nw = 1 }} The '''Compartmental OED problem''' looks for an optimal measurement strategy to determine a single parameter in a one-dimensional ODE model, where we can directly measure the single state. The following description is taken from TODO. Here we consider the open one-compartment model with first-order absorption input fitted by Button (unpublished Ph.D. thesis, Texas A&M University, 197...")
14:19, 25 August 2025 RobertLampel talk contribs created page File:Oscillating OED.png
14:19, 25 August 2025 RobertLampel talk contribs uploaded File:Oscillating OED.png
14:14, 25 August 2025 RobertLampel talk contribs created page Oscillating OED (Created page with "{{Dimensions |nd = 1 |nx = 4 |nw = 1 }} The '''Oscillating OED problem''' looks for an optimal measurement strategy to determine a single parameter in a one-dimensional ODE model, where can directly measure the single state. The optimal integer control functions shows bang bang behavior. == Mathematical formulation == For a single parameter <math>p</math> the original initial value problem is given...")
07:54, 25 August 2025 RobertLampel talk contribs created page File:LV Comp init 2.png
07:54, 25 August 2025 RobertLampel talk contribs uploaded File:LV Comp init 2.png
07:54, 25 August 2025 RobertLampel talk contribs created page File:LV Comp init 1.png
07:54, 25 August 2025 RobertLampel talk contribs uploaded File:LV Comp init 1.png
07:34, 25 August 2025 RobertLampel talk contribs created page LV Competitive (Created page with "{{Dimensions |nd = 1 |nx = 3 |nw = 1 }} This '''Lotka Volterra problem with explicit inclusion of a shared resource''' is a variant of the Lotka Volterra fishing problem. Its dynamics are given via a three-dimensional ODE model. == Mathematical formulation == The optimal control problem is given by <math> \begin{array}{llclr} \displaystyle \min_{u} & \int_0^{t_f} && (x_0(t) - 1)^2 + (x_1(t) - 1)^2 + (x_2(t) - 1)...")
07:14, 25 August 2025 RobertLampel talk contribs created page File:LV Shared init 2.png
07:14, 25 August 2025 RobertLampel talk contribs uploaded File:LV Shared init 2.png
07:14, 25 August 2025 RobertLampel talk contribs created page File:LV Shared init 1.png
07:14, 25 August 2025 RobertLampel talk contribs uploaded File:LV Shared init 1.png
06:48, 25 August 2025 RobertLampel talk contribs created page LV Shared Resource (Created page with "{{Dimensions |nd = 1 |nx = 3 |nw = 5 |nre = 3 }} This '''Lotka Volterra problem with explicit inclusion of a shared resource''' is a variant of the Lotka_Volterra_fishing_problem. Its dynamics are given via a three-dimensional Category:OED_model. == Mathematical formulation == The mixed-integer optimal control problem is given by <math> \begin{array}{llclr} \displaystyle \min_{x, w} & x_2(t_f) \\[1.5ex] \mbox{s.t.} & \d...")
13:32, 22 August 2025 RobertLampel talk contribs created page File:Exponential OED.png
13:32, 22 August 2025 RobertLampel talk contribs uploaded File:Exponential OED.png
13:11, 22 August 2025 RobertLampel talk contribs created page Exponential OED (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Exponential OED problem''' was formulated as minimal design problem that to highlight one important difference between single and multiple shooting. We are interested in finding an optimal experimental design to determine the parameter in a one-dimensional ODE model, where can directly measure the single state. The optimal integer control functions shows :Category:Chattering|b...")
12:38, 22 August 2025 RobertLampel talk contribs created page File:Van der Pol OED.png
12:38, 22 August 2025 RobertLampel talk contribs uploaded File:Van der Pol OED.png
11:39, 22 August 2025 RobertLampel talk contribs created page Van der Pol OED (Created page with "{{Dimensions |nd = 1 |nx = 11 |nw = 2 |nc = 4 |nre = 11 }} The '''Lotka Experimental Design problem''' looks for an optimal fishing strategy to be performed on a fixed time horizon to control the biomasses of both predator as prey fish as described in Lotka Volterra fishing problem. The goal here, however, is to minimize the uncertainty of a follow-up parameter estimation problem. In addition to the fishing decision the question whe...")
08:09, 22 August 2025 RobertLampel talk contribs created page File:Fermenter.png
08:09, 22 August 2025 RobertLampel talk contribs uploaded File:Fermenter.png
07:01, 22 August 2025 RobertLampel talk contribs created page Fermenter (Created page with "{{Dimensions |nd = 1 |nx = 9 |nw = 3 }} The '''Fermenter problem''' describes a fermentation process with two substrates <math>S_1</math> and <math>S_2</math> , and two products <math>P</math> and <math>G</math>. Enzyme biomass concentration is modeled by a state <math>E</math>. Further states are the fermentation volume <math>V</math> and the accumulated product <math>P_{\text{acc}}</math> and substrates <math>S_{1,\text{acc}}</math> and <math>S_{2...")
06:10, 22 August 2025 RobertLampel talk contribs uploaded a new version of File:Mountain Car.png
14:12, 21 August 2025 RobertLampel talk contribs created page File:Ocean.png
14:12, 21 August 2025 RobertLampel talk contribs uploaded File:Ocean.png
13:50, 21 August 2025 RobertLampel talk contribs created page Ocean (Created page with "{{Dimensions |nd = 1 |nx = 1 |nw = 1 }} The '''Ocean problem''' describes fossil fuel consumption and sequestration into the ocean [169]. It is a two box model where <math>S</math> describes the carbon stock in the atmosphere and upper layer ocean, <math>R</math> describes the carbon stock in fossil reserve and <math>D_L</math> the carbon stock in the deeper layer. The dynamics are given by an ODE model. The optimal control...")
13:14, 21 August 2025 RobertLampel talk contribs created page File:LQR.png
13:14, 21 August 2025 RobertLampel talk contribs uploaded File:LQR.png
13:14, 21 August 2025 RobertLampel talk contribs created page Linear Quadratic Regulator (Created page with "{{Dimensions |nd = 1 |nx = 1 |nw = 1 }} The '''Linear Quadratic Regulator problem''' is a one-dimensional toy ODE model which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term. The optimal integer control functions exhibits a singular arc. == Mathematical formulation == <math> \begin{array}{lll} \displaystyle \min_{x,w} && \int_0^{1...")
10:55, 21 August 2025 RobertLampel talk contribs created page File:Denbigh.png
10:55, 21 August 2025 RobertLampel talk contribs uploaded File:Denbigh.png
09:18, 21 August 2025 RobertLampel talk contribs created page Denbigh Reaction (Created page with "{{Dimensions |nd = 1 |nx = 3 |nw = 1 }} The '''Mountain Car problem''' s based on the system of chemical reactions initially considered by Denbigh (1958), which was also studied by Aris (1960) and more recently by Luus (1994): <math> \begin{align} A + B &\rightarrow X \\ X &\rightarrow Q \\ X &\rightarrow Y \\ A + X &\rightarrow P \end{align} </math> where X is an intermediate, Y is the desired product, and P and Q are waste prod...")
14:47, 20 August 2025 RobertLampel talk contribs created page File:Mountain Car.png
14:47, 20 August 2025 RobertLampel talk contribs uploaded File:Mountain Car.png
14:46, 20 August 2025 RobertLampel talk contribs created page Mountain Car (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Mountain Car problem''' proposes a vehicle stuck in a “well.” It lacks the power to directly climb out of the well, but instead must accelerate repeatedly forwards and backwards until it has achieved the energy necessary to exit the well. The problem is a popular machine learning test case. It first appeared in the PhD thesis of Andrew Moore in 1990. [Moo90]. The implementation here is taken from [...")
09:47, 20 August 2025 RobertLampel talk contribs created page File:Tubular Reactor.png
09:47, 20 August 2025 RobertLampel talk contribs uploaded File:Tubular Reactor.png
09:42, 20 August 2025 RobertLampel talk contribs created page Tubular Reactor (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Tubular Reactor problem''' is a two-dimensional ODE model. It aims to maximize the value of the second differential state at the end of the time interval. The optimal integer control functions exhibits a singular arc. == Mathematical formulation == <math> \begin{array}{lll} \displaystyle \min_{w} && -x_2(1) dt \\ \text{subject to} \...")
09:05, 20 August 2025 RobertLampel talk contribs created page File:Bryson-Denham.png
09:05, 20 August 2025 RobertLampel talk contribs uploaded File:Bryson-Denham.png
09:02, 20 August 2025 RobertLampel talk contribs created page Bryson Denham (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 1 }} The '''Bryson-Denham problem''' is a two-dimensional toy ODE model. It aims to minimize a quadratic Lagrange term. The optimal integer control functions exhibits a singular arc. == Mathematical formulation == <math> \begin{array}{lll} \displaystyle \min_{u} && \int_0^{1} \frac{1}{2} \cdot w(t)^2 dt \\ \text{subject to} \\ \quad \dot{x}(t)...")
08:24, 20 August 2025 RobertLampel talk contribs created page File:Rao Mease.png
08:24, 20 August 2025 RobertLampel talk contribs uploaded File:Rao Mease.png
07:54, 20 August 2025 RobertLampel talk contribs created page Rao Mease (Created page with "{{Dimensions |nd = 1 |nx = 1 |nw = 1 }} The '''Rao Mease problem''' is a very sensitive one-dimensional toy ODE model which is especially suited for multiple shooting solvers. It aims to minimize a quadratic Lagrange term. The optimal integer control functions shows bang bang behavior. == Mathematical formulation == <math> \begin{array}{lll} \displaystyle \min_{x,w} && \int_0^{10} (x(t)^2 + w(...")
07:25, 20 August 2025 RobertLampel talk contribs created page File:Toy OED.png
07:25, 20 August 2025 RobertLampel talk contribs uploaded File:Toy OED.png
06:43, 20 August 2025 RobertLampel talk contribs created page Toy OED (Created page with "{{Dimensions |nd = 1 |nx = 4 |nw = 1 }} The '''Toy OED problem''' looks for an optimal measurement strategy to determine a single parameter in a one-dimensional ODE model, where can directly measure the single state. The optimal integer control functions shows bang bang behavior. == Mathematical formulation == We are interested in estimating the parameters <math>p_2</math> and <math>p_4</math> of t...")