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- 07:53, 3 February 2026 RobertLampel talk contribs uploaded File:Moon Landing.png
- 07:51, 3 February 2026 RobertLampel talk contribs created page Moon Landing (Created page with "{{Dimensions |nd = 1 |nx = 3 |nw = 2 }} The '''Moon Landing problem''' is a simplification of a spacecraft trying to land on the moon's surface. Its objective is to minimize the fuel consumption during the landing maneuver while landing savely on the ground with zero vertical velocity. The implementation here is taken from [1]. Its dynamics are given by a two-dimensional ODE model. == Mathematical formulatio...")
- 08:03, 27 January 2026 RobertLampel talk contribs created page File:Jackson OED.png
- 08:03, 27 January 2026 RobertLampel talk contribs uploaded File:Jackson OED.png
- 07:31, 27 January 2026 RobertLampel talk contribs created page Jackson OED (Created page with "{{Dimensions |nd = 1 |nx = 13 |nw = 3 }} The '''Jackson OED problem''' is a variation of the Jackson problem. It looks for optimal time intervals to measure the three states in order to minimize the uncertainty of a follow-up parameter estimation problem for the two unknown parameters. The mathematical equations form a small-scale ODE model. It also includes state sensitivities, the Fisher information matrix entries and...")
- 15:57, 26 January 2026 RobertLampel talk contribs created page File:Dielectrophoretic Particle OED.png
- 15:57, 26 January 2026 RobertLampel talk contribs uploaded File:Dielectrophoretic Particle OED.png
- 15:49, 26 January 2026 RobertLampel talk contribs created page Dielectrophoretic Particle OED (Created page with "{{Dimensions |nd = 1 |nx = 13 |nw = 3 }} The '''Dielectrophoretic Particle OED problem''' is a variation of the Dielectrophoretic Particle problem. It looks for optimal time intervals to measure the two states in order to minimize the uncertainty of a follow-up parameter estimation problem for the two unknown parameters. The mathematical equations form a small-scale ODE model. It also includes state sensitivities, the F...")
- 14:39, 20 January 2026 RobertLampel talk contribs uploaded a new version of File:Van der Pol OED.png
- 10:26, 25 November 2025 RobertLampel talk contribs created page File:Hang Glider.png
- 10:26, 25 November 2025 RobertLampel talk contribs uploaded File:Hang Glider.png
- 09:49, 25 November 2025 RobertLampel talk contribs created page Hang Glider (Created page with "{{Dimensions |nd = 1 |nx = 4 |nw = 2 }} The '''Hang Glider problem''' is a classical benchmark in optimal control. This description is taken from [1]. It consists of steering a hang glider from an initial horizontal position and altitude to a target altitude while maximising the horizontal distance travelled. The glider dynamics incorporate lift, drag, gravity, and the effect of a thermal updraft. The control variable is the lift coeff...")
- 12:06, 24 November 2025 RobertLampel talk contribs created page File:Robbins.png
- 12:06, 24 November 2025 RobertLampel talk contribs uploaded File:Robbins.png
- 12:01, 24 November 2025 RobertLampel talk contribs created page Robbins (Created page with "{{Dimensions |nd = 1 |nx = 3 |nw = 1 }} The '''Robbins problem''' is a classical benchmark in optimal control. This description is taken from [1]. == Mathematical formulation == <p> <math> \begin{array}{lll} \displaystyle \min_{u} && \int_0^T (\alpha \cdot x_1(t) + \beta \cdot x_1(t)^2 + \gamma \cdot u(t)^2) \\ \text{subject to} \\ \quad \dot{x_1}(t) & = & x_2(t)),\\ \quad \dot{x_2}(t) & = & x_3(t), \\ \quad \dot{x_3}(t) & = & u(t),...")
- 10:49, 24 November 2025 RobertLampel talk contribs created page File:Jackson.png
- 10:49, 24 November 2025 RobertLampel talk contribs uploaded File:Jackson.png
- 10:39, 24 November 2025 RobertLampel talk contribs created page Jackson (Created page with "{{Dimensions |nd = 1 |nx = 6 |nw = 3 }} The '''Jackson problem''' is a classical benchmark in optimal control. This description is taken from [1]. It consists of controlling a three-dimensional system in which the first two states interact linearly under the effect of a single control input, while the third state accumulates based on the complementary control. The objective is to minimise the third state at the final time, while satisf...")
- 10:33, 24 November 2025 RobertLampel talk contribs created page File:Ducted Fan.png
- 10:33, 24 November 2025 RobertLampel talk contribs uploaded File:Ducted Fan.png
- 10:02, 24 November 2025 RobertLampel talk contribs created page Ducted Fan (Created page with "{{Dimensions |nd = 1 |nx = 4 |nw = 1 }} The '''Ducted Fan problem''' is a classical nonlinear benchmark in optimal control with multiple input and state constraints. This description is taken from [1]. It models the planar motion of a ducted fan aircraft, described by its horizontal and vertical positions <math>( x_1 , x_2 )</math> , the angle <math>\alpha</math> with respect to the vertical, and their velocities <math>( v_1 , v_2 , v_...")
- 09:57, 24 November 2025 RobertLampel talk contribs uploaded a new version of File:Double Oscillator.png
- 09:56, 24 November 2025 RobertLampel talk contribs created page File:Double Oscillator.png
- 09:56, 24 November 2025 RobertLampel talk contribs uploaded File:Double Oscillator.png
- 09:30, 24 November 2025 RobertLampel talk contribs created page Double Oscillator (Created page with "{{Dimensions |nd = 1 |nx = 4 |nw = 1 }} The '''Double Oscillator problem''' is a benchmark in constrained optimal control illustrating the control of coupled mechanical systems with damping and stiffness effects. This description is taken from [1] It consists of two masses connected by springs and a damper, with one mass directly influenced by an external periodic force and the other influenced indirectly through the coupling and a con...")
- 09:18, 24 November 2025 RobertLampel talk contribs created page File:Dielectrophoretic Particle.png
- 09:18, 24 November 2025 RobertLampel talk contribs uploaded File:Dielectrophoretic Particle.png
- 08:57, 24 November 2025 RobertLampel talk contribs created page Dielectrophoretic Particle (Created page with "{{Dimensions |nd = 1 |nx = 2 |nw = 2 }} The '''Dielectrophoretic Particle problem''' is a classical time-optimal control benchmark for microfluidic particle manipulation. This description is taken from [1] It models the motion of a particle under a dielectrophoretic force, where the control voltage applied to electrodes directly influences the particle trajectory. Both the particle position and an auxiliary state related to its dipole...")
- 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 <p> <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 <p> <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...")
