# Technical Document Extraction: Control Value Over Time
## Chart Title
- **Title**: `C_I = 1, C_u = 0`
## Axes
- **X-axis (Horizontal)**:
- Label: `Time (t)`
- Range: `0` to `5`
- Ticks: Incremented by `1`
- **Y-axis (Vertical)**:
- Label: `Control value (u_opt)`
- Range: `0.0` to `0.7`
- Ticks: Incremented by `0.1`
## Legend
- **ODE**: Solid blue line
- **KOL-δ**: Dashed red line
- **KOL-m**: Dashed purple line
## Key Trends
1. **ODE (Blue Line)**:
- Starts at `0.7` at `t = 0`.
- Decreases stepwise to `0.0` by `t = 5`.
- Sharp transitions between discrete control values.
2. **KOL-δ (Red Dashed Line)**:
- Begins at `0.5` at `t = 0`.
- Exhibits frequent fluctuations between `0.1` and `0.7`.
- Ends at `0.1` at `t = 5`.
3. **KOL-m (Purple Dashed Line)**:
- Starts at `0.6` at `t = 0`.
- Remains relatively stable compared to KOL-δ, with minor fluctuations.
- Ends at `0.0` at `t = 5`.
## Observations
- All three control strategies exhibit stepwise behavior, suggesting discrete control actions.
- ODE demonstrates the most significant overall decline in control value.
- KOL-δ shows the highest variability, while KOL-m maintains moderate stability.
- All strategies converge to `0.0` by `t = 5`, indicating a shared endpoint in control value.
