# Technical Document Extraction: Control Value Analysis ## Chart Title - **Title**: `C_I = 1e3, C_u = 1e-1` ## Axes Labels - **X-axis**: `Time (t)` - Range: `0` to `5` - Increment: `1` - **Y-axis**: `Control value (u_opt)` - Range: `0.0` to `0.7` - Increment: `0.1` ## Legend - **ODE**: Blue line - **KOL-δ**: Red line - **KOL-m**: Purple line ## Key Trends and Data Points 1. **ODE (Blue Line)** - Initial value: `0.7` at `t = 0` - Sharp drop to `0.45` at `t ≈ 0.5` - Stabilizes between `0.45` and `0.5` from `t ≈ 1` to `t ≈ 4` - Final value: `0.3` at `t = 5` 2. **KOL-δ (Red Line)** - Initial value: `0.7` at `t = 0` - Sharp drop to `0.3` at `t ≈ 0.5` - Oscillatory behavior with peaks at `0.55` (e.g., `t ≈ 2.5`, `t ≈ 3.5`) - Final value: `0.35` at `t = 5` 3. **KOL-m (Purple Line)** - Initial value: `0.4` at `t = 0` - Gradual decline to `0.35` at `t ≈ 4` - Minor fluctuations around `0.35` to `0.4` - Final value: `0.35` at `t = 5` ## Observations - **ODE** exhibits the most significant initial drop and stabilization. - **KOL-δ** shows erratic oscillations after the initial drop. - **KOL-m** demonstrates the smoothest decline with minimal fluctuations. - All lines converge near `0.35` at `t = 5`. ## Embedded Text - **Title Parameters**: - `C_I = 1e3` (Inflow coefficient) - `C_u = 1e-1` (Control coefficient)