Sure, I can help with that. Below is a test case generator for the "Battle Town" problem statement.

```python
import random

def tcgen():
    T = random.randint(1, 100) # Number of datasets
    datasets = []

    for _ in range(T):
        H = random.randint(1, 20)  # Height of the map (1 ≤ H ≤ 20)
        W = random.randint(1, 20)  # Width of the map (1 ≤ W ≤ 20)

        # Generate a random map
        elements = ['.', '*', '#', '-', '^', 'v', '<', '>']
        map_ = []

        for i in range(H):
            row = "".join(random.choices(elements, k=W))
            map_.append(row)

        # Ensure there is exactly one tank on the map
        tank_positions = '^v<>'
        tank_placed = False
        while not tank_placed:
            r = random.randint(0, H - 1)
            c = random.randint(0, W - 1)
            if map_[r][c] == '.':
                map_[r] = map_[r][:c] + random.choice(tank_positions) + map_[r][c + 1:]
                tank_placed = True

        # Generate a random sequence of actions
        actions = 'UDLR' + 'S' * 5  # Add more 'S' to increase shooting probability
        action_sequence = "".join(random.choices(actions, k=random.randint(1, 100)))

        # Append the dataset
        datasets.append((H, W, map_, action_sequence))

    return T, datasets

# Example usage
if __name__ == "__main__":
    T, datasets = tcgen()
    print(T)
    for H, W, map_, action_sequence in datasets:
        print(H, W)
        for row in map_:
            print(row)
        print(action_sequence)
        print()  # Newline for separating datasets
```

This test case generator follows these steps:

1. Randomly determine the number of datasets \( T \) (1 ≤ \( T \) ≤ 100).
2. For each dataset:
   - Randomly determine the dimensions \( H \) (1 ≤ \( H \) ≤ 20) and \( W \) (1 ≤ \( W \) ≤ 20) of the map.
   - Generate a random map with `.` (flat terrain), `*` (brick wall), `#` (iron wall), `-` (water).
   - Ensure there is exactly one tank on the map (`^`, `v`, `<`, `>`).
   - Generate a random sequence of actions `U`, `D`, `L`, `R`, and `S`.
3. Return the number of datasets and the list of datasets.

This generator will help you create various test scenarios for the "Battle Town" problem.