Bandwidth reduction methods for packetized Model Predictive Control over lossy networks. Multi-horizon MPC formulation with communication-rate reduction for networked control systems. Use for: networked MPC, bandwidth-efficient control, 5G/IoT control systems, packetized control, offloaded MPC. Activation: packetized MPC, bandwidth reduction, networked control, multi-horizon MPC, lossy network control.
Controller design for offloaded Model Predictive Control operating over lossy communication channels with bandwidth-efficient transmission strategies.
This methodology addresses the challenge of implementing MPC when the controller is offloaded to a remote location (edge/cloud) and communicates with the plant over a lossy network. It introduces two complementary bandwidth-reduction methods:
| Method | Mechanism | Benefit |
|---|---|---|
| Multi-horizon MPC | Variable prediction steps | Fewer optimization variables |
| Rate reduction | Skip transmissions | Lower communication frequency |
Standard MPC: N uniform steps → N optimization variables
Multi-horizon MPC: Variable step sizes → fewer variables
Example:
- Step 1-2: Fine resolution (short steps)
- Step 3-5: Coarse resolution (longer steps)
- Result: Same prediction horizon, fewer variables
Implementation:
Strategy: Skip packet transmissions when possible
Standard: Transmit at every sampling instant
Proposed: Transmit only when necessary
Conditions for skipping:
- Predicted trajectory remains valid
- No significant disturbance detected
- Buffer contains valid control sequence
Buffer Management:
At each time step:
1. Run multi-horizon MPC (reduced variable count)
2. Decide: transmit new trajectory or use buffer?
3. If transmitting: send compressed trajectory
4. If not transmitting: apply buffered control
Theorem: Under minimal assumptions on packet loss, the system remains recursively feasible.
Assumptions:
Proof Sketch:
Guarantees hold for:
Even under:
For the rate-reduction strategy:
||y - y_ref|| ≤ ε
where ε depends on:
- Transmission rate
- System dynamics
- Disturbance magnitude
| Metric | Standard MPC | Proposed Method | Improvement |
|---|---|---|---|
| Bandwidth Usage | 100% | ~40% | 60% reduction |
| Computational Load | Baseline | ~70% | 30% reduction |
| Tracking Error | ε | 1.1ε | Minimal degradation |
def design_multi_horizon_steps(horizon, n_fine, n_coarse):
"""
Design non-uniform prediction horizon
Args:
horizon: Total prediction horizon
n_fine: Number of fine-resolution steps
n_coarse: Number of coarse-resolution steps
Returns:
step_sizes: Array of step sizes
"""
# Fine steps for immediate future
fine_steps = [1] * n_fine
# Coarse steps for distant future
coarse_step_size = (horizon - n_fine) / n_coarse
coarse_steps = [coarse_step_size] * n_coarse
return fine_steps + coarse_steps
def should_transmit(current_state, predicted_state, threshold):
"""
Decide whether to transmit new control packet
Args:
current_state: Current measured state
predicted_state: State predicted in last transmission
threshold: Deviation tolerance
Returns:
bool: True if transmission needed
"""
deviation = norm(current_state - predicted_state)
return deviation > threshold
class ControlBuffer:
def __init__(self, horizon):
self.buffer = []
self.horizon = horizon
def update(self, control_trajectory):
"""Store new control trajectory"""
self.buffer = control_trajectory.copy()
def get_control(self, k):
"""Get control at step k from buffer"""
if k < len(self.buffer):
return self.buffer[k]
else:
# Extrapolate or use terminal control
return self.buffer[-1]
def is_valid(self, current_time, last_receive_time, max_age):
"""Check if buffer is still valid"""
age = current_time - last_receive_time
return age < max_age
Cloud-Based MPC:
IoT Control Systems:
5G Industrial Control:
Multi-Agent Systems:
| Network Type | Loss Rate | Latency | Suitability |
|---|---|---|---|
| Wired Ethernet | <0.1% | <1ms | Excellent |
| WiFi | 1-5% | 5-50ms | Good |
| 4G | 1-10% | 20-100ms | Good |
| 5G | <1% | 1-10ms | Excellent |
| LoRaWAN | 5-30% | 100ms-2s | Fair |
| Method | Bandwidth | Robustness | Complexity |
|---|---|---|---|
| Standard MPC | High | Low | Low |
| Event-triggered | Medium | Medium | Medium |
| Packetized MPC | Low | High | Medium |
| Self-triggered | Low | Medium | High |
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