██ CLEARANCE: ALPHA-01  ·  MISSION: ENGAGE  ·  PLATFORM: SIM
ALT   10,000 M
VEL   1021.08 M/S
G-FORCE 32.6 G
T-I-M-E  00:08.00
Callsign: MAVERICK  ·  Autonomous Guidance  ·  2025

Guidance
Core
Maverick

I compared three autopilot guidance laws, SFI, LQR, and MPC, on missile longitudinal dynamics. MPC gave the fastest time to target at 8 seconds. I built it in MATLAB with CasADi/IPOPT.

8.00s
MPC Time to Target
IPOPT
NLP Solver
1021
M/S Velocity
3
Controllers Compared
MISSION ID: MAVERICK-01  ·  OBJECTIVE: INTERCEPT  ·  STATUS: COMPLETE
MODULE SFI  EAGLE
MODULE LQR  TALON
MODULE MPC  VIPER
13.8s
SFI time to target
baseline
10.0s
LQR time to target
optimal regulator
8.0s
MPC time to target
fastest · confirmed
6.06
MPC total Σ|u|
lowest effort
Mission footage
MATLAB simulation: SFI vs LQR vs MPC · Missile longitudinal dynamics · CasADi / IPOPT
Mission briefing

Engage.
Intercept.
Evaluate.

My goal was to compare three autonomous guidance laws on a linear short period missile model. I measured each controller on trajectory accuracy, control effort, and time to target. I ran the simulations in MATLAB. MPC was solved online with CasADi and IPOPT at every timestep, over a 50 step engagement.


The missile dynamics model uses Mracek & Ridgely's short period approximation. It is a two state system (angle of attack α, pitch rate q) driven by fin deflection δp. I confirmed controllability and observability analytically before I designed the controllers.


VIEW MISSION FILES ON GITHUB →
Controller dossiers

Three Pilots

Module SFI  ·  Callsign: EAGLE
State-Feedback Integral
Augmented state feedback with integral action. I placed the gains by pole placement on the augmented short period model. It has low average actuator effort. I used it as the baseline that I measured everything else against.
Speed
38
Accuracy
45
Efficiency
82
Module LQR  ·  Callsign: TALON
LQR with Integral
Optimal infinite horizon regulator. I solved the DARE to obtain K_aug = [K, K_i]. It gives zero steady state Az error, reliable transient response, and low compute cost. This makes it suitable for embedded autopilots.
Speed
62
Accuracy
95
Efficiency
71
Module MPC  ·  Callsign: VIPER
Model Predictive Control
Finite horizon NLP solved online with CasADi + IPOPT. It enforces the actuator bounds (u ∈ [−0.3, 0.2]) directly. It had the fastest engagement and the lowest total Σ|u|. It needs solver warm starting for real time ops.
Speed
95
Accuracy
68
Efficiency
88
Viper: MPC Formulation

Predictive
Intercept

I solve the MPC problem again at every timestep over a horizon of N=10 steps. The CasADi symbolic model uses discretised longitudinal dynamics. It minimises tracking cost plus control effort while it keeps the actuator bounds across the whole horizon.


A soft terminal constraint pushes the predicted 3D position toward the impact point [10500m, 300m]. This gives the controller spatial awareness beyond the immediate tracking goal.

  • State: α (angle of attack), q (pitch rate)
  • Control: δp (fin deflection), bounded [−0.3, 0.2] rad
  • Horizon: N=10, timestep Ts=0.1s, 50 simulation steps
  • Qy = diag([2, 0.5]), R = 1 for the tracking vs effort tradeoff
  • Terminal cost: Qterm = 0.01·I on 3D position error
  • 3D trajectory integrated symbolically inside the NLP
CasADi / IPOPT: MPC Loop
# Symbolic short-period dynamics x_next = Ad·x + Bd·u # Tracking cost across horizon cost += (Cx - y_ref)ᵀ · Qy · (Cx - y_ref) + u_k · R · u_k # 3D trajectory integrated symbolically x_pred(k+1) = x_pred(k) + Vel·cos(θ)·Ts z_pred(k+1) = z_pred(k) + Vel·sin(θ)·Ts # Soft terminal constraint → impact point cost += (p_N - target)ᵀ · Qterm · (p_N - target) # Solve with IPOPT, apply u[:,0] sol = nlpsol('ipopt', nlp, opts) u0 = sol.x[nx*(N+1):][:,0] # receding horizon
After-action report

Performance Matrix

Metric SFI: Eagle LQR: Talon MPC: Viper
Time to Target (s) 13.80 10.00 8.00 ✓
Avg Control Effort (rad) 0.04 0.10 0.08
Final Az Error (g) 19.91 0.00 ✓ 14.97
Total Control Effort Σ|u| 48.94 10.34 6.06 ✓

✓ = best in category  ·  MPC: fastest engagement and lowest total effort  ·  LQR: perfect steady state accuracy