Closed-loop control¶

This page compares complete controllers. Each benchmark problem runs a full simulated episode, solving one optimization problem per control step, once with Scaly's generated functions and once with CasADi's. Everything else stays the same:

SQP runs Scaly's sequential quadratic programming solver, with PIQP for the quadratic subproblems.
IPOPT runs the same IPOPT 3.14.19 library on both sides.

The time per step is the solver's own time, averaged over every step of the episode and over five fresh processes. It leaves out Python, the plant simulation and building the controller.

Where the time goes¶

Each bar splits the step into function evaluation, the objective, constraint and derivative values the solver asks for, and the rest of the solver's work. Each problem has its own time axis.

The rest of the solver takes about the same time on both sides, as it should, since it is the same code. What changes is function evaluation. It dominates unbumpercars, which evaluates a neural network for every pair of cars, so there Scaly makes the whole step 7 to 9× faster. On the race car, function evaluation was already a small part of the step, and the whole step gets only 5 to 7% faster.

Measured times¶

Problem	Solver	Scaly, ms	CasADi, ms	Speedup	Function-evaluation speedup
Race-car MPC	SQP	2.49	2.67	1.07×	4.2×
Race-car MPC	IPOPT	4.71	4.96	1.05×	2.1×
Neural-process MPC	SQP	1.27	1.84	1.45×	2.2×
Neural-process MPC	IPOPT	3.61	4.48	1.24×	1.8×
Chain of masses	SQP	6.27	14.43	2.30×	53×
Chain of masses	IPOPT	6.78
Unbumpercars	SQP	11.33	106.58	9.41×	10.5×
Unbumpercars	IPOPT	21.11	146.56	6.94×	8.3×

Times are per control step. The benchmark has no CasADi version of the chain controller with IPOPT.

Do both sides do the same work?¶

Both sides should take the same solver iterations and ask for the same function evaluations at every step, since only the source of the generated functions changes. They do for every controller except unbumpercars with SQP, where 5 of the 1,000 steps take a different number of iterations. The two trajectories still agree to within 5×10⁻⁹, but that controller's speedup compares slightly different amounts of work.