MPC

ssqpy.solvers.MPC (ssqp::solvers::MPC in C++) is a thin helper around ssqp for real-time, receding-horizon control: it repeatedly re-solves the OCP for the system's current state with a small iteration budget, applies the first control of the resulting trajectory, and warm-starts the next solve from the previous solution plus fresh state feedback.

mpc = ssqpy.solvers.MPC(
    model,
    sqp_iters=5,
    qp_iters=50,
    keep_convergence_data=False,
)

mpc.reinitialize(initial_state)

while running:
    state = read_state_from_system()
    x, u = mpc.step(state)
    apply_controls(u.stage(0))

Parameters

MPC.Params (or keyword arguments to the constructor) cap the iteration budget independently of whatever ssqpParams/admmParams/hpipmParams are passed alongside them; the MPC-level sqp_iters and qp_iters are what actually bound the per-step solve time:

• sqp_iters: maximum SSQP iterations per MPC step (default keeps this low, e.g. 5–10, since MPC relies on warm-starting rather than solving to full convergence every step)

• qp_iters: maximum QP solver iterations per SSQP iteration

• keep_convergence_data: whether to retain per-step ssqpConvergenceData, retrievable via mpc.getConvergenceData(), for logging/analysis

Warm-starting

• reinitialize(state): reset the warm start to a given state with zero controls.

• reinitialize(states, controls): reset the warm start to full state/control trajectories.

• step(state): the typical receding-horizon call, using state as feedback for stage 0, and the previous solution (shifted) as the warm start for the rest of the horizon.

• step(states, controls): warm-start explicitly with the given trajectories instead of the previous solution.

• step(): advance using the current internal guess as-is.

Every step variant returns the full (x, u) FlatVec trajectories; in a control loop you typically only apply u.stage(0) before the next step call.

See examples/mujoco_mpc and examples/real_mpc for complete simulated and real-system MPC loops.