The re-solve-from-scratch loop
No training, no reward signal. Every control cycle, MPC measures the current state, solves an optimization problem against a known dynamics model over a horizon, applies only the first control, then throws the rest away and re-solves next cycle.
Cycle-time budgets across domains
The same re-solve loop has to fit inside wildly different deadlines depending on the plant — this is the range the book's real-time machinery has to cover, log-scaled.
Why structure exploitation matters
A naive dense Newton factorization over an N-step horizon costs O(N³). Because each stage only couples to its immediate neighbor — block-banded, not dense — a Riccati-style recursion solves the exact same problem in O(N).
The block-banded KKT matrix
Hover a cell. Each stage k only couples to k−1 and k+1 — everything off that band is exactly zero and never needs to be materialized.
Riccati recursion vs condensing
Riccati recursion is dynamic programming in a numerical-optimization costume: one backward sweep computing feedback gains, two cheap sweeps recovering the trajectory — linear in horizon length N. Condensing eliminates the states up front and collapses everything into one dense QP over the controls — cheaper for short horizons, especially when state dimension n dwarfs control dimension m.
Moving horizon estimation vs the Kalman filter
MHE is the optimization-based counterpart to the Kalman filter: a sliding window of recent measurements, re-solved every step, which is why it can enforce constraints a closed-form recursive filter can't (e.g. "this concentration can't go negative").
Why particle filtering got cut past 5 dimensions
The book drops particle filtering from its main text once state dimensionality climbs past five — sampling can't keep up. MHE's optimization-based approach sidesteps that specific failure mode.