Control Strategies — Cross-Cutting Comparison

This note compares every control strategy referenced across the Engineering library — PID (Ziegler-Nichols / Cohen-Coon / IMC / lambda tuning), state-space (LQR / LQG / pole-placement), MPC (linear / nonlinear NMPC / economic EMPC / tube / robust), adaptive (MRAC / STC), robust (H-infinity / mu-synthesis / sliding-mode), nonlinear (feedback linearization / backstepping / Lyapunov), data-driven (system ID / DMDc / Koopman / EDMD / SINDy), learning-based (RL — policy gradient / SAC / PPO / iLQR), event-triggered, distributed/consensus, gain scheduling, fuzzy, neural — on model knowledge required, computational budget, robustness, hard-constraint handling, online vs offline, MIMO support, and criticality. Decision tree at the end picks by model availability, constraints, actuator/sensor budget, and safety class.

See also

• classical-control
• state-space-methods
• mpc-control
• adaptive-control
• h-infinity-robust
• sliding-mode-control
• digital-control
• system-identification
• gnc
• spacecraft-attitude-control
• pid-control
• mpc-for-robots
• impedance-control
• rl-for-control

1. The taxonomy

LINEAR SISO                           LINEAR MIMO STATE-SPACE
  P / PI / PID                         pole-placement
   ↳ Ziegler-Nichols 1942               LQR (Kalman 1960)
   ↳ Cohen-Coon 1953                    LQG (Kalman + LQR + Kalman filter)
   ↳ IMC tuning (Rivera-Morari 1986)    H-infinity (Doyle-Glover-Khargonekar-Francis 1989)
   ↳ Lambda tuning (Smith-Corripio)      μ-synthesis (Doyle-Wall-Stein 1982)
   ↳ AMIGO (Åström-Hägglund 2004)        observer-based output feedback
  lead/lag, PI w/ feedforward
  notch / anti-windup                  ADAPTIVE
                                         MRAC (Model Reference Adaptive Control)
PREDICTIVE / OPTIMIZATION                STC (Self-Tuning Control)
  Linear MPC (Cutler-Ramaker DMC 1980)   L1-adaptive
  Linear MPC (Richalet IDCOM 1976)       gain scheduling
  NMPC (nonlinear MPC)                   Lyapunov-based parameter adaptation
  Economic MPC (Rawlings et al)
  Tube MPC (robust)                    NONLINEAR
  Explicit MPC (Bemporad et al 2002)     feedback linearization
  Stochastic MPC                         backstepping (Krstic et al 1995)
  Distributed MPC                        Lyapunov-based design
  Hierarchical MPC                       sliding-mode control (Utkin 1977)
                                         super-twisting (Levant 2003)
LEARNING / DATA-DRIVEN                   high-gain observer
  iterative learning control (ILC)
  RL (PPO, SAC, DDPG, TD3, A2C)       SAFETY-CRITICAL
  iLQR / DDP (differential dyn prog)     control barrier functions (CBF, Ames et al 2019)
  Model-based RL (PILCO, MBPO)           safety filters
  Imitation learning                     supervisory control (Ramadge-Wonham 1987)
  Koopman operators (Williams-Kevrekidis-Rowley 2015)
  Dynamic Mode Decomposition + control (DMDc)
  SINDy + control (Brunton et al 2016)
  Neural ODEs for control

OTHER                                  COMMUNICATION-AWARE
  Fuzzy logic control (Mamdani 1975)     event-triggered control
  Neural network control                 self-triggered control
  Cascade control                        networked control (delays, dropouts)
  Override / split-range                 distributed consensus control
  Feedforward / disturbance rejection

2. The model-knowledge axis — the deciding question

Strategy	Model required	Model fidelity needed
PID	none (or step-test fit)	low — first-order + dead time often enough
Gain scheduling	LTI at operating points	per-point linearization
Pole-placement	LTI state-space (A, B, C)	accurate (placement is sensitive)
LQR	LTI (A, B) + cost weights (Q, R)	accurate; sensitive to Q/R selection
LQG	LTI + noise covariances (W, V)	accurate
H-infinity	LTI + weighting filters	accurate; weights are design knobs
μ-synthesis	LTI + uncertainty structure	accurate model + uncertainty bounds
Sliding-mode	bound on uncertainty	qualitative — knows magnitude of disturbance
Linear MPC	LTI (A, B) + constraint set	accurate over horizon
NMPC	nonlinear ODE/DAE + constraints	accurate (online integration)
Tube MPC	nominal + uncertainty set	accurate nominal + bound on uncertainty
Adaptive (MRAC, STC)	structure + uncertain parameters	structural + parameter ID online
Backstepping / FB linearization	exact nonlinear model	very accurate (assumes invertibility)
iLQR / DDP	nonlinear model	accurate, gradients differentiable
MBRL (PILCO, MBPO)	learned approximate model	partial — learns from data
Model-free RL (PPO, SAC)	none	n/a — learns from interaction
Imitation learning	none (expert demos)	n/a — learns from demos
ILC	repeat structure of task	model not strictly required; converges over trials
Fuzzy logic	linguistic rules	qualitative

PID is so dominant in industry (~90% of regulatory loops) precisely because it needs no model — a step test gives you a first-order-plus-dead-time fit and the tuning rule does the rest. Modern model-based controllers (MPC, H-infinity, NMPC) need accurate models, which is expensive to identify and maintain.

3. Computational budget — when can you afford which?

Strategy	Online compute / step	Memory	Typical update rate
PID	nanoseconds	bytes	1 kHz–100 kHz easily
Lead/lag	nanoseconds	bytes	100 kHz
Pole-placement / state feedback	µs	KB	10 kHz–1 MHz (FPGA)
LQR (precomputed gain)	µs	KB	10 kHz–1 MHz
LQG (precomputed Kalman + LQR)	µs	KB	10 kHz
Linear MPC (QP, embedded)	100 µs – 10 ms (depends on horizon × vars)	MB	100 Hz – 1 kHz (auto, drone, motor)
Linear MPC (large industrial DMC)	100 ms – 5 s	MB	1 Hz typical (process industry)
NMPC	10–100 ms (with NLP solver)	MB	10–100 Hz (drone)
Tube MPC	similar to LMPC + offline robust set	MB	similar
Explicit MPC	µs (lookup table)	MB–GB (piecewise affine table)	1 kHz easily
H-infinity (precomputed)	µs	KB	10 kHz
μ-synthesis (precomputed)	µs	KB	10 kHz
Sliding-mode	µs	bytes	10 kHz
Adaptive (MRAC)	µs	KB	1–10 kHz
iLQR / DDP (each trajectory opt)	ms–s (offline or per task)	MB	n/a — trajectory optimizer
Model-free RL (deployment)	µs (NN forward pass)	MB	1 kHz (after training)
Model-free RL (training)	hours-days	GB	n/a
Imitation learning (deployment)	µs (NN forward pass)	MB	1 kHz
Fuzzy (Mamdani)	µs	KB	1 kHz

Embedded MPC is the surprising-growth area. By 2024, solvers like qpOASES, HPIPM, OSQP, FORCES PRO, ACADO Toolkit, do-mpc, CasADi make 100 Hz MPC viable on Cortex-M / TI C2000 / NVIDIA Jetson. NVIDIA Drive, Tesla Autopilot, Boston Dynamics Atlas, Skydio drones all run MPC online.

4. Constraint handling — the MPC kingdom

Strategy	Hard constraints natively?	Soft constraints?	Multiple objectives
PID + anti-windup	NO (clamping via anti-windup, fragile)	partial	no — SISO
Override / split-range	partial	partial	hierarchical
LQR / LQG	NO	NO (penalize in cost)	weighted-sum
H-infinity	NO	partial via weighting	frequency-domain trade-off
Sliding-mode	NO	NO	stabilization-only
MPC	YES (in QP)	YES (slack variables)	YES (Pareto cost weights)
Tube MPC	YES (under uncertainty)	YES	YES
Stochastic MPC	chance constraints (P[X ∈ S] ≥ 1-α)	YES	risk-aware
NMPC	YES (nonlinear constraints)	YES	YES
Model-free RL (with safety wrapper)	partial (via penalty in reward)	yes	YES (reward shaping)
CBF (control barrier function)	YES (filter-based)	partial	safety + nominal control

MPC’s defining advantage is native constraint handling. Refinery, distillation column, autonomous vehicle path planning, drone trajectory tracking — anywhere actuator saturation, slew limits, or safety limits are routinely active, MPC dominates.

5. MIMO and cross-coupling

Strategy	MIMO?	Notes
PID	SISO; n × n decentralized	works if cross-coupling small or operator-detuned
Decoupling (BIH, RGA)	SISO + static decouplers	works for moderate coupling
Pole-placement / LQR	MIMO native	the canonical MIMO method
H-infinity	MIMO native	excellent for ill-conditioned plants
Decentralized MPC	MIMO partial (per-subsystem)	scalable, ignores interactions
Centralized MPC	MIMO native	optimal but doesn’t scale
Hierarchical MPC	MIMO via plant decomposition	scalable + accounts for interaction
NMPC	MIMO native	computational cost is the limit
Sliding-mode	MIMO partial	requires careful sliding surface design
Backstepping	MIMO	recursive design

For a 50-variable refinery column, PID with operator-tuned interaction overrides has been the practical workhorse since 1970, and DMC-class linear MPC sits on top to coordinate. Centralized MIMO MPC is theoretically optimal but practically dominated by hierarchical / decentralized variants for any plant > ~20 manipulated variables.

6. Robustness — handling model uncertainty

Strategy	Robustness story
PID	empirical robustness via low gain + low bandwidth
Gain scheduling	piecewise LTI; assumes slow operating-point change
H-infinity	minimize
μ-synthesis	structured uncertainty Δ; D-K iteration
Sliding-mode	bounded uncertainty; chattering reduction via boundary layer or super-twisting
Robust MPC (tube)	nominal + tube around it; constraint tightening
Stochastic MPC	chance constraints; assumes stochastic model
Adaptive	online parameter ID handles uncertainty
Backstepping w/ Lyapunov	Lyapunov-stable under bounded uncertainty
RL (domain randomization)	trained over distribution of dynamics

H-infinity is the canonical robust design. μ-synthesis improves on it by handling structured uncertainty (e.g., parameters ranging over an interval). Both became dominant in aerospace flight control in the 1990s–2000s (F-117, JSF, X-31).

7. Stability proofs — what’s available

Strategy	Stability tool
Linear MPC	Lyapunov function = optimal cost (Mayne-Rawlings 2000; Mayne et al Constrained Linear MPC 2018)
LQR	Riccati equation + Schur decomp
H-infinity	Riccati + γ-iteration
Sliding-mode	Lyapunov function = sliding surface²
Backstepping	virtual control + recursive Lyapunov
Feedback linearization	exact cancellation; assumes invertibility
NMPC	terminal cost + invariant set (Rawlings)
Adaptive	Lyapunov-Krasovskii / barrier
RL	empirical (no general stability proof for deep RL)
CBF	invariance of safe set under filter
ILC	contraction mapping on trial space

The Mayne-Rawlings 2000 paper “Constrained Linear Model Predictive Control: Stability and Optimality” was the seminal MPC stability result and remains the textbook proof.

8. Real-world applications — strategy to industry

Strategy	Industry / application
PID	every regulatory loop — refinery temperature, distillation reflux, paper machine consistency, HVAC zone, hard disk head, beam current in particle accelerators, blood-glucose pump, EV battery thermal, motor speed/torque, drone attitude inner loop
Cascade PID	hot end of plastic extruder, jet engine fuel + spool speed
DMC / IDCOM (linear MPC)	5000+ refineries, petrochemicals, pulp & paper, cement; Honeywell Profit Controller, AspenTech DMC3, Yokogawa Exasmoc
NMPC	autonomous racing (drones, F1-style), Boston Dynamics Spot/Atlas, ITER plasma control, oil-platform stationkeeping
Embedded MPC	EV powertrain torque-vectoring (Tesla, Rivian, Lucid), HVAC building MPC (Carrier, Daikin BACS), drone trajectory (Skydio, DJI Inspire)
LQR / LQG	aerospace inner loops, missile autopilots, helicopter blade control
H-infinity / μ-synthesis	flight control (F-117, F-22, F-35, JSF, X-31, X-29), satellite attitude (CNES, ESA missions), high-speed rail tilting (Pendolino)
Sliding-mode	satellite attitude (low-cost smallsats), brushless motor torque control, robot manipulator
Adaptive (MRAC)	aircraft autopilot post-failure (Rohrs et al 1985 cautionary tale); modern reborn via L1-adaptive (Hovakimyan-Cao 2010)
Gain scheduling	aircraft envelope (every commercial jet), gas turbine startup, missile autopilot
iLQR / DDP	ANYmal quadruped (RSL ETH Zurich), Boston Dynamics Atlas, Tesla Optimus footstep planning
Model-based RL (MBPO, PILCO)	research; some published demos in robotics
Model-free RL (PPO, SAC)	OpenAI Five Dota 2, DeepMind AlphaStar, AlphaFold-RL, ANYmal sim-to-real (Hwangbo et al 2019), Boston Dynamics Atlas dancing (partial), Google data-center cooling (DeepMind 2016, 40% energy savings)
Imitation learning (BC + DAgger)	Tesla Autopilot perception-to-control parts, robotic manipulation foundation models (RT-2, Octo, OpenVLA)
ILC	semiconductor lithography wafer-stage (ASML), printed circuit board pick-and-place, rotorcraft repeated maneuvers
Koopman operators / DMDc	fluid systems, structural control, building control
SINDy	research (Brunton et al); discovers governing eqns from data
CBF (control barrier functions)	autonomous driving safety filter (Ames et al), adaptive cruise control safety, robot manipulation safety wrapper
Networked / distributed	grid frequency, smart-grid voltage, multi-vehicle platooning
Event-triggered	low-power IoT control, networked sensor systems
Fuzzy	Japanese consumer products (Hitachi train brake 1987, Sony camcorder auto-focus), still common in HVAC

9. Online vs offline computation

Strategy	Offline	Online
PID	tuning + scheduling	execution
State feedback / LQR	gain computation	matrix multiply
H-infinity / μ-synthesis	full design + γ-iteration	matrix multiply
Sliding-mode	surface design	execution
MPC	constraint set, terminal weights	QP / NLP solve per step
Explicit MPC	piecewise affine table (offline)	table lookup
Adaptive	reference model	online ID + update
iLQR / DDP	none	trajectory rollout + backward pass
Model-free RL	training (hours-days-weeks)	NN forward pass
Imitation learning	training	NN forward pass
ILC	trial structure	trial-by-trial update

The explicit MPC (Bemporad-Borrelli-Morari 2002) story is unique — solve the parametric QP offline, store the resulting piecewise-affine control law as a lookup table. Microcontroller-friendly execution at 100 kHz; impractical for large state dimensions because the table explodes.

10. Safety / criticality — which is OK for what?

Strategy	DAL / SIL-suitability	Notes
PID	DAL A / SIL 3 routinely	extensively certified; mature analysis
State feedback / LQR	DAL A / SIL 3	aerospace standard
H-infinity / μ-synthesis	DAL A / SIL 3	aerospace certification path well-known
Sliding-mode	DAL B-C; less mature certification	chattering concerns; super-twisting safer
MPC (linear)	DAL B; growing acceptance	EASA / FAA evaluating
NMPC	DAL B-C; mostly research	online solver non-determinism is the hurdle
Adaptive	historically problematic (Rohrs et al 1985); L1-adaptive (2010) certifiable	F-35 partial use
RL	DAL D / not certified	safety filters (CBF) are how it gets close
Imitation learning	DAL D	no proofs
ILC	DAL B-C	repeatable systems

In aviation (DO-178C), nuclear (IEC 61508), automotive (ISO 26262), railway (CENELEC EN 50128), medical (IEC 62304) — PID + state-feedback / LQR are the certifiable defaults. Anything beyond requires extensive validation; ML-based controllers (RL, IL) live in DAL D / non-safety functions or are filtered through verifiable safety layers (CBF, supervisory control).

11. Data-driven and learning-based — the 2020–2026 wave

Method	Origin	What’s new
DMDc (Proctor-Brunton-Kutz 2016)	DMD for controlled systems	linear surrogate from data
Koopman + control (Korda-Mezić 2018, Williams et al 2015)	Koopman lifting + LMPC	data-driven linear MPC
EDMD (Extended DMD, Williams et al 2015)	Koopman with dictionary	scales to high-dim
SINDy + control (Brunton-Proctor-Kutz 2016)	sparse identification of nonlinear dynamics	discovers governing eqns
MPC via Gaussian Process	Hewing-Kabzan-Zeilinger 2017+	GP as data-driven nonlinear model
Diff-DP / iLQR through learned dynamics	DeepMind, Google Brain 2018+	differentiable simulator
PILCO (Deisenroth-Rasmussen 2011)	model-based RL w/ GP	sample-efficient
MBPO (Janner et al 2019)	Dyna-style + NN model	sample efficient
PPO (Schulman et al 2017)	clipped policy gradient	dominant model-free for robot
SAC (Haarnoja et al 2018)	max-ent off-policy	continuous control gold standard
iLQR/DDP at scale (Tassa et al 2014; modern MuJoCo/PhysX integrations)	trajectory opt	quadruped, humanoid
Diff-MPC (Amos et al 2018)	embed MPC in NN	hybrid IL + MPC
Domain randomization (Tobin et al 2017, Peng et al 2018)	sim-to-real	broad applicability
Iterative LQR with learned residuals	hybrid model + learning	autonomous racing
Foundation models for control (RT-2, OpenVLA 2024)	VLA models	imitation learning at scale
Diffusion policies (Chi et al 2023)	denoising diffusion as policy	smooth multimodal actions

12. The certification + verifiability question

Approach	Verification
Lyapunov + Linear (PID, LQR, LQG, H∞)	Lyapunov function + Hurwitz; numeric robustness margins
MPC	invariant set + terminal cost; formal recursive feasibility proofs
Sliding-mode	Lyapunov + reaching time bound
Adaptive	Lyapunov-Krasovskii w/ persistent excitation
ILC	norm-contraction in trial space
RL / IL	empirical only; formal verification an open problem
CBF / safety filter	invariance proof of safe set

Modern aerospace + automotive practice: use ML/RL for perception and high-level planning; use classical control for the low-level safety-critical loops; apply CBF as a safety filter between.

13. Decision tree — pick a control strategy

What do you have / need?
├─ No model, slow plant, SISO, single controlled variable
│    → PID. Tune via Ziegler-Nichols or IMC. Stop here.
├─ Slow plant, MIMO with weak coupling
│    → Decentralized PID + override / split-range / cascade.
├─ Slow plant, MIMO with strong coupling + constraints
│    → Linear MPC (DMC / Profit Controller / AspenTech DMC3).
│    → Hierarchical: PID inner loops + MPC supervisor.
├─ Aerospace inner loop (fast, accurate, well-modeled)
│    → State-space LQR / LQG; H-infinity for robust.
│    → Gain-schedule across envelope.
├─ Aerospace + uncertainty / actuator failure handling
│    → H-infinity or μ-synthesis; L1-adaptive on top.
├─ Robotics arm position/force
│    ├─ Position → PID + computed torque feedforward
│    ├─ Force → impedance control (Hogan 1985)
│    └─ Hybrid → impedance + admittance switching
├─ Mobile robot trajectory tracking
│    ├─ Slow + flat → pure pursuit, Stanley, LQR-trajectory
│    └─ Fast + dynamic → NMPC / iLQR
├─ Legged robot
│    └─ NMPC for centroidal dynamics + low-level torque control.
│    → ANYmal RSL stack, Boston Dynamics MIT Cheetah lineage.
├─ Drone (quadrotor)
│    ├─ Position → cascade PID (industry standard, PX4/Ardupilot)
│    └─ Aggressive maneuvers → MPC / iLQR + learned residuals
├─ Industrial plant w/ economic objective
│    → Economic MPC (EMPC): optimize \$/h directly.
├─ Plant w/ stochastic disturbances + chance constraints
│    → Stochastic MPC.
├─ Battery thermal / charging
│    → MPC (linear, w/ thermal model).
├─ Power grid frequency / voltage
│    → AGC + droop + distributed consensus; MPC at substation.
├─ HVAC building
│    → Cascade PID at zone + MPC at supervisor (Daikin, Carrier).
├─ Fast, hard nonlinearity (chemical reactor at autocatalysis)
│    → NMPC w/ small horizon + warm-start.
├─ Discontinuous actuator (relay, brake, switch)
│    → Sliding-mode (super-twisting if chattering issue).
├─ Hysteresis / unknown nonlinearity
│    → Adaptive control or RL.
├─ Repetitive task (semiconductor wafer stage, paint robot)
│    → ILC.
├─ Safety-critical w/ learned component
│    → CBF as safety filter; RL as nominal.
├─ Highly nonlinear + only data (no model)
│    → MBRL (PILCO, MBPO) or model-free RL.
│    → DMDc / Koopman for linear surrogate + LMPC.
├─ Discrete event / supervisory layer
│    → Ramadge-Wonham supervisory control; PLC ladder logic; STL specs.
└─ Multi-vehicle / multi-agent
     → Consensus, distributed MPC, leader-follower, flocking (Olfati-Saber).

14. Anti-patterns

1. Detuning PID by 50% to handle a coupled MIMO plant — robust but slow; use a decoupler or MPC.
2. NMPC w/ a 50-step horizon on a microcontroller — won’t converge in time; use shorter horizon or explicit MPC.
3. LQR with Q = I, R = I without analysis — magic gains; tune Q/R by Bryson’s rule.
4. H-infinity without weighting filters — design is degenerate.
5. Adaptive control deployed without persistent excitation — Rohrs et al 1985 — parameters drift, instability.
6. RL trained in sim deployed on hardware without domain randomization — sim-to-real gap; Hwangbo et al 2019 ANYmal is the canonical correct approach.
7. PID with derivative on measurement noise — amplifies noise; filter D term or move D to setpoint.
8. MPC w/ infeasible initial condition — design with soft constraints or robust tube.
9. Linear MPC on a strongly nonlinear plant — use NMPC or gain-scheduled LMPC.
10. Sliding-mode without boundary layer or super-twisting — chattering destroys actuators.

15. The 2024–2026 frontier

• Embedded NMPC at 1 kHz on Cortex-A / ARM v9 (acados, HPIPM, FORCES PRO) for drones and EV powertrain.
• CBF-RL hybrid (Ames et al; Cheng-Khojasteh-Ames-Sun-Burdick 2019) — RL nominal + CBF safety filter standard in safety-critical RL.
• Learning-based gain scheduling — neural network maps state to control gain.
• Diffusion policies (Chi-Feng-Du-Burchfiel-Tedrake 2023) — multimodal action distributions.
• Foundation models for robotics control (RT-2, OpenVLA, Octo 2024) — VLAs (vision-language-action) generalizing across tasks.
• Sim-to-real via massive parallel sim (Isaac Gym, MuJoCo MJX, Genesis 2024).
• Differentiable simulator + iLQR (Dojo, Brax, MJX) — autograd through physics for trajectory opt.
• Tube MPC with learning — robust MPC with online uncertainty refinement.
• Quantum control (PID + optimal control for qubits) — gate calibration via CRAB, GRAPE, Krotov.
• Network-aware control for 5G / 6G — event-triggered + age-of-information aware.
• Energy-aware MPC for HVAC, EV charging, smart grid — economic MPC with carbon-cost as objective.

Adjacent

• Classical SISO — classical-control for PID, Bode, Nyquist, frequency-domain.
• State-space depth — state-space-methods for LQR, observers, MIMO.
• MPC depth — mpc-control for full receding-horizon stack.
• Adaptive — adaptive-control for MRAC, STC, L1-adaptive.
• H-infinity — h-infinity-robust for robust frequency-domain MIMO.
• Sliding-mode — sliding-mode-control for variable structure.
• Digital control — digital-control for discrete-time, sampling, anti-aliasing.
• System ID — system-identification for the model that controllers use.
• GNC — gnc for aerospace guidance navigation control integration.
• Spacecraft — spacecraft-attitude-control for attitude control specifics.
• Robotics PID — pid-control for joint-level low-level.
• Robotics MPC — mpc-for-robots for whole-body and centroidal MPC.
• Robot impedance — impedance-control for force-control + compliance.
• RL for control — rl-for-control for sim-to-real and policy learning.
• Optimization — _compare_optimization-methods for the QP / NLP / RL optimization underlying control.

When to pick what

The fastest narrowing: slow + SISO → PID; slow + MIMO + constraints → linear MPC; fast aerospace inner loop → LQR / H-infinity; fast + nonlinear + constraints → NMPC; uncertain actuator failure → adaptive (L1) or H-infinity; discontinuous + bounded uncertainty → sliding-mode (super-twisting); repetitive task → ILC; safety-critical w/ learned component → RL + CBF; certifiable + reliable → PID + state-space. The single biggest practical lesson is start with PID, prove you need more, then climb the ladder — most control problems are solved by PID + cascade + override + feedforward; reach for MPC when constraints bind; reach for adaptive or RL only when the model is unknown or time-varying and certification is not the gating factor.