7.3 LQR and Robust-Controller CCD

Core idea¶

LQR and Robust-Controller CCD must be treated as a system-level decision rather than an isolated technique. For an active suspension under full preview, finite-horizon MPC, reactive feedback, and noisy estimation, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are $p$ , controller and estimator $c$ , information architecture $a_I$ , and $\mathcal I_t$ . The chapter-level formulation is

u(t)=\pi(\mathcal I_t;c),\quad\mathcal I_t=\{y_{0:t},r_{0:t+T_p},\hat x(t)\}.

For this section, trace how the choice changes state estimator, the active constraints, and the implementable engineering design. A method is useful only when its assumptions are explicit and its result answers the same system question as the baseline.

Optimal plant versus prediction horizon.

Engineering interpretation¶

Ask three questions:

Which physical, informational, computational, or economic resource changed?
Which objective component or active constraint made the change valuable?
Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to design estimator. Record units and assumptions before optimization, report component objectives and margins afterward, and verify the result using an independent calculation or higher-fidelity model.

Activity 7.3: quantify lqr and robust-controller ccd¶

Activity 7.3: quantify lqr and robust-controller ccd

For a closed-loop precision positioner, compare three formulations for LQR and Robust-Controller CCD using 200 validation scenarios.

Formulation	Mean cost	Cost SD	95th-percentile cost	Violations
Nominal	1.030	0.109	1.240	21
Risk-aware	1.080	0.071	1.190	8
Robust	1.150	0.043	1.220	0

Compute empirical violation probabilities and test a 3% limit.
Calculate coefficient of variation and a risk score equal to mean plus 1.645 standard deviations.
Rank only feasible formulations by risk score.
Repeat if every violation count increases by four and report the resulting design decision.
State which uncertainty samples, seeds, and model versions must accompany the result.