19.1 Why Optimized Trajectories Are Not Sufficient

Core idea¶

Why Optimized Trajectories Are Not Sufficient must be treated as a system-level decision rather than an isolated technique. For an active-suspension rig progressing from ideal torque to estimator-based real-time control and HIL, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are ideal $u^*$, policy $\pi$, sampling, latency, quantization, estimator, hardware, and validation residuals. The chapter-level formulation is

For this section, trace how the choice changes optimal trajectory, 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.

Engineering interpretation¶

Ask three questions:

1. Which physical, informational, computational, or economic resource changed?

2. Which objective component or active constraint made the change valuable?

3. Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to realize controller. 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 19.1: quantify why optimized trajectories are not sufficient¶