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6.8 OLOC as a Performance Upper Bound

Core idea

OLOC as a Performance Upper Bound must be treated as a system-level decision rather than an isolated technique. For an active suspension with complete road preview and a wave-energy converter with known future waves, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are pp, u(t)u(t), x(t)x(t), and known d(t)d(t). The chapter-level formulation is

minp,u,xΦ+Ldt  s.t.  x˙=f(t,x,u,p,d).\min_{p,u,x}\Phi+\int L\,dt\;\mathrm{s.t.}\;\dot x=f(t,x,u,p,d).

For this section, trace how the choice changes optimal control, 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 identify phases. 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 6.8: quantitative design audit