Chapter 13: Uncertain, Robust, and Reliable CCD

Designing systems that continue to work outside the nominal model¶

UCCD makes uncertainty explicit in objectives, dynamics, equalities, inequalities, and feasibility claims. Alternative formulations encode average value, failure probability, risk, set-based protection, or imprecise knowledge.

Learning objectives¶

After completing this chapter, you should be able to:

explain and apply uncertainty sources;
explain and apply propagation;
explain and apply risk formulation;
explain and apply robust design;
formulate and verify the chapter methods on a suspension with uncertain mass, road, damping, measurement noise, and actuator efficiency.

Mathematical lens¶

The recurring quantities are $\theta$ , design $p,c$ , random trajectories, failure events, and risk $\alpha$ :

\min\mathbb E[J]\;\mathrm{s.t.}\;\mathbb P(g_i\le0)\ge1-\alpha_i.

Running example¶

The recurring example is a suspension with uncertain mass, road, damping, measurement noise, and actuator efficiency. Retaining one system prevents apparent improvements from being caused by changed physics, information, loads, or metrics.

Recommended workflow¶

classify uncertainty.
choose representation.
propagate.
optimize risk.
validate failures.

Chapter map¶

Sources of Uncertainty in CCD
Aleatory and Epistemic Uncertainty
Uncertain Plant Variables
Environmental and Operating Uncertainty
Sensor, Actuator, and Control-Channel Uncertainty
Model-Form Uncertainty
Stochastic-in-Expectation CCD
Chance-Constrained CCD
Probabilistic Robust CCD
Worst-Case Robust CCD
Conditional Value-at-Risk
Fuzzy and Possibilistic Formulations
Robust and Stochastic MPC Within CCD
Uncertainty Propagation