CAD.3:11 - SoTA-Echoing

How can a command domain support continued constrained operation? The selected line is robust error containment, constraint tightening and a separate continuation argument in :4.1–4.4. It adapts Stamouli and colleagues’ constraint-propagation construction, §§4–5. Their reported output-constraint guarantee is at slow samples; the all-fast-sample input extension has an additional condition. Here each claimed time interval is explicit, and direct set inclusion establishes invariance without extending a decrease-only condition into a global bound. The price is a sufficient domain that may exclude useful commands.

A serious alternative for a fixed qualified loop is a governor’s joint state-command admissible set (CAD.Reference:4.5.1). It can retain relations discarded by one common error envelope. Castroviejo-Fernandez and colleagues, §§4–6, especially Proposition 2 further use observer-error bounds and a sequence of admissible sets with a proved successor relation. Adapt that idea when a worst-case constant disturbance envelope is unnecessarily restrictive; the extra assumptions on estimation and disturbance variation, and the set computation, must be worth the enlarged domain. This motivates the return in :4.3 rather than weakening a hard constraint.

A predictive safety filter is another alternative when the requested object is a plant input and a finite backup trajectory can be computed. Milios, Wabersich, Berkel and Schwenkel, §§II–IV distinguish recursive constraint satisfaction from additional stability guarantees and supply separate stabilizing conditions. Adopt that distinction in :4.4 and CAD.4:4.2. Such a filter needs its model, terminal ingredients and online computation; inserting it after the tracker changes the law analyzed in CAD.2.

For continuous dynamics, the Matni–Ames–Doyle treatment, §4.5 supplies a distinct safety-transfer line. Section :4.5 adapts the connection through an explicit error margin, conditional on remaining in the derivative and Lipschitz domains; it does not assume that every nonlinear controller supplies those premises. Reopen the selected containment construction when conservatism prevents the task, the admitted switching or disturbance changes, or the intended claim changes from constraint satisfaction to convergence or completion.