Epimorphism plus monomorphism implies equivalence in the homotopy category

Certainty Equivalence Implies Detectability

It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator's output error e p , for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend. The fact that certain...

Certainty equivalence implies detectability 1

It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator's output error ep, for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend. The fact that certainty...

Homotopy Coherent Category Theory

Unitarity plus causality implies localizability

We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution U . We require that this global evolution U be unitary, in accordance with quantum theory, and that this global evolution U be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a b...

The Homotopy Type of the Cobordism Category