control-theory.
4 of 1538 NOTE documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| NOTE-576 | The Method of Characteristics Revisited: A Viability Approach | Viability is a property of a constraint set under a dynamics: K is viable if from every state some evolution stays in K, invariant if all do. Nagumo’s theorem reduces viability to a tangency condition. When K is not viable, the viability kernel is the largest viable part of it, and everything else in K leaves in finite time. Stability in the Lyapunov sense is not discussed. | Read |
| NOTE-1025 | Bousquet and Slotine — Contraction and near-decomposability | Under contraction of the fast modules and of the reduced slow system, and coupling terms bounded affinely in the off-manifold state, a nearly decomposable system stays within O(ε) of its singular-perturbation reduction, uniformly in time after a transient of order (1/β_f + 1/(εβ_g)) log(1/ε), for ε below an explicit critical separation ε_c. Deterministic trajectory error only. Remark 8 prints ε_c inverted, and the slow-error bound needs an unstated d_g = 0. | Read |
| NOTE-1466 | Saligrama — information before commitment in safe adaptive control | A safe adaptive controller must stay safe under every model it has not ruled out. Its first action that leaves no safe continuation under an alternative is a commitment, and the evidence for it must be in hand before the action: what that action reveals comes too late. With the information gathered before commitment measured as a KL divergence between stopped records, a data-processing argument bounds any uniformly safe policy’s regret below by the cost of not committing with probability ½e^{−I_pre} − α. So bounded pre-commitment information leaves a fixed fraction of the oracle gap, and a linear gap gives linear regret. Safe recovery at O(√(T log T)) is proved when a safe experiment is repeatable, informative and returns to a common state. | Read |
| NOTE-1477 | Kolathaya & Ames — input-to-state safe control barrier functions | Defines input-to-state safety of a set C = {h ≥ 0}: under a bounded input disturbance d, the larger set C_d = {h + γ(‖d‖∞) ≥ 0} is forward invariant, for a class-K γ. A barrier condition with a disturbance term, ḣ ≥ −α(h) − ι(‖d‖), implies it (Theorem 1). Given an ordinary control barrier function, adding L_g hᵀ to a safeguarding controller, or the constraint term −εL_g h L_g hᵀ in a CLF–CBF quadratic program, yields such a function with ι(‖d‖) = ‖d‖²/(4ε) (Theorem 2). The enlargement is a class-K function of the disturbance bound in barrier units, quadratic in the universal construction; it is not proportional to the bound. | Read |