Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Control theory — the analysis and design of feedback — stability and Lyapunov certificates, invariance, viability and barrier certificates, input-to-state stability and small-gain conditions, contraction, adaptive, dual and safe control, and controller synthesis under constraints; dynamical systems without a control input stay with complex-systems (ADR-066).
8 of 2004 LIT documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| LIT-714 v2 | The Method of Characteristics Revisited: A Viability Approach | Aubin (1999), lecture notes on arXiv. A set K is viable under a system if from each state in K at least one evolution stays in K, and invariant if every evolution does. By Nagumo’s theorem K is viable exactly when the dynamics point into K’s contingent cone at each state. The viability kernel of K is the largest viable subset of K; its complement in K is a repeller. The capture basin of a target is the set of states from which it can be reached in finite time. | Active — read 2026-10-05 (NOTE-576): the introduction and chapters 1–2 of the author’s arXiv lecture notes, the parts that define viability. Worth reading as the shortest first-hand statement the record holds of Aubin’s viability concepts: a set is viable if from every state at least one evolution stays in it, invariant if all do, and the viability kernel is the largest viable subset of a constraint set. Chapters 3 onward apply these to Hamilton–Jacobi equations and were not read. Stands in for the unread monograph LIT-738. |
| LIT-738 v3 | Viability Theory | Aubin (1991; reprinted 2009), Birkhäuser: the monograph that founds viability theory, the study of which evolutions of a dynamical or controlled system can remain in a given constraint set, and of the set of initial states from which one can. Unread: registered from metadata; the definitions are read in Aubin’s 1999 mini-course notes LIT-714. | Unavailable — registered 2026-10-05 from Crossref and the author’s own list of his books, not read: no lawful full text could be reached. Springer serves the 2009 reprint behind a bot challenge, which was not passed. Aubin’s 1999 mini-course notes (LIT-714, read) state the definitions this book is cited for: a viable evolution, viability and invariance, the viability kernel and the capture basin. Filed because an essay the owner is writing cites “Aubin’s mathematical theory of viability” for the difference between stability and viability. It stays Unavailable until a copy is supplied, not on merit. |
| LIT-1292 v3 | A contraction based, singular perturbation approach to near-decomposability in complex systems | Bousquet & Slotine (arXiv 2015, unpublished). Recasts Simon’s near-decomposability as a singularly perturbed system, fast module states x̃ and slow states y with ẏ = O(ε), and bounds the error of the reduced slow system with nonlinear contraction theory. If each module is contracting, the reduced slow system is contracting, and the coupling terms grow at most affinely in |x̃| and |y|, then below an explicit critical separation ε_c, after a transient of order (1/β_f + 1/(εβ_g)) log(1/ε), the fast states stay O(ε) from their quasi-steady values and the slow states O(ε) from the reduced trajectory, for all later time. A worked building example with a negative conductance shows multiple equilibria and instability above ε_c. Deterministic; bounds trajectory error, not dependence; proofs are sketches with a printed inversion in Remark 8. | Active — read 2026-10-20 (NOTE-1025) in full; worth reading for the only rate the record holds for Simon’s near-decomposability: with contracting fast modules (rate β_f) and a contracting reduced slow system (rate β_g), and coupling perturbations bounded affinely in the off-manifold state, Lemma 3 and Theorem 1 keep the fast variables within O(ε) of their quasi-steady manifold and the slow variables within O(ε) of the reduced system, uniformly in time after a transient of (1/β_f + 1/(εβ_g)) log(1/ε), for every ε below an explicit critical timescale separation ε_c = β_f / [χ_f(α_f,x + χ_g α_f,y α_g,x / β_g)]; and for Remark 6, that the micro states act on the macro level through their quasi-steady values, “an aggregation in time”, not an ensemble aggregate. Read it knowing that it is a five-page preprint, never published in a journal, whose proofs are sketches; that Remark 8 prints ε_c inverted (the worked example’s value √2/7 is the reciprocal of the printed expression, and matches Hypothesis 2); that Lemma 3’s O(ε) bound on the slow error needs d_g = 0, which the proof’s last line assumes silently while the worked example lists d_g = 1; that it is deterministic throughout and bounds trajectory error only, not any information-theoretic dependence; that the slow coordinates and the partition are given, not found; and that ε_c is sufficient and in linear checks conservative by factors of 3 to 50. |
| LIT-1880 v2 | When Can Safe Controllers Adapt? Information before Commitment | Saligrama (2026). A safe adaptive controller must stay safe under every model not yet ruled out. Its first action that leaves no safe continuation under an alternative is a commitment, and the observation that action produces comes too late to justify it. With the information before commitment measured as a KL divergence between stopped records, every uniformly safe policy forfeits at least about ½e^{−I} of the value reachable only by committing. Acting on an exclusion at risk α needs about log(1/(2α)) nats beforehand. Bounded information and a linear gap give linear regret, shown for a headroom-limited device and for constrained linear regulation. Finite information can still certify a smaller candidate list. Safe recovery at O(√(T log T)) holds when a safe experiment is repeatable, informative and returns to a common state. | Active — read in full 2026-10-31 (NOTE-1466), with the main proofs; worth reading for the precise sense in which evidence must precede commitment: the observation a committing action produces cannot justify it, and bounded information before commitment leaves a fixed fraction of the oracle gap to every uniformly safe controller (THEORY-1254). It also proves the positive case, safe recovery from a repeatable informative experiment, and shows certainty equivalence failing at an active constraint (THEORY-1256). |
| LIT-1893 v2 | Input-to-State Safety With Control Barrier Functions | Kolathaya & Ames (2019). Defines input-to-state safety for a safe set C = {h ≥ 0}: under an input disturbance bounded by ‖d‖∞, the larger set {h + γ(‖d‖∞) ≥ 0} stays forward invariant, for some class-K γ. A barrier inequality with a disturbance penalty, ḣ ≥ −α(h) − ι(‖d‖), implies it. Adding a damping term εL_g hᵀ to any barrier controller, or the matching constraint to a CLF–CBF quadratic program, gives ι = ‖d‖²/(4ε). The paper’s examples show that nominal barrier controllers, including the standard quadratic program, can leave the safe set without bound under small disturbances. | Active — read in full 2026-10-31 (NOTE-1477); worth reading as the short statement of graded robust safety: under a bounded input disturbance a barrier-function controller keeps the state not in the safe set but in a set enlarged by a class-K function of the disturbance, and a damping term along the barrier’s input direction delivers this with an enlargement of ‖d‖²/(4ε) (THEORY-1267). It is not the robust box invariance CASE-190 certifies, which is THEORY-134’s. |
| LIT-1972 v2 | Using chaos to direct trajectories to targets | Shinbrot et al. (1990), doi:10.1103/PhysRevLett.65.3215. Registered unread from the exchange “Assess SDT Coverage” of 2026-11-02 (A18). The targeting half of chaos control: a one-shot use of sensitivity to reach a target quickly, against OGY’s holding. | Unavailable — searched 2026-11-03 for a lawful full text and none was reached, so it is not read and no NOTE is filed. OpenAlex and Unpaywall (noreply address) report it closed; PubMed has the abstract only; journals.aps.org returns a bot check to this client. Web searches found the 1992 experimental follow-up’s portal record at Aberdeen and a São Paulo thesis on targeting, but no copy of this letter. It stays Unavailable until a copy is supplied. |
| LIT-1986 v2 | A Survey of Viability Theory | Aubin (1990), doi:10.1137/0328044. Registered unread from the exchange “Assess SDT Coverage” of 2026-11-02 (A21). Aubin’s survey. THEORY-134 holds the viability kernel from the 1999 notes (LIT-714); the robust, discriminating kernel A21 uses is not held. | Unavailable — searched 2026-11-03 for a lawful full text and none was reached, so it is not read and no NOTE is filed. OpenAlex and Unpaywall (noreply address) report it closed; epubs.siam.org returned 403 to this client. Web searches found citations and Aubin’s later book (Viability Theory, Birkhäuser), which is not this work, and no free copy. THEORY-134 holds the viability kernel from LIT-714; the robust and discriminating kernels A21 uses remain unread. It stays Unavailable until a copy is supplied. |
| LIT-1997 v2 | Controlling chaos | Ott et al. (1990), doi:10.1103/PhysRevLett.64.1196. Registered unread from the exchange “Assess SDT Coverage” of 2026-11-02 (A16, A17). The method the owner called “very wu-wei” (U17): small parameter perturbations, timed by the system’s own wandering, hold it on an unstable periodic orbit. The control is small but continues while the orbit is held. Grounds CLAIM-541 and CLAIM-542. | Unavailable — searched 2026-11-03 for a lawful full text and none was reached, so it is not read and no NOTE is filed. OpenAlex and Unpaywall (noreply address) report it closed; PubMed has the abstract only. journals.aps.org returned a Cloudflare bot check (403) to this client, and was not tried again. The paper is one of PRL’s fifty-year milestone letters; whether APS makes milestone letters free to read could not be confirmed, since the milestones page returned 403 and the Wayback Machine is blocked by this session’s egress policy. If it is free, the owner can open journals.aps.org/prl/abstract/10.1103/PhysRevLett.64.1196, and this should be Unfetched. Yorke’s own list of cited papers (yorke.umd.edu/cited100+.html) did not answer. Web searches found no author or course copy. CLAIM-541 and CLAIM-542 describe the method second-hand. |