Agent skill · vasilyu1983
foundations-control-theory
Control-theory primitives for PID, MPC, Kalman, stability, anti-windup, dead-time, breakers, and limits. Use when tuning autoscaling, retries, or agent loops.
What it needs
About 12k tokens when loaded.
What this skill does
Control Theory Foundations 12 applied control-theory primitives for feedback control and dynamical systems, backed by a formal theory map. Each primitive owns a specific failure mode in any system that must reach and hold a target state despite disturbances, delays, noise, or nonlinearities. Primitives are domain-agnostic: the same PID loop that controls CPU utilization controls budget pacing and retry rates; the same circuit breaker that isolates a failing database isolates a failing LLM tool. Contents Quick Reference Primitive Index Formal Supporting Theory Anti-Patterns Misuse Boundaries Expert Judgment Decision Checklist Composition Recipes Workflow ASCII Flow Navigation Fact-Checking --- Quick Reference Primitive Problem It Solves Key Parameters ----------- ------------------ ---------------- PID Control Drive output to setpoint despite steady-state error and disturbances Kp, Ki, Kd; tuned via Ziegler-Nichols Feedback vs. Feedforward Reactive-only loops ignore predictable disturbances Plant model accuracy; disturbance measurability Observability & Controllability States you cannot see or reach make the loop fail silently Controllability matrix rank; observability matrix rank Lyapunov Stability No proof that a loop converges; may oscillate or diverge Lyapunov function V(x); dV/dt < 0 condition MPC One-step control ignores future constraints and couplings Horizon N; cost matrices Q, R; constraint bounds Kalman Filter Noisy measurements degrade controller and monitoring accuracy Process noise Q; measurement noise R; model (A, B, C) Dead-Time Compensation Transport lag causes oscillation or instability Dead time L; plant model (delay-free) Anti-Windup Integrator saturates during limit-clamping → overshoot on release Actuator min/max; tracking constant Tt Gain Scheduling Single fixed-gain controller fails across operating regimes Scheduling variable σ; per-regime gain tables Circuit Breaker & Backpressure Cascading failure; unbounded queue growth Failure threshold; …
How to use it
Reference it in AdaL, Claude Code, Cursor or any coding agent — nothing to install:
@skills vasilyu1983/foundations-control-theory