Nonlinear & Optimal Control Design

← Back to Domain-Specific Families

Abstractions about designing controllers for dynamical systems, covering nonlinear stabilization techniques (backstepping, feedback linearization, sliding mode control, Lyapunov redesign), optimal and robust control formulations (optimal control, H-infinity loop-shaping, trajectory optimization), and analytical tools like the Kalman-Yakubovich-Popov lemma.

14 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Backstepping — A recursive nonlinear-control design method for strict-feedback systems that constructs a stabilizing controller and Lyapunov function stage by stage.
• Closed-loop transfer function — Collapse a linear feedback interconnection into the net input-to-output map—typically G(s)/(1+G(s)H(s)) for negative feedback—whose denominator exposes stability, sensitivity, and loop-gain effects.
• Dead-beat control — A discrete-time control design that drives a controllable system's state or output exactly to its target in the minimum finite number of sampling steps.
• Feedback linearization — A nonlinear-control technique that uses state or output transformations and a compensating input law to cancel modeled nonlinearities and expose linear closed-loop dynamics.
• Flatness (systems theory) — A nonlinear-system property in which all states and inputs can be parameterized by a flat output and finitely many of its derivatives, without integrating differential equations.
• H-infinity loop-shaping — A robust-control design that first frequency-shapes a plant and then optimizes a stabilizing controller against normalized coprime-factor uncertainty.
• Hamiltonian (control theory) — The function combining instantaneous objective and state dynamics through costate variables in optimal control, whose pointwise optimization is required by Pontryagin's maximum principle.
• Inertia wheel pendulum — An underactuated control-system model consisting of a pendulum with a motor-driven reaction wheel whose internal torque regulates the pendulum angle.
• Kalman–Yakubovich–Popov lemma — A theorem equating a frequency-domain positivity condition for a linear system with existence of a state-space quadratic certificate.
• Lyapunov redesign — A nonlinear-control method that augments a nominal stabilizing feedback law using a known Lyapunov function to preserve stability under matched uncertainty.
• Optimal control — The selection of a time-dependent control policy for a dynamical system that minimizes or maximizes an objective while satisfying dynamics and constraints.
• Self-tuning — An adaptive control or computing architecture that measures its own performance, estimates how tunable parameters affect an objective and changes those parameters online to maintain or improve operation under changing conditions.
• Sliding mode control — A nonlinear variable-structure control method using discontinuous feedback to drive trajectories onto a designed switching manifold and maintain reduced-order motion along it.
• Trajectory optimization — The computation of a state-and-control path that extremizes a performance objective while satisfying dynamics, boundary conditions and path constraints, usually as an open-loop optimal-control solution.