Invariantkontroll

Invariantkontroll is a term used in control theory to describe approaches that aim to preserve or enforce invariants in dynamical systems through controller design. Invariants are properties or conditions that should remain true for all future times, such as safety constraints, state bounds, or performance requirements. The concept is applied across continuous- and discrete-time systems and in linear as well as nonlinear settings.

Core ideas include the use of invariant sets, which are regions of the state space that the system cannot leave under the chosen control law. Forward invariance ensures that once the state enters such a set, it remains there for all future times. Tools commonly associated with invariantkontroll include barrier certificates, Lyapunov-based methods for proving invariance, and control barrier functions, which provide conditions under which safety constraints are preserved while achieving stabilization or tracking objectives.

Practically, invariantkontroll often involves designing control laws that guarantee state trajectories stay within safe or feasible regions. Techniques include projection-based methods, where the control action is adjusted to keep the state inside the invariant set, and model predictive control with explicit invariant constraints. Sum-of-squares techniques may be used for polynomial systems to certify invariants.

Applications span autonomous robotics, aerospace, process and chemical engineering, and power systems, especially where safety, reliability, and constraint satisfaction are critical. Challenges include computational complexity, conservatism, and modeling accuracy, which can limit scalability in high-dimensional or highly uncertain systems. Invariantkontroll therefore sits at the intersection of safety verification, robust control, and formal methods.