Design methods

Quantum mechanics

Control (management)

Chaotic

Engineering

Orbit (dynamics)

Aerospace engineering

CHAOS (operating system)

Bifurcation

Biology

Chaotic systems

Control engineering

Computer security

Synchronization of chaos

Computer science

Controller (irrigation)

Mechanical engineering

Physics

Nonlinear system

Mathematics

Agronomy

Attractor

Control of chaos

Mathematical analysis

Artificial intelligence

Crisis

Control theory (sociology)

Periodic orbits

Chaos occurs widely in artificial and natural nonlinear systems and its irregular behavior is usually undesirable. Controlling chaos, that is, stabilization of chaotic systems, is one of major subjects in nonlinear control problems. In this paper we propose a computer-aided design method of stabilizing controllers for continuous-time chaotic systems. It is known that infinitely many unstable periodic orbits are embedded in chaotic attractors. Therefore, finding an unstable periodic orbit out of them and designing a controller which stabilizes it, we can obtain a controller which suppresses chaotic behavior and make the transition to the stable periodic orbit. First we propose a method for finding an unstable periodic orbit in a chaotic attractor. Second we propose a design method of feedback controllers which stabilize it. The performance of the proposed method is shown through numerical experiments.

Computer-aided design method of stabilizing controllers for chaotic systems