Abstract
We present an algorithm to allow full placement of all stability exponents (Poincar\'e or Lyapunov) in a controlled chaotic system. The linear quadratic regulator of classical control theory is recast to allow specification of the controlled system Lyapunov exponents and initial and final principal dynamical directions. In the process, a positive definite functional of the control is minimized. The boundary value problem that must be solved is linear, and converges in one iteration. Successful results are reported, applying the method to the Duffing oscillator, the Lorenz system, and the restricted problem of three bodies, for both periodic orbits and general trajectories. \textcopyright{} 1996 The American Physical Society.
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