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Nonlinear open-plus-closed-loop (NOPCL) control of dynamic systems. (English) Zbl 0958.93041

The authors consider the entrainment (or asymptotic tracking) control problem, where the goal is to find a control \(u\) such that the solution \(x(t)\) of the system \(\dot{x}=F(x,t)+u(t)\) satisfies \(\lim_{t\to\infty}|x(t)-g(t)|=0\) for some prescribed function \(g(t)\).
For the solution to this problem the authors propose a time-varying feedback controller, denoted as nonlinear-open-plus-closed-loop or NOPLC control. This method extends the OPCL control proposed by E. A. Jackson and I. Grosu [Physica D 85, No. 1–2, 1–9 (1995; Zbl 0888.93034)] by taking into account higher order derivatives of \(F\).
It is shown that the resulting control law solves the problem, at least for a nonempty set of initial conditions called the basin of entrainment. For special cases like, e.g., the Lorenz, Roessler, Duffing and other systems, the basin of entrainment is shown to be global.

MSC:

93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations

Citations:

Zbl 0888.93034
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References:

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