AN OPEN-PLUS-CLOSED-LOOP (OPCL) CONTROL OF COMPLEX DYNAMIC-SYSTEMS

A new method of controlling arbitrary nonlinear dynamic systems, dx/dt = F(x, t)(x is an element of R(n)), is presented. It is proved that t here exists solutions, x(t), in the neighborhood of any arbitrary 'goa l' dynamics g(t) that are entrained to g(t), through the use of an add itive controlling action, K(g, x, t) = H(dg/dr,g) + C(g, t)(g(t) - x), which is the sum of the open-loop (Hubler) action, H(dg/dt, g), and a suitable linear closed-loop (feedback) action C(g, t). Examples of so me newly obtained entrainment capabilities are given for the Duffing a nd Van der Pol systems. For these and the Lorenz, and Rossler systems proofs are given for global basins of entrainment for all goal dynamic s that can be exponentially bounded in time. The basin of entrainment is also established for the Chua system, as well as the possibility of a coexisting basin of attraction to another fixed point.