Title :
Disturbance-generated bifurcation in a prototype adaptive system with e1-modification law
Author :
Bai, Shi ; Salam, Fathi M A
Author_Institution :
Dept. of Electr. Eng. & Syst. Sci., Michigan State Univ., E. Lansing, MI, USA
fDate :
10/1/1988 12:00:00 AM
Abstract :
The e1-modification law has been proposed by K.S. Narendra and A.M. Annaswamy (ibid., vol.32, no.2, pp.134-5, 1987) for robust model reference adaptive control in the presence of bounded disturbances. Using this law, it is shown by the present authors that, in the case of regulation, a prototype adaptive control system with a single unknown pole and an unknown constant disturbance at its input possesses multiple equilibria and undergoes various bifurcations. Simulations and local analysis give a complete characterization of the possible dynamics exhibited by the disturbance adaptive system. As the constant disturbance is varied, saddle-node bifurcation, (subcritical) Hopf bifurcation, and saddle-connection bifurcation occur in that order. Consequently, in this case, the e1-modification law is qualitatively equivalent to the σ-modification law
Keywords :
adaptive control; control system analysis; model reference adaptive control systems; Hopf bifurcation; MRACS; disturbance generated bifurcation; dynamics; e1-modification law; model reference adaptive control; pole; prototype adaptive system; saddle-connection bifurcation; saddle-node bifurcation; Adaptive control; Adaptive systems; Analytical models; Bifurcation; Chaos; Fluctuations; Limit-cycles; Programmable control; Prototypes; Robust control;
Journal_Title :
Automatic Control, IEEE Transactions on