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Stabilization of nonlinear systems: Radial optimal control approach

100%

Sangelaji Z. , Banks S. P.

Systems Science

2003

tom Vol. 29, nr 4

29-41

This paper represents the optimal control of nonlinear systems based upon the associated angular approach. In the latter a general class of nonlinear systems is converted to two associated systems: a nonlinear equation on a sphere (spherical), and a radial differential system. By decoupling the two subsystems and considering only the radial system, a finite-horizon radial optimal control is designed which minimizes the radial cost function. Successive approximation technique is then introduced in which the equations are replaced by a sequence of linear, time-varying approximations. The resulting optimal control is then applied to the original angular system. This control forces the original angular system to the origin.

Frequency analysis of nonlinear dynamical systems and the control of vibration

100%

Banks S. P. , Tomas-Rodriguez M.

Archives of Control Sciences

2003

tom Vol. 13, no. 3

269-279

In this paper we shall consider nonlinear vibrating systems which can be written in form x= A(x)+B(x)u. We shall introduce a sequence of linear, time-varying approximations which can be studied in the frequency domain. A spectral optimal control theory will be developed.