Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source - Piccirillo, V. [UNESP]; Balthazar, José Manoel [UNESP]; Pontes, B. R.; Felix, J. L. P. [UNESP] (Springer, 2009)
In this paper, an optimal linear control is applied to control a chaotic oscillator with shape memory alloy (SMA). Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function, which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. This work is presented in two parts. Part I considers the so-called ideal problem. In the ideal problem, the excitation source is assumed to be an ideal harmonic excitation.
Keywords: Chaos control; Shape memory alloy; Nonlinear dynamic; Linear feedback control