Abstract
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.
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Piccirillo, V., Balthazar, J.M., Jr. Pontes, B.R. et al. Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source. Nonlinear Dyn 55, 139–149 (2009). https://doi.org/10.1007/s11071-008-9350-6
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DOI: https://doi.org/10.1007/s11071-008-9350-6