The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the unde...The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.展开更多
The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lue system. Basic properties ...The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lue system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.展开更多
基金the National Natural Science Foundation of China under Grant No.60574016
文摘The infinite-horizon linear quadratic regulation （LQR） problem is settled for discretetime systems with input delay. With the help of an autoregressive moving average （ARMA） innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems.
文摘The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lue system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.
