Reply by the Authors to K. B. Li and L. Chen

Abstract

We thank K. B. Li and L. Chen for their comments on our papers. The comment on "Partial Integrated Missile Guidance and Control with Finite Time Convergence" can be summarized and categorized as follows.1) The updating law may be not necessary for the control law to guarantee the finite time convergence.2) The control command may also become quite large or even exceed the physical limitation.We make the following reply to the comments. 1) Under the assumption that the initial estimation valued max 0 satisfies the inequality d max −d max 0σ < 0, point 1 of the comment is correct, namely, the updating law in the original paper is actually not necessary to guarantee the finite time convergence to zero of sliding variable s.However, ifd max t is not updated by the adaptive law as stated in the comment, then it will be difficult to determine how large the constantd max should be chosen in practice to satisfy the inequality d max −d max tσ < 0 under the consideration that the bound of disturbance d max is unknown. We also ignore this point in our original paper. In the following, a small modification is introduced to the updating law in the original paper, with which finite time convergence will be guaranteed under the initial estimation valuê d max 0 arbitrarily chosen and the bound of disturbance d max unknown.2) Point 2 of the comment is not correct. We can get the following results from the proof of theorem 1 in; hence, the control command will not become quite large.3) Here, a small modification is introduced to the updating law, namely, Eq. (4) in [1] to guarantee the finite time convergence under the initial estimation valued max 0 arbitrarily chosen and the bound of disturbance d max unknown. In this case, the updating law is very necessary.The updating law is modified as follows:the initial valued max 0 is an arbitrarily positive constant, σ ≥ 1 and 0 < ε < 1. s is the sliding variable, and s x 2 αjx 1 j ρ sgnx 1 ; see Eq.(2) in [1]. We rewrite theorem 1 as follows.Theorem 1: Consider the system _ x 1 x 2 ; _ x 2 fx; t bx; tu dx; t with the terminal sliding variable s x 2 αjx 1 j ρ sgnx 1 . Under the conditions that the bound of disturbance d max is unknown and the initial estimation valued max 0 is arbitrarily chosen, using the control law u bx; t −1 −fx; t −d max σs∕jsj − λx 1 x 2 − kjsj γ sgns, namely, Eq. (3) in [1] and the modified updating law Eq. (1), the states of the system can reach the sliding surface in finite time and then converge to the origin along the sliding surface in finite time, too. The updating law Eq. (1) has actually the following form: _d max 8 < :σjsj; jsj ≥ ε σjsj arccos jsj; jsj < ε and jsj≢0 0;jsj ≡ 0When jsj ≥ ε,d max t d max 0 σ∫ t 0 jsj dτ ≥d max 0 σεt. Hence, σd max t − d max ≥ σd max 0 − d max σ 2 εt. It is obtained that, when t ≥ T 1 withthe inequality d max −d max tσ < 0 holds. In summary, as long as jsj≢0, σd max t − d max will be always larger than an increasing linear function of time t. Hence, there exists finite time T, for any t ≥ T, the inequality d max −d max tσ < 0...

The tetraquark system in a chiral quark model*

“…Tables 4 to 27 list the calculated results of low-lying tetraquark states. In particular, real-range computations on the lowest-lying masses of each tetraquark system in the allowed quantum numbers are presented in Tables 4,6,8,10,12,14,16,18,20,22,24,and 26. Therein, the considered meson-meson, diquark-antidiquark, and K-type configurations are listed in the first column; if available, the experimental value of the noninteracting di-meson threshold is labeled in parentheses. In the second column, each channel is assigned with an index, which indicates a particular combination of spin ( ), flavor ( ), and color ( ) wave functions, which are shown explicitly in the third column.…”

Dissipative stabilization of quantum-feedback-based multipartite entanglement with Rydberg atoms

“…This kind of correlation is so peculiar that a measurement made on either of the particles apparently collapses the state of system instantaneously, even when the particles are separated by a large distance. Although this 'spooky action at a distance' has made Einstein thought that quantum mechanics is not a complete [2], the observations of quantum entanglement have been continuously demonstrated in experiments with linear photons system [3][4][5], cavity quantum electrodynamics (QED) system [6,7], and trapped ions systems [8][9][10], etc. Nowadays, quantum entanglement, as a fundamental feature in quantum mechanics, has greatly promoted the development of quantum information.…”