A necessary and sufficient RHC stabilizability condition for stochastic control with delayed input

Receding horizon control for continuous‐time mean‐field systems

“…Remark In fact, Theorem 1 contains standard RHC stabilization results when the system has no state and input expectation. That is, when $$$ \bar{A}=\overline{B}=\overline{C}=\overline{D}=\overline{Q}=\overline{R}=0 $$$, the above inequalities ()–() become $$$$ {\displaystyle \begin{array}{ll}& Q+{H}_1^{\prime }R{H}_1+{\left(A+B{H}_1\right)}^{\prime }P+P\left(A+B{H}_1\right)\\ {}& +{\left(C+D{H}_1\right)}^{\prime }P\left(C+D{H}_1\right)\le 0,\end{array}} $$$$ which is exactly the result of [28] without input delay.…”

“…The RHC stabilization of continuous‐time mean‐field system is discussed in this paper. Our results are mainly based on previous works presented in [28] and extend it to the mean‐field case without input delays. The main contributions are as follows: (1) The explicit form of RHC controller is given; (2) on the basis of properly designing the optimal cost function, an inequality condition is obtained to ensure the stability of the system in the mean square sense.…”

Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates

“…e dynamics of nonlinear phenomena can be analyzed by means of the corresponding nonlinear evolution equations. ere has been considerable work carried out on the control problem of nonlinear systems, such as those in chaotic and stochastic systems [15][16][17][18][19]. Solitons, resulted from the balance between the effects of nonlinearity and dispersion [20], have been studied in fields such as nonlinear optics, plasma physics, and condensed matter physics [3,[21][22][23].…”

Distributed RHC stabilization for discrete‐time large‐scale systems with imposed constraints

“…In this paper, we refer to the methods in our other works using RHC to stabilize subsystems and proposed a new method of distributed RHC. We are concerned with the stabilization problem of distributed RHC for a class of discrete‐time large‐scale systems with constraints.…”