Recent zbMATH articles in MSC 34H05https://www.zbmath.org/atom/cc/34H052021-04-16T16:22:00+00:00WerkzeugRelaxation for a class of control systems with unilateral constraints.https://www.zbmath.org/1456.340172021-04-16T16:22:00+00:00"Papageorgiou, Nikolaos S."https://www.zbmath.org/authors/?q=ai:papageorgiou.nikolaos-s"Vetro, Calogero"https://www.zbmath.org/authors/?q=ai:vetro.calogero"Vetro, Francesca"https://www.zbmath.org/authors/?q=ai:vetro.francescaThe paper is concerned with a nonlinear feedback control system of type
\[
\left\{\begin{array}{ll}-x' \in A(x(t))+f(t,x(t))u(t)\\
x(0)=x_0, \quad u(t) \in U(t,x(t))\end{array}\right.
\]
in a time interval \(T=[0,b]\). Here, \(A:D(A)\subset \mathbb{R}^N \to 2^{\mathbb{R}^N}\) is a maximal monotone mapping and the control constraint multifunction \(U:T\times \mathbb{R}^N \to 2^{\mathbb{R}^N} \setminus \{ \emptyset \}\) has nonconvex values. It is assumed that \(U(t, \cdot )\) is lower semicontinuous for a.a. \(t\in T\). The authors introduce a control relaxed system by \(Q\)-regularization (in the sense of Cesari). Then, they show that every original state is a relaxed state and the set of the original states is dense in the set of the relaxed states, which is closed in \(C(T, \mathbb{R}^N)\).
Reviewer: Petru Jebelean (Timişoara)Hybrid projective combination-combination synchronization in non-identical hyperchaotic systems using adaptive control.https://www.zbmath.org/1456.340632021-04-16T16:22:00+00:00"Khan, Ayub"https://www.zbmath.org/authors/?q=ai:khan.ayub"Chaudhary, Harindri"https://www.zbmath.org/authors/?q=ai:chaudhary.harindriSummary: In this paper, we investigate a hybrid projective combination-combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination-combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.