Mohammad Keyanpour

This paper addresses the observer‐based output‐feedback boundary control design for a system of ‐coupled parabolic partial differential equations (PDEs) with spatially varying diffusion coefficients without any ordering conditions. First, a boundary observer is proposed to estimate the system states, with its gain determined by considering a stable target system and using a backstepping transformation method. To design an observer‐based boundary controller for ‐coupled parabolic PDE systems, we construct a backstepping transformation that maps the observer dynamics into a stable target system, yielding the associated kernel and boundary control law, which is the main contribution of this work. Furthermore, analytical solutions to two sets of kernel equations are derived to determine the controller and observer gains. By employing Lyapunov stability analysis, we prove that the proposed output‐feedback architecture guarantees exponential stability of the entire closed‐loop system. Finally, numerical simulations are conducted to validate the theoretical results of the proposed method.

This research explores the stabilization of a wide class of coupled dynamical systems, consisting of partial and ordinary differential equations with spatially varying coefficients. The main challenge in controlling these systems is the presence of variable spatial coefficients, which prevents the use of conventional control design methods. To address this challenge, we introduce an innovative approach employing deep neural networks, specifically DeepONet. A key advantage of this method is that it removes the need for pre-solving differential equations. The ability of DeepONet to approximate nonlinear operators is utilized to design a backstepping control strategy that ensures exponential stability of the system. The efficiency of the proposed method in stabilizing complex coupled systems is demonstrated through simulation results.

The paper is devoted to the study of boundary finite-time control for a reaction-diffusion (RD) system with switching time-delayed input. The RD system with switching time-delay input is converted to a switching system of RD equation cascaded with a transport equation with non-delay boundary input. Next, a novel switching controller is designed for the cascaded RD-transport system based on the backstepping technique, and this causes the closed-loop system to be convergence in a finite-time. Simulation results are provided to exhibit the effectiveness of the proposed method.

In this paper, we study a non-convex min–max fractional problem of quadratic functions subject to convex and non-convex quadratic constraints. First, by using the Dinkelbach-type method, we transform the fractional problem into a univariate nonlinear equation. To evaluate this equation, we need to solve a non-convex quadratically constrained quadratic programming (QCQP) problem. To solve this problem, we propose a new method. In the proposed method, first, by using relaxation and convexification of non-convex constraints of non-convex QCQP problem, an upper bound and a lower bound of the optimal value is obtained. By using these bounds, we construct a parametric QCQP problem with two constraints. Then, by solution of the new problem, the parameters of this problem are updated for the next iteration. We show that the sequence of solutions of new problems is convergent to a global optimal solution of the non-convex QCQP problem. Numerical results are given to show the applicability of the proposed method.

This study focuses on the observer and observer-based output feedback control design for a one-dimensional wave equation with van der Pol type nonlinear boundary condition and Dirichlet boundary control. The contribution of this work is divided into two parts. Firstly, the anti-collocated backstepping observer design for the nonlinear wave system is investigated, and the asymptotical stability analysis of the observer error is studied. Secondly, an output feedback observer-based controller is set up by using boundary displacement measurement only to stabilize the nonlinear wave system; also the asymptotical stability of the closed-loop system is shown. The validity of the theoretical results is demonstrated by numerical simulations.

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to two quadratic constraints in the complex space. Using the classical Dinkelbach method, we transform the problem into a parametric nonlinear equation. We show that an optimal parameter can be found by employing the S-procedure and semidefinite relaxation technique. A key element to solve the original problem is to use the rank-one decomposition procedure. Finally, within the new algorithm, semidefinite relaxation is compared with the bisection method for finding the root on several examples. For further comparison, the solution of fmincon command of MATLAB also is reported.