arXiv subjects

Haishan Zhang

Publications and source records attributed to Haishan Zhang.

3 recordsLinked to original sources

arXiv2025

Interior-Point-based H2 Controller Synthesis for Compartmental Systems

This paper addresses the problem of the optimal $H_2$ controller design for compartmental systems. In other words, we aim to enhance system robustness while maintaining the law of mass conservation. We perform a novel problem transformation and establish that the original problem is equivalent to an new optimization problem with a closed polyhedron constraint. Existing works have developed various first-order methods to tackle inequality constraints. However, the performance of the first-order method is limited in terms of convergence speed and precision, restricting its potential in practical applications. Therefore, developing a novel algorithm with fast speed and high precision is critical. In this paper, we reformulate the problem using log-barrier functions and introduce two separate approaches to address the problem: the first-order interior point method (FIPM) and the second-order interior point method (SIPM). We show they converge to a stationary point of the new problem. In addition, we propose an initialization method to guarantee the interior property of initial values. Finally, we compare FIPM and SIPM through a room temperature control example and show their pros and cons.

math.OC↗

arXiv2025

Sparse $H_\infty$ Controller for Networked Control Systems: Non-Structured and Optimal Structured Design

This paper provides a comprehensive analysis of the design of optimal structured and sparse $H_\infty$ controllers for continuous-time linear time-invariant (LTI) systems. Three problems are considered. First, designing the sparsest $H_\infty$ controller, which minimizes the sparsity of the controller while satisfying the given performance requirements. Second, designing a sparsity-promoting $H_\infty$ controller, which balances system performance and controller sparsity. Third, designing a $H_\infty$ controller subject to a structural constraint, which enhances system performance with a specified sparsity pattern. For each problem, we adopt a linearization technique that transforms the original nonconvex problem into a convex semidefinite programming (SDP) problem. Subsequently, we design an iterative linear matrix inequality (ILMI) algorithm for each problem, which ensures guaranteed convergence. We further characterize the first-order optimality using the Karush-Kuhn-Tucker (KKT) conditions and prove that any limit point of the solution sequence generated by the ILMI algorithm is a stationary point. For the first and second problems, we validate that our algorithms can reduce the number of non-zero elements and thus the communication burden through several numerical simulations. For the third problem, we refine the solutions obtained in existing literature, demonstrating that our approaches achieve significant improvements.

math.OC↗

arXiv2024

Quantitative determination of the orbital-selective Mott transition and quantum entanglement in the orbital-selective Mott phase

We examine the orbital-selective Mott transition in the non-hybridized two-band Hubbard model using the dynamical mean-field theory. We find that the orbital-selective Mott transition could be quantitatively depicted by the {local two-qubit fidelity}. Furthermore, within the orbital-selective Mott phase, the combined characteristics of the two orbitals lead to the presence of quantum entanglement, which is characterized by the non-semi-integer values of local two-qubit fidelity. It is demonstrated that the Hund's coupling results in the ground states of both wide and narrow bands exhibiting the specific superposition states, indicating the existence of quantum entanglement within orbital-selective Mott phase. Without Hund's coupling, there are no specific superposition states, nor does quantum entanglement occur within the orbital-selective Mott phase. The mechanisms underlying the orbital-selective Mott transition show prominent variations depending on the presence or absence of Hund's coupling and its transverse terms.

cond-mat.str-el↗