Interior-Point-based H2 Controller Synthesis for Compartmental Systems

TL;DR

This paper develops interior-point methods for optimal H2 controller design in compartmental systems, improving convergence speed and precision while ensuring mass conservation, with practical comparisons demonstrated through a temperature control example.

Contribution

It introduces novel interior-point algorithms (FIPM and SIPM) for H2 controller synthesis in compartmental systems, addressing limitations of existing first-order methods.

Findings

FIPM and SIPM converge to stationary points.

The methods outperform traditional approaches in speed and accuracy.

Practical effectiveness shown in temperature control example.

Abstract

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.