Abstract

In this paper, we propose a novel vector-space optimization framework for contraction theory-based control design with input saturation. Conventional Linear Matrix Inequality (LMI) optimization frameworks suffer from computational complexity issues for high-dimensional systems and limited flexibility in handling various constraints, including input saturation. Moreover, there exists ill-posed problem in the objective function minimizing the condition number of the contraction metric. To address these issues, we project the contraction metrics onto the trajectory error vector space, leading to a simplified vector-space optimization framework within a lower-dimensional effective space. Furthermore, energy-based constraints are incorporated to obtain a finite number of locally optimal solutions and to maintain sufficient control effort. In addition, convex input saturation constraints are integrated to handle the practical limitations of actuators. The effectiveness and feasibility of the proposed method are validated through numerical simulations using the Lorenz system.

Additional Comments

Prof. Sesun You is Assistant Professor at Keimyung University, Daegu, South Korea. His biographical information can be found at his Google Scholar profile.