Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS

Abstract

‘Co-design’ problems try to simultaneously design the physical and control components to improve the overall system performance. However, existing co-design paradigms cannot deal with complex frequency temporal domain specifications. In this paper, we investigate the co-design problem for a class of linear parameter-varying (LPV) systems with frequency temporal domain specifications. Firstly, the frequency temporal domain specifications are written in a formal language called spectral temporal logic (STL). Secondly, the satisfaction conditions of the spectral temporal logic specifications have been transformed into non-linear matrices inequality forms with necessary and sufficient conditions. Thirdly, the co-design problem is transformed into a non-convex optimisation problem with mixed-integer linear matrix inequalities (MILMIs) constraints, and then an iterative algorithm is proposed to solve the co-design problem with semidefinite programming (SDP). Finally, the performance of the algorithm and the expressiveness of spectral temporal logic are illustrated with the applications to micro-electromechanical systems (MEMS).

Keywords:

• Co-design
• micro-electromechanical systems
• spectral temporal logic
• mixed-integer linear matrix inequality

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Key R&D Program of China [grant number 2021YFB3301402], partially supported by the National Natural Science Foundation of China [grant number 52305105], the Basic and Applied Basic Research Foundation of Guangdong Province [grant numbers 2022A1515240027 and 2023A1515010812], the Basic and Applied Basic Research Foundation of Guangzhou [grant number 2023A04J1582].