Temporal Logic Inference for Fault Detection of Switched Systems With Gaussian Process Dynamics
Gang Chen* et al.
IEEE Transactions on Automation Science and Engineering, 2021
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In this article, we present a method for constructing the fault detector in the form of signal temporal logic (STL) formulas, which can be understood by human users and formally proven to detect faults with probabilistic satisfaction guarantees, for a class of switched nonlinear systems with partially unknown dynamics. First, the partially unknown internal dynamics are approximated by the Gaussian process with stability guarantees. Second, a novel temporal logic inference algorithm is proposed to find the fault detector, which takes advantage of the internal properties of temporal logic and searches for the optimal formula along a partially ordered direction. Moreover, the algorithm is not allowed for missing faults but allowed for false alarms during the temporal logic inference process. In addition, we simulate finitely many trajectories with Chua’s circuit and infer the temporal logic formulas with the Gaussian optimization. The results show that the proposed method can find a temporal logic formula to detect the faulty trajectory with a probability guarantee. Note to Practitioners—The method proposed in this article can be used to detect faults for switched systems with partially unknown dynamics. STL is used to describe the behaviors of the system, which acts as a classifier and detector, such that all normal behaviors of the system will satisfy the description, while the faulty behaviors will violate the description. Moreover, STL formulas can be understood by human operators, which is important for the timely response to faulty events. For example, the normal behavior of a smart grid can be described as follows: “if the smart grid is safe, it should reach 9 kV within 15 min when the voltage to region A is above 12 kV,” which can be expressed with STL. Due to the unknown dynamics, the Gaussian process regression is applied to estimate the model and the region that is robust to noises.

                @article{chen2021temporal,
                  title={Temporal Logic Inference for Fault Detection of Switched Systems With Gaussian Process Dynamics},
                  author={Chen, Gang, et al.},
                  journal={IEEE Transactions on Automation Science and Engineering},
                  year={2021},
                  publisher={IEEE}
                }

          

Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS
Gang Chen, Zhaodan Kong, Longhan Xie
International Journal of Control,2024
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‘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).

          @article{chen2024control,
            title={Control/physical systems co-design with spectral temporal logic specifications and its applications to MEMS},
            author={Chen, Gang and Kong, Zhaodan and Xie, Longhan},
            journal={International Journal of Control},
            pages={1--16},
            year={2024},
            publisher={Taylor \& Francis}
          }