Fault-tolerant Control Design Based On The Bmi Method Indicators

Fault-tolerant control is a kind of control that can guarantee the systems run stably and keep the desired performance even if there are failures in the systems. Fault-tolerant control technology provides one way for the control of systems in complex environments.With bilinear matrix inequality (BMI), linear matrix inequality (LMI) and matrix analysis as tools, this paper attempts to study the fault-tolerant control problems for a class of linear continuous-time systems with multi-index constraint and provides effective algorithms to solve the desired output feedback gain. Its purpose is to provide basis theoretically and numerically for the fault-tolerlant control of engineering systems with multi-requirements. The main content of this paper is as follows.1) Fault-tolerant output-feedback control with pole assignmentFirst, a new BMI formulation is provided for the solvability of the control problem. Then following the existing path-following method for solving BMI problem, an iterative LMI algorithm is proposed to locally search the desired output-feedback gain. Furthermore, while the pole placement problem admits a desired output-feedback, by minimizing the sum of the absolute value of the gain matrix elements, an algorithm is proposed to find a low-cost output feedback gain. The low-cost here means the feedback gain has as more zero elements as possible.The similar study is extended to uncertain system.2) Fault-tolerant output-feedback control with pole assignment and H-infinityThe above method to solve pole-constrained output-feedback is extended respectively to the problems with regional pole placement and H-infinity bound. An iterative algorithm is proposed to solve the associated problems respectively. Moreover, an algorithm is also given to solve the H-infinity output-feedback gain under constraints of pole assignment.3) Fault-tolerant output-feedback control with constraints on pole and varianceBy perturbation linearization of BMI, fault-tolerant output-feedback control is studied for systems with constraints on pole assignment and steady output variance, and an algorithm is proposed to solve the corresponding problems iteratively.For the three classes of fault-tolerant control problems considerded, numerical experiments are provided respectively to demonstrate the effectiveness of the provided algorithms.