What does "Satisfaction Guaranteed" Mean?

Satisfactory fault-tolerant control ^[1] is a fault-tolerant control concept proposed for traditional fault-tolerant control that rarely considers the multiple operating condition constraints and multi-performance requirements of modern practical engineering control systems, drawing on the results of multi-objective optimization and satisfactory control. It does not pursue the optimal solution for fault-tolerant control objectives, but seeks the largest solution set that simultaneously meets multiple condition constraints and control performance requirements, in order to obtain a satisfactory and feasible "eclectic" sub-optimal solution to ensure that the control system fails. It still operates safely with acceptable or satisfactory overall performance. At present, satisfactory fault-tolerant control mainly studies the problem of fault-tolerant control combining multiple performance indicators and multiple constraints.

Satisfactory fault-tolerant control

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Satisfactory fault-tolerant control ^[1] is a fault-tolerant control concept proposed for traditional fault-tolerant control that rarely considers the multiple operating condition constraints and multi-performance requirements of modern practical engineering control systems, drawing on the results of multi-objective optimization and satisfactory control. It does not pursue the optimal solution for fault-tolerant control objectives, but seeks the largest solution set that simultaneously meets multiple condition constraints and control performance requirements, in order to obtain a satisfactory and feasible "eclectic" sub-optimal solution to ensure that the control system fails. It still operates safely with acceptable or satisfactory overall performance. At present, satisfactory fault-tolerant control mainly studies the problem of fault-tolerant control combining multiple performance indicators and multiple constraints.

In order to ensure that the satisfactory fault-tolerant control strategy is solvable, the initial main research idea is to integrate the expected H index, regional pole, variance and other desired index constraints into a modified algebra Lypaunov equation or a modified Riccati equation. From this modified algebra Starting from the positive definite solution matrix of the equation (usually called configurable matrix), the matrix decomposition and generalized inverse theory of the matrix are used to derive a control strategy that meets all desired performance indicators. However, as the expected index increases, finding such modified Lypaunov equations or algebraic Riccati equations becomes more and more difficult, and the constraints of such equations greatly limit the breadth of the satisfactory control solution set. Currently, the linear matrix inequality (LMI) method is used to describe multiple expectations and constraints with multiple linear matrix inequality. Through variable substitution and matrix operations, the range of values for the constraint index constraint The solution problem is transformed into a linear programming problem constrained by the LMI group, so that the fault-tolerant control problem with multiple indexes and multiple operational constraints is transformed into a linear programming problem with the LMI group constraint. This programming problem is solved using the popular Matlab / LMI calculation software Provides a new method for satisfactory fault-tolerant control design.