Research On Satisfactory Fault-Tolerant Control With Multi-objective Constraint

For a class of linear uncertain systems with uncertraints which donnot satisfy maching conditions, the design methods of satisfactory fault-tolerant (SFT) control with multi-objecive constraints have been studied. Under a continuous fault model of the actuator, the problems of consistent and conservatism for multi-objective constraints are analyzed by linear matrix inequality apparoach. The simulations for longitude control of one kind aircraft indicate the validity of the proposed methods. The main contents of the paper are outlined as follows:Firstly, based on pole assignment theory, the problem of SFT control for linear uncertain systems with circular pole index constraint is studied. Sufficient conditions for existence and a design method of SFT controller are provided. If the controller exists, then a region of the controller is given. In addition, multi-objective constrained control can be considered and designed.Secondly, based on state feedback, the design method of SFT control is presented for linear uncertain systems with circular pole index and H_∞index. The range of H_∞index is analyzed, which is consistent with circular pole index. By the above consistent analysis, sufficient conditions for existence and a design method of SFT controller are provided.Thirdly, the problem of SFT control for linear uncertain systems with circle pole index, H_∞index and H₂ index constraints is produced. The consistency conditions of multi-objective fault-tolerant performance are set up. Additionally, sufficient conditions for existence and a design method of SFT controller with constrains of consistent indices are developed.Finally, by exploiting the Projection Lemma and Schur complement theorem, the extend LMI constraint conditions of the circular pole index, H_∞index and H₂ index are presented. Then the design of SFT controller with extend multi-objective constraints is accomplished. This method leads to the use of different Lyapuov functions to deal with the multi-objective constrained control problem, and then reduces the design conservatism of SFT controller with multi-objective constraints.