Fault accommodation in bilinear systems – a logic-dynamic approach

The purpose of this study is to investigate the problem of fault accommodation in bilinear dynamic systems.

Solution to this problem is related to constructing the control law which provides full decoupling with respect to the fault effects. The so-called logic-dynamic approach will be used to solve this problem. The main steps of this approach are: replacing the initial bilinear system by certain linear one, solving the problem under consideration for this linear system by well-known linear methods with some restrictions, taking into account the bilinear term to correct the obtained linear solution.

Existing conditions of the fault accommodation problem in a form of rank equalities and inequalities are formulated. Calculating relations for the control law and the auxiliary systems are given.

The suggested method allows determining such a control law that preserves the main performances of the system in the faulty case, while the minor performances may degrade.

The main advantage of the logic-dynamic approach is a possibility to solve the problem of fault accommodation for nonlinear systems by linear methods without decreasing the main properties of the obtained solution.