This paper presents numerical methods for solving the Modified Filter Algebraic Riccati Equation (MFARE) for synthesis of H-infinity fault detection filters. Two methods are presented, namely the gamma-iteration and then rewriting the MFARE in Linear Matrix Inequalities (LMIs) and casting it as a convex optimization problem. Each algorithm has to ensure the condition for a global convergence and also has to deliver an optimal solution. Not at least the computational cost has to be as small as possible.
Słowa kluczowe: Modified Filter Algebraic Riccati Equation, linear-quadratic optimization problem, H-infinity optimization, gamma-iteration, LMI.
Zaprezentowano metodę numeryczną rozwiązywania równania MFARE (Modified Filter Algebraic Riccati Equation). Badano dwie metody - iterację gamma i przepisywanie równania w postać Linear Matrix Inequantities.
Keywords: MFARE - Modified Filter Algebraic Riccati Equation, optymalizacja H-infinity
Diesel engines have become more complex and powerful in the past decade, moreover lots of the mechanical functions are being replaced by electric and electronic devices, which are controlled by the ECU. In order to ensure the strict environment policies, these devices and the ECU as well have to make sure the reducing of fuel consumption and the emission of pollutant species. On the top of this the ECU is also equipped with reliable fault diagnose system to detect possible actuator, sensor and component failures in the engine. The subject of our investigation is a robust model-based fault detection filtering of faults in the air-path of diesel engines. When designing a H-infinity filter, the filter gain can be obtained by solution of a Modified Filter Algebraic Riccati Equation (MFARE), which is one of the central and most difficult tasks in the synthesis, see e.g. in , ,  and . One way to get there is an applying gamma-iteration, another one, which is more state of the art, is using LMIs. Several investigations of robust control have been carried out in the past two decades using LMIs, see e.g. , , . As a result, it has been stated, that LMIs are effective and powerful tools for handling complex, but standard problems, such as a fast computing of global optimum within some pre-specified accuracy. As even it is to be done in our case, solving the H-infinity optimization problem to specify the filter. This paper is organized as follows: after the introduction, in Section II we shortly revisit the problem of H-infinity optimization and describe the MFARE. In Section III MFARE is converted to an LMI as an optimization problem. In Section IV an algorithm called gamma-iteration is implemented to solve the MFARE, then it is formulated as a linear objective minimization problem using LMI. Deriving the Modified Filter Algebraic Riccati Equation for robust H-infinity detection filtering The optimal H-infinity [...]
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