Identification of LPV systems using successive approximations

Abstract

In this paper a successive approximation approach for MIMO linear parameter varying (LPV) systems with affine parameter dependence is proposed. This new approach is based on an algorithm previously introduced by the authors, which elaborates on a convergent sequence of linear deterministicstochastic state-space approximations. In the previous algorithm the bilinear term between the time varying parameter vector and the state vector is allowed to behave as a white noise process when the scheduling parameter is a white noise sequence. However, this is a strong limitation in practice since, most often than not, the scheduling parameter is imposed by the process itself and it is typically a non white noise signal. In this paper, the bilinear term is analysed for non white noise scheduling sequences. It is concluded that its behaviour depends on the input sequence itself and it ranges from acting as an independent colored noise source, mostly removed by the identification algorithm, down to a highly input correlated signal that may be incorrectly assumed as being part of the system subspace. Based on the premise that the algorithm performance can be improved by the noise energy reduction, the bilinear term is expressed as a function of past inputs, scheduling parameters, outputs, and states, and the linear terms are included in a new extended input.

LPV-ARX representations of LPV state-space models with affine dependence

“…Linear parameter-varying (LPV) systems are usually defined as linear timevarying systems, where the time varying coefficients are functions of a certain time-varying signal, the so-called scheduling variable [1], [2]. Practical use of LPV systems is stimulated by the fact that LPV control design [3][4][5][6][7][8][9] and identification [10][11][12][13][14][15][16][17][18][19][20] are well developed. Despite these advances, there are important gaps in system theory for LPV systems.…”

“…More precisely, the system parameters were meromorphic functions of the scheduling variables and its derivatives (continuous-times), or of the current and future values of the scheduling variable (discrete-time). However, from a practical point of view, LPV state-space representations with static and affine dependence (affine dependence on the instantaneous value of the scheduling variable) are preferable [9][10][11][12][13][14][15][16][17][18][19][20]. We will use the abbreviation LPV-SSA for the latter class of state-space representations.…”

Leakage detection and location in gas pipelines through an LPV identification approach

“…The model was identified from operational data using an algorithm described in [10,11]. The leakage is detected with a Kalman filter where the fault is treated as an additional state.…”