The major bottleneck in state-of-the-art Linear Parameter Varying (LPV) subspace methods is the curse-of-dimensionality during the first regression step. In this paper, the origin of the curse-of-dimensionality is pinpointed and subsequently a novel method is proposed which does not suffer from this bottleneck. The problem is related to the LPV sub-Markov parameters. These have inherent structure and are dependent on each other. But state-of-the-art LPV subspace methods parametrize the LPV sub-Markov parameters independently. This means the inherent structure is not preserved in the parametrization. In turn this leads to a superfluous parametrization with the curse-of-dimensionality. The solution lies in using parametrizations which preserve the inherent structure sufficiently to avoid the curse-of-dimensionality. In this paper a novel method based on tensor regression is proposed. This novel method is named the Predictor-Based Tensor Regression method (PBTR). This method preserves the inherent structure sufficiently to avoid the curse-of-dimensionality. Simulation results show that PBTR has superior performance with respect to both state-of-the-art LPV subspace techniques and also non-convex techniques.@en

In this paper, we present a novel multiple input multiple output (MIMO) linear parameter varying (LPV) state-space refinement system identification algorithm that uses tensor networks. Its novelty mainly lies in representing the LPV sub-Markov parameters, data and state-revealing matrix condensely and in exact manner using specific tensor networks. These representations circumvent the ‘curse-of-dimensionality’ as they inherit the properties of tensor trains. The proposed algorithm is ‘curse-of-dimensionality’-free in memory and computation and has conditioning guarantees. Its performance is illustrated using simulation cases and additionally compared with existing methods.@en

With advancing technology, systems are becoming increasingly interconnected and form more complex networks. Additionally, more measurements are available from systems due to cheaper sensors. Hence there is a need for identification methods specifically designed for networks. For dynamic networks with known interconnection structures, several methods have been proposed for obtaining consistent estimates. We suppose that the internal variables in the network are measured with noise, but that there are external reference signals present in the network that are known exactly. A method that is able to deal with this situation is the two stage method, which solves several open loop identification problems sequentially. In this paper it is shown that solving the problems simultaneously leads to estimates with lower variance.@en

Linear Parameter Varying (LPV) subspace identification methods suffer from an exponential growth in number of parameters to estimate. This results in problems with ill-conditioning. In literature, attempts have been made to address the ill-conditioning by using regularization. Its effectiveness hinges on suitable a priori knowledge. In this paper we propose using a novel, alternative regularization. That is, we first show that the LPV sub-Markov parameters can be organized into several tensors which are multi-linear low-rank by construction. Namely, their matricization along any mode is a low-rank matrix. Then we propose a novel convex method with tensor nuclear norm regularization which exploits this low-rank property. Simulation results show that the novel method can have higher performance than the regularized LPV-PBSIDopt technique in terms of variance accounted for.@en