Finite Time LTI System Identification
Authors: Tuhin Sarkar, Alexander Rakhlin, Munther A. Dahleh
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 6. Experiments. The experiments in this paper are for the single trajectory case. A detailed analysis for system identification from multiple trajectories can be found in Tu et al. (2017). Suppose that the LTI system generating data, M, has transfer function given by G(z) = α0 + P l=1 αlρlz l, ρ < 1 (20) where αi N(0, 1). M is a finite dimensional LTI system or order 150 with parameters as M = (C R1 150, A R150 150, B R150 1). For these illustrations, we assume a balanced system and choose R = 1, δ = 0.05. We estimate β0.6 = 15, β0.9 = 40, β0.99 = 140, pick Ut N(0, 1) and {wt, ηt} {N(0, 1), N(0, I)} respectively. We note that our algorithm requires the knowledge of universal constant c. Theoretically, it can be shown that c < 100 but in practice a value c 16 works well for simulations. Figure 1: Variation of Hankel size = ˆd with T for different values of ρ. Figure 2: Variation of ||M c Mk||op for different values of ρ. Here k = ˆd for our algorithm and k = log (T). Furthermore, || ||op is the Hankel norm. Finally, for the case when ρ = 0.9, β = 40, we show the model errors for SSREGEST and our algorithm as T increases. Although asymptotically both algorithms perform the same, it is clear that for small T our algorithm is more robust to the presence of noise. |
| Researcher Affiliation | Academia | Tuhin Sarkar EMAIL Department of Electrical Engineering and Computer Sciences Massachusetts Institute of Technology Cambridge, MA 02139, USA Alexander Rakhlin EMAIL Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139, USA Munther A. Dahleh EMAIL Department of Electrical Engineering and Computer Sciences Massachusetts Institute of Technology Cambridge, MA 02139, USA |
| Pseudocode | Yes | Algorithm 1 Learn System(T, d, m, p) Input T = Horizon for learning d = Hankel Size m = Input dimension p = Output dimension Output System Parameters: ˆH0,d,d... Algorithm 2 Choice of d Output ˆH0, ˆd, ˆd, ˆd... Algorithm 3 Hankel2Sys(T, ˆd, k, m, p) Input T = Horizon for Learning ˆd = Hankel Size m = Input dimension p = Output dimension Output System Parameters: ( ˆC ˆd, ˆA ˆd, ˆB ˆd) |
| Open Source Code | No | The paper does not provide any explicit statements about releasing code, a link to a code repository, or mention of code in supplementary materials for the methodology described. |
| Open Datasets | No | The paper describes generating its own simulated data for experiments: "Suppose that the LTI system generating data, M, has transfer function given by G(z) = α0 + P l=1 αlρlz l, ρ < 1 (20) where αi N(0, 1). M is a finite dimensional LTI system or order 150 with parameters as M = (C R1 150, A R150 150, B R150 1). For these illustrations, we assume a balanced system and choose R = 1, δ = 0.05. We estimate β0.6 = 15, β0.9 = 40, β0.99 = 140, pick Ut N(0, 1) and {wt, ηt} {N(0, 1), N(0, I)} respectively." It does not use or provide access information for a publicly available dataset. |
| Dataset Splits | No | The paper uses simulated data rather than an external dataset that would require predefined splits. Therefore, it does not provide information about training/test/validation dataset splits. |
| Hardware Specification | No | The paper describes the parameters and conditions for its simulations in Section 6 'Experiments' but does not specify any hardware details (e.g., GPU, CPU models, memory) used to run these simulations. |
| Software Dependencies | No | The paper describes the mathematical and statistical aspects of the system identification and simulation parameters in Section 6 'Experiments'. However, it does not mention any specific software libraries, tools, or their version numbers that were used for implementation or running the experiments. |
| Experiment Setup | Yes | For these illustrations, we assume a balanced system and choose R = 1, δ = 0.05. We estimate β0.6 = 15, β0.9 = 40, β0.99 = 140, pick Ut N(0, 1) and {wt, ηt} {N(0, 1), N(0, I)} respectively. We note that our algorithm requires the knowledge of universal constant c. Theoretically, it can be shown that c < 100 but in practice a value c 16 works well for simulations. |