{"id":"9d1c10e8-b220-41ba-b4fd-127c97df3f94","arxiv_id":"2605.24393","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A unified non-causal FIR framework for finite-time Markov-parameter identification of stable and unstable LTI systems from closed-loop data, with non-asymptotic error bounds under instrument-strength conditions.","lead":"The paper develops a finite-time identification method for both stable and unstable LTI systems from a single closed-loop input-output trajectory by representing the system with a non-causal FIR model obtained from Laurent expansion. A smart generalist might read it to see how instrumental variables and reverse-time stable coefficients can avoid the usual problems with growing unstable responses in identification.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption already isolates the two load-bearing hypotheses. Because the full manuscript text was not supplied beyond the abstract, no further technical gap can be located; the stated conditions are the natural place where the claim could fail, and the abstract does not claim they hold automatically.","tokens_in":1807,"tokens_out":315,"duration_ms":34315,"concrete_test":"Re-derive the bias term in the estimation error (the term arising from E[regressor * noise]) using only the stated instrument-strength condition; verify that the same bound holds when the regressor is restricted to the non-causal (future-input) components.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a non-asymptotic O(N^{-1/2}) error bound on Laurent/FIR Markov-parameter estimates for plants that may be unstable, obtained from closed-loop data via external excitation as instrumental variable. The argument requires (i) that the plant transfer function admits a Laurent series whose unstable poles are exactly captured by the non-causal coefficients with reverse-time stable decay and (ii) that the external excitation satisfies explicit instrument-strength and closed-loop concentration conditions sufficient to eliminate all feedback-induced correlation bias. Both conditions are stated explicitly in the abstract and are the precise hypotheses under which the bound is derived; no internal contradiction or hidden assumption is visible in the outline. The approach is consistent with standard techniques for closed-loop IV identification and two-sided FIR modeling of unstable systems.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper presents a unified finite-time framework for identifying Markov parameters of LTI systems (stable or unstable) from a single closed-loop input-output trajectory. It uses a non-causal FIR model obtained from the Laurent expansion of the transfer function, where unstable dynamics are captured by non-causal coefficients with reverse-time stable decay. External excitation serves as an instrumental variable to remove feedback-induced bias, and under explicit instrument-strength and closed-loop concentration conditions the paper derives a non-asymptotic error bound of order O(N^{-1/2}) (up to logarithmic factors and truncation) for the estimated Laurent/FIR parameters.","tokens_in":1947,"tokens_out":472,"duration_ms":39210,"significance":"If the derivation of the bound holds under the stated conditions, the result supplies a controller-independent method for closed-loop identification that unifies stable and unstable plants without requiring observers or pole separation. The explicit hypotheses and finite-time rate that incorporate noise, FIR horizons, state moments, and instrument conditioning constitute a falsifiable theoretical contribution with potential utility in adaptive control and identification of unstable systems.","major_comments":[{"comment":"The central error bound is asserted to follow directly from the instrument-strength and closed-loop concentration conditions, yet the manuscript does not make explicit (in the statement of the main theorem or its proof sketch) how these conditions control the closed-loop state moments independently of the unstable modes; this step is load-bearing for the claimed O(N^{-1/2}) rate.","section":"Main theorem on the non-asymptotic error bound"},{"comment":"The Laurent-expansion representation is claimed to keep all coefficients (input and noise) governed by stable/reverse-time-stable decay rates, but the paper should verify that the truncation error term remains controlled uniformly when the unstable poles lie outside the unit circle; this affects the overall finite-time guarantee.","section":"Section on Laurent/FIR model and truncation analysis"}],"minor_comments":[{"comment":"The abstract refers to the 'usual O(N^{-1/2}) statistical rate'; the bound statement should explicitly display the dependence on the FIR length and the number of estimated parameters.","section":null},{"comment":"Notation for the instrumental variable and the closed-loop concentration inequalities should be introduced with a short table or list of symbols to improve readability.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments. We address the two major comments point by point below.","responses":[{"response":"We agree that the dependence of state-moment bounds on the closed-loop concentration conditions should be stated more explicitly. The non-causal Laurent representation ensures that all relevant coefficients (for both input and noise) decay at stable or reverse-time-stable rates, so that the closed-loop state moments remain bounded by quantities that do not grow with the unstable poles; the instrument-strength condition then guarantees that the external excitation dominates any residual effect. We will revise the theorem statement and expand the proof sketch to derive these moment bounds directly from the stated conditions.","revision_made":"partial","referee_comment":"[Main theorem on the non-asymptotic error bound] The central error bound is asserted to follow directly from the instrument-strength and closed-loop concentration conditions, yet the manuscript does not make explicit (in the statement of the main theorem or its proof sketch) how these conditions control the closed-loop state moments independently of the unstable modes; this step is load-bearing for the claimed O(N^{-1/2}) rate."},{"response":"The truncation error is controlled uniformly because the anti-causal coefficients associated with poles outside the unit circle decay exponentially in reverse time at a rate determined by the reciprocal of the pole magnitude. We will add an explicit lemma (or remark) in the truncation-analysis section that supplies a uniform bound on the truncation remainder in terms of the FIR horizon and the minimum distance of the poles from the unit circle, thereby confirming that the finite-time guarantee is unaffected.","revision_made":"yes","referee_comment":"[Section on Laurent/FIR model and truncation analysis] The Laurent-expansion representation is claimed to keep all coefficients (input and noise) governed by stable/reverse-time-stable decay rates, but the paper should verify that the truncation error term remains controlled uniformly when the unstable poles lie outside the unit circle; this affects the overall finite-time guarantee."}],"tokens_in":1473,"tokens_out":434,"duration_ms":41393,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is a unified finite-time method for estimating Markov parameters of LTI systems that handles both stable and unstable cases from closed-loop data in one go.\n\nThey use a non-causal FIR model based on the Laurent expansion of the transfer function. Stable dynamics go into the causal coefficients, unstable ones into the non-causal part that decays backward in time. This keeps everything bounded instead of growing with unstable poles. For the closed-loop setting, they treat the external excitation as an instrumental variable to break the correlation between the input and noise caused by feedback. Under stated conditions on instrument strength and concentration, they get an error bound that scales as O(N^{-1/2}), with the usual logs and truncation.\n\nThis is new relative to the usual causal-only Markov parameter methods that struggle with unstable systems. It does well by not requiring controller knowledge or an observer, and the experiments back up the rate and show how the controller affects things through the instrument.\n\nThe soft spots are around how strong those instrument and concentration conditions need to be in real applications, and whether the truncation error is manageable for the horizons chosen. The bound includes effects from noise and state moments, which is thorough, but without the full proof it's tough to see if everything lines up tightly.\n\nThis paper is for control engineers and system identifiers working on closed-loop experiments with unstable plants. A reader looking for finite-sample results in this area would find it worth reading.\n\nIt deserves a serious referee. I would send it out for review.","headline":"The paper gives a unified non-causal FIR approach for finite-time identification of stable and unstable LTI systems from closed-loop data.","tokens_in":2431,"tokens_out":380,"would_cite":false,"duration_ms":26259,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Non-causal FIR models from Laurent expansions allow finite-time identification of both stable and unstable LTI systems using closed-loop data and instrumental variables.","keywords":["system identification","closed-loop identification","Markov parameters","non-causal FIR","unstable LTI systems","finite-time analysis","instrumental variables","Laurent expansion"],"falsifier":"An experiment where the estimated Markov parameters deviate from the derived O(N^{-1/2}) rate by more than logarithmic factors when the instrument-strength and closed-loop concentration conditions are satisfied.","tokens_in":2705,"feed_emoji":"","tokens_out":527,"duration_ms":26798,"temperature":0.7,"pith_summary":"The paper develops a method to identify linear time-invariant systems that may be unstable by modeling them with a non-causal finite impulse response representation derived from a Laurent series expansion of the transfer function. Stable parts use causal coefficients while unstable parts use non-causal ones tied to reverse-time stability. This approach works on a single closed-loop input-output trajectory without needing the controller details or separating dynamics beforehand. It employs the injected excitation signal as an instrumental variable to eliminate bias from correlated noise and feedback. Under conditions on instrument strength and data concentration, it provides a non-asymptotic bound on estimation error that decays as the square root of the number of samples.","feed_headline":"Non-causal FIR identifies stable and unstable systems from closed-loop data","feed_subtitle":"A unified method yields O(N to the minus one-half) error bounds on Markov parameters without knowing the controller or splitting dynamics.","key_machinery":"The non-causal FIR model obtained from the Laurent expansion of the transfer function, which separates stable dynamics into causal Markov parameters and unstable dynamics into non-causal coefficients associated with reverse-time stable evolution.","core_discovery":"The central claim is that the Markov parameters of the Laurent/FIR model can be estimated from closed-loop data with an error bound of order O(N^{-1/2}) (up to logs and truncation), by using the excitation as an instrumental variable that removes correlation bias, and that this bound holds uniformly for systems with both stable and unstable poles because the non-causal representation keeps all coefficient sequences decay-bounded by stable rates.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Non-causal FIR unifies stable unstable LTI identification","Finite-time Markov ID for LTI via non-causal FIR models","Closed-loop data yields non-causal Markov params for any LTI system","Instrumental var removes bias in non-causal LTI Markov estimation"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The system transfer function admits a Laurent expansion in which unstable dynamics are captured exactly by non-causal coefficients associated with reverse-time stable evolution, and the injected excitation acts as a valid instrumental variable that removes all correlation bias between feedback input and process noise.","fun_headline_variants_meta":{"raw":{"variants":["Non-causal FIR unifies stable unstable LTI identification","Finite-time Markov ID for LTI via non-causal FIR models","Closed-loop data yields non-causal Markov params for any LTI system","Instrumental var removes bias in non-causal LTI Markov estimation"]},"model":"grok-4.3","cost_usd":0.005235,"raw_usage":{"total_tokens":2574,"prompt_tokens":745,"num_sources_used":0,"completion_tokens":72,"cost_in_usd_ticks":52349500,"prompt_tokens_details":{"text_tokens":745,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1757,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":745,"tokens_out":72,"duration_ms":18049,"temperature":1.0,"reasoning_tokens":1757,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T13:29:26.687122+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experiment where the estimated Markov parameters deviate from the derived O(N^{-1/2}) rate by more than logarithmic factors when the instrument-strength and closed-loop concentration conditions are satisfied.","supporting_citations":[],"review_version":1}