{"paper":{"title":"Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Partial integral equations turn impulse-to-peak analysis and optimal state-feedback design for linear PDEs into solvable convex optimization problems.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Javad Mohammadpour Velni, Sachin Shivakumar, Tristan Thomas","submitted_at":"2026-04-03T19:01:27Z","abstract_excerpt":"Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial differential equation (PDE) systems due to the lack of a universal transfer function and state-space representation. Recently, however, partial integral equation (PIE) representation was proposed as the desired state-space representation of a PDE, and Lyapunov stability theory was used to solve various control problems, such as stability and optimal ${H}_\\infty"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we utilize this PIE framework, and associated Lyapunov techniques, to formulate the I2P response analysis problem as a solvable convex optimization and obtain provable bounds for the I2P-norm of linear PDEs. Moreover, by establishing strong duality between primal and dual formulations of the optimization problem, we develop a constructive method for I2P optimal state-feedback control of PDEs","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The partial integral equation representation is an exact and complete state-space model for the linear PDEs considered, allowing Lyapunov-based convex optimization to produce non-conservative bounds and controllers without hidden approximation errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The authors use partial integral equations and Lyapunov techniques to cast impulse-to-peak norm analysis as convex optimization and derive optimal state-feedback controllers for linear PDEs via strong duality.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Partial integral equations turn impulse-to-peak analysis and optimal state-feedback design for linear PDEs into solvable convex optimization problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"232d2ff0b334bd68294fe5d684c6bbe47fca6977651d4ac36b07fee3a200b753"},"source":{"id":"2604.03399","kind":"arxiv","version":2},"verdict":{"id":"69019bd0-caaf-496e-959b-1f14136e35a1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T18:07:49.609967Z","strongest_claim":"we utilize this PIE framework, and associated Lyapunov techniques, to formulate the I2P response analysis problem as a solvable convex optimization and obtain provable bounds for the I2P-norm of linear PDEs. Moreover, by establishing strong duality between primal and dual formulations of the optimization problem, we develop a constructive method for I2P optimal state-feedback control of PDEs","one_line_summary":"The authors use partial integral equations and Lyapunov techniques to cast impulse-to-peak norm analysis as convex optimization and derive optimal state-feedback controllers for linear PDEs via strong duality.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The partial integral equation representation is an exact and complete state-space model for the linear PDEs considered, allowing Lyapunov-based convex optimization to produce non-conservative bounds and controllers without hidden approximation errors.","pith_extraction_headline":"Partial integral equations turn impulse-to-peak analysis and optimal state-feedback design for linear PDEs into solvable convex optimization problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.03399/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"806b4fe90a51e944bdc3915597577e1ca7174725893a1b17ebc5aee315d1ec5f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}