Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914622612701184 |
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| author | Thomas, Tristan Shivakumar, Sachin Velni, Javad Mohammadpour |
| author_facet | Thomas, Tristan Shivakumar, Sachin Velni, Javad Mohammadpour |
| contents | 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 ${H}_\infty$ control. In this work, 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 and demonstrate the effectiveness of the method on various examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs Thomas, Tristan Shivakumar, Sachin Velni, Javad Mohammadpour Optimization and Control Systems and Control 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 ${H}_\infty$ control. In this work, 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 and demonstrate the effectiveness of the method on various examples. |
| title | Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.03399 |