Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problems of trajectory generation and tracking for general 2 × 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output.  solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which re derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2×2 linear hyperbolic systems. For tracking the desired trajectory  employ a PI control law on the tracking error of the output.  prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel “non-diagonal” Lyapunov functional.
['Pierre-Olivier Lamare', 'Nikolaos Bekiaris-Liberis', 'Alexandre M. Bayen']
I am writing a research paper on a idea Control of 2 × 2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking
[{"from": "human", "value": "I am writing a research paper on a idea Control of 2 \u00d7 2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problems of trajectory generation and tracking for general 2 \u00d7 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output.  solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which re derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2\u00d72 linear hyperbolic systems. For tracking the desired trajectory  employ a PI control law on the tracking error of the output.  prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel \u201cnon-diagonal\u201d Lyapunov functional."}]