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This paper proposes a new gradient-based optimization approach for designingoptimal feedback kernels for parabolic distributed parameter systems withboundary control. Unlike traditional kernel optimization methods for parabolicsystems, our new method does not require solving non-standard Riccati-type orKlein-Gorden-type partial differential equations (PDEs). Instead, the feedbackkernel is parameterized as a second-order polynomial whose coefficients aredecision variables to be tuned via gradient-based dynamic optimization, wherethe gradient of the system cost functional (which penalizes both kernel andoutput magnitude) is computed by solving a so-called costate PDE instandardform. Special constraints are imposed on the kernel coefficients to ensurethat, under mild conditions, the optimized kernel yields closed-loop stability.Numerical simulations demonstrate the effectiveness of the proposed approach.

A Gradient-based Kernel Optimization Approach for Parabolic Distributed Parameter Control Systems