Solar energy paper index
Optimal control of symmetry-breaking dynamics near criticality
One-line summary
A solar energy research paper on Optimal control of symmetry-breaking dynamics near criticality.
Engineering notes
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Chinese explanation / 中文解读
中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。
Original abstract
We study the problem of optimal control for dynamical systems near a pitchfork bifurcation, motivated by the role of external cues in guiding symmetry-breaking transitions in cell-fate selection and other natural processes. Using an asymptotic expansion of the optimality conditions obtained from the Pontryagin maximum principle, the leading-order optimal control law for a general n-dimensional system is examined across three dynamical regimes distinguished by scaling of control strength with respect to the distance from criticality. While in the strong control limit the results reduce to known approximations from linear-quadratic control, we derive generalized amplitude equations for the co-evolution of state and costate variables describing the optimized trajectory in the weak and intermediate control regimes. These control normal forms are validated against numerical solutions of the full optimal control problem for a canonical model of a bistable biochemical switch. The bifurcation structure of the optimal control problem is analyzed in the weak control regime. Finally, we demonstrate the construction of asymptotic solutions in the long time limit in this regime using boundary-layer methods.
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