TY - JOUR

T1 - Saddle type hybrid limit cycle for the hybrid optimal pollution-controlproblem

AU - Ву, Ийлунь

AU - Тур, Анна Викторовна

AU - Е, Пэйчэнь

PY - 2026/4/30

Y1 - 2026/4/30

N2 - Based on prior studies focusing on single-parameter, single-switch hybrid optimal pollution-control problems with linear pollution loss, this paper extends the framework to multi-parameter and multiple-switch scenarios. By modeling key parameters as periodic piecewise-constant functions with predefined switching instants, we formulate a generalized hybrid optimal control problem. The corresponding periodic solutions are established, and the convergence behaviors of the system are analyzed under both linear and quadratic pollution loss functions. The study systematically compares the system’s convergence behavior under linear and quadratic pollution loss functions, revealing significant differences in the resulting equilibrium trajectories and stability characteristics. Our results reveal distinct dynamical properties, including the emergence of saddle-type hybrid limit cycles. The theoretical results provide new insights into the hybrid dynamics of pollution control systems and highlight the role of parameter switching in shaping long-term sustainable control strategies.

AB - Based on prior studies focusing on single-parameter, single-switch hybrid optimal pollution-control problems with linear pollution loss, this paper extends the framework to multi-parameter and multiple-switch scenarios. By modeling key parameters as periodic piecewise-constant functions with predefined switching instants, we formulate a generalized hybrid optimal control problem. The corresponding periodic solutions are established, and the convergence behaviors of the system are analyzed under both linear and quadratic pollution loss functions. The study systematically compares the system’s convergence behavior under linear and quadratic pollution loss functions, revealing significant differences in the resulting equilibrium trajectories and stability characteristics. Our results reveal distinct dynamical properties, including the emergence of saddle-type hybrid limit cycles. The theoretical results provide new insights into the hybrid dynamics of pollution control systems and highlight the role of parameter switching in shaping long-term sustainable control strategies.

KW - Hybrid optimal control

KW - Invariant solution

KW - Saddle-type hybrid limit cycle

KW - Stable manifold

UR - https://www.mendeley.com/catalogue/bd8fbab5-cbaf-3d89-ba45-9ea7e6bd8c2c/

U2 - 10.1007/s11071-026-12499-4

DO - 10.1007/s11071-026-12499-4

M3 - Article

VL - 114

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 9

M1 - 629

ER -