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<p>This paper presents a unified control-optimization framework that integrates Sliding Mode Control (SMC), Pontryagin’s Minimum Principle (PMP), and Grey Wolf Optimization (GWO) for the simultaneous optimization of prostate cancer treatment parameters. The SMC scheme provides a robust baseline control law that stabilizes the Androgen Deprivation Therapy (ADT) model against uncertainties. PMP is then applied to formalize the optimal control problem and derive the necessary state-costate dynamics, embedding the SMC-derived control structure. Finally, GWO is used as a numerical solver to handle the nonlinear two-point boundary value problem defined by PMP when closed-form solutions are impractical. The decision variables in GWO correspond to discretized control inputs over the treatment horizon, constrained by the PMP equations and biological bounds. A biologically referenced parameter set is used and robustness was confirmed through sensitivity analysis under ± 20% parameter perturbations. Comparative analysis with Genetic Algorithm (GA), Teaching–Learning-Based Optimization (TLBO), and Newton–Raphson methods shows that the proposed framework achieves statistically significant improvements in clinically relevant metrics, including treatment duration and drug toxicity index. Model-based simulations suggest that optimized treatment schedules can reduce cancer cell burden and minimize drug exposure under idealized conditions; however, these findings are theoretical and require further clinical validation.</p>

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Concurrent cancer cell optimization using Pontryagin minimum principle and grey Wolf optimization-based sliding mode control

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Priya Dubey,
  • Surendra Kumar,
  • Sudhansu Kumar Mishra,
  • Subrat Kumar Swain

摘要

This paper presents a unified control-optimization framework that integrates Sliding Mode Control (SMC), Pontryagin’s Minimum Principle (PMP), and Grey Wolf Optimization (GWO) for the simultaneous optimization of prostate cancer treatment parameters. The SMC scheme provides a robust baseline control law that stabilizes the Androgen Deprivation Therapy (ADT) model against uncertainties. PMP is then applied to formalize the optimal control problem and derive the necessary state-costate dynamics, embedding the SMC-derived control structure. Finally, GWO is used as a numerical solver to handle the nonlinear two-point boundary value problem defined by PMP when closed-form solutions are impractical. The decision variables in GWO correspond to discretized control inputs over the treatment horizon, constrained by the PMP equations and biological bounds. A biologically referenced parameter set is used and robustness was confirmed through sensitivity analysis under ± 20% parameter perturbations. Comparative analysis with Genetic Algorithm (GA), Teaching–Learning-Based Optimization (TLBO), and Newton–Raphson methods shows that the proposed framework achieves statistically significant improvements in clinically relevant metrics, including treatment duration and drug toxicity index. Model-based simulations suggest that optimized treatment schedules can reduce cancer cell burden and minimize drug exposure under idealized conditions; however, these findings are theoretical and require further clinical validation.