Optimization of the Islamic Banking System Using the Linear Quadratic Regulator (LQR)-PSO: Implications for Performance Stability and Financing Risk Mitigation
DOI:
https://doi.org/10.24252/iqtisaduna.v12i2.70885Keywords:
Islamic Banking, Profit-Sharing Ratio, Optimal Control, LQR-PSO, Risk Mitigation, Systemic StabilityAbstract
Islamic banking profit-sharing ratios (mudharabah and musyarakah) have largely relied on intuitive, static, and reactive approaches, creating a systemic trade-off between profitability (ROA) and non-performing financing (NPF) risk. This study proposes a Linear Quadratic Regulator (LQR) tuned via Particle Swarm Optimization (PSO) to automate dynamic, data-driven profit-sharing adjustments. The banking system is modeled via three nonlinear differential equations for financing volume (F), return on assets (R), and NPF (N). Linearization confirms full controllability, showing the profit-sharing ratio can effectively stabilize bank performance. Simulation shows LQR-PSO markedly accelerates disturbance decay relative to both the uncontrolled system and a manual LQR, while substantially cutting cumulative error (ISE and ITAE). LQR-PSO alone contains peak NPF at its initial level without overshoot, whereas manual LQR triggers a transient NPF surge. These findings guide the Asset Liability Committee (ALCO) and regulators in designing adaptive, risk-aware profit-sharing policies consistent with the ihtiyathprinciple and hifz al-mal.
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