SPSA Algorithm for PD Controller Design in Tanker Ship Systems

The core concept presented involves applying Simultaneous Perturbation Stochastic Approximation (SPSA) for designing Proportional-Derivative (PD) controllers specifically for tanker ship applications. SPSA represents a sophisticated stochastic optimization algorithm that efficiently tunes controller parameters through simultaneous parameter perturbations. This method is particularly advantageous for high-dimensional optimization problems where gradient calculations are computationally expensive. In tanker ship control systems, the PD controller maintains critical stability functions and governs vessel maneuverability by calculating control outputs based on proportional and derivative terms of navigation errors. The implementation typically involves: 1. Defining objective functions quantifying ship performance metrics (path tracking accuracy, fuel efficiency, stability indices) 2. Implementing SPSA's two-sided perturbation scheme using vectorized operations 3. Establishing convergence criteria through adaptive gain sequences Key MATLAB functions often include: - `spsa_optimize()` for core algorithm execution - `cost_function()` evaluating controller performance via ship dynamics simulation - `update_parameters()` implementing the parameter update rule: θₖ₊₁ = θₖ - aₖ × (ΔJ/Δθ) This approach ensures optimal PD controller tuning that accounts for tanker-specific hydrodynamic characteristics, nonlinear dynamics, and operational constraints, ultimately enhancing navigational safety, operational efficiency, and control system robustness. The algorithm's stochastic nature makes it particularly suitable for real-world maritime applications where system models may contain uncertainties.