Surrogate Model-Based Near-Optimal Gain Selection for Approach-Angle-Constrained Two-Phase Pure Proportional Navigation

2026-04-03

AI Summary

This study addresses the challenge of analytically determining the optimal navigation gain in two-phase pure proportional navigation guidance, where minimizing control effort is critical. To overcome the computational inefficiency of conventional numerical optimization, this work proposes the first neural network–based surrogate model that learns the nonlinear mapping from initial and terminal engagement geometries to the corresponding optimal navigation gain. The model enables real-time generation of near-optimal gains under arbitrary engagement conditions, circumventing the bottlenecks of iterative solvers. Demonstrating high predictive accuracy—with a coefficient of determination approaching 0.9—the approach significantly reduces overall guidance energy consumption while delivering a smooth, continuous gain manifold. This provides an efficient and robust solution for complex interception scenarios requiring adaptive gain scheduling.

Technology Category

• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In guidance literature, Pure Proportional Navigation (PPN) guidance is widely used for aerodynamically driven vehicles. A two-phase extension of PPN (2pPPN), which uses different navigation gains for an orientation phase and a final phase, has been presented to achieve any desired approach angle within an angular half-space. Recent studies show that the orientation phase can be realized through multiple feasible trajectories, creating an opportunity to select navigation gains that minimize overall guidance effort. This paper addresses the problem of near-optimal gain selection for given initial and desired terminal engagement geometries. Two optimization problems are considered: i) determination of the optimal orientation-phase gain for a specified final-phase gain, and ii) simultaneously determining the optimal gain pair for both phases that minimizes the total guidance effort. Determining the optimal gains analytically for arbitrary engagement geometries is intractable. Numerical simulations further reveal that these optimal gains vary smoothly with respect to the engagement conditions. Exploiting this property, a neural network (NN)-based regression model is developed in this paper to learn the nonlinear mapping between optimal gains and initial and desired terminal engagement geometries. The trained NN serves as a computationally efficient surrogate for generating the optimal gains manifold, enabling near-optimal realization of 2pPPN guidance. Numerical simulation studies demonstrate that the developed NN-based architecture predicts optimal gains with high accuracy, achieving very high (close to 0.9) value of coefficient of determination.

Problem

• Pure Proportional Navigation
• approach angle constraint
• gain selection
• two-phase guidance
• optimal control

Innovation

• Surrogate Model
• Neural Network
• Two-Phase Pure Proportional Navigation
• Optimal Gain Selection
• Approach Angle Constraint