Expanded Time-to-Go Polynomial Guidance Laws With Arbitrary Time-Varying Gain Functions

This paper presents an expanded form of Time-to-Go Polynomial Guidance (TPG), which generalizes constant-gain TPG to accommodate arbitrary time-varying functions. The proposed guidance law, Expanded TPG (ETPG), utilizes time-varying gain functions with suitable convergence values, providing greater flexibility in shaping TPG's guidance commands for diverse mission objectives while preserving its terminal properties. Numerical simulations with various gain functions validate the performance of ETPG and demonstrate its advantages, particularly in anti-air missile scenarios with decreasing acceleration constraints.