2013/07/28 by Debra A. Lewis, Lewis, Debra
Engineering · Physics and Astronomy · #37N35 #49J15 #Advanced Thermodynamics and Statistical Mechanics #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.1307.7395
openalex publication_date 2013/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A moderation incentive is a continuously differentiable control-dependent cost term that is identically zero on the boundary of the admissible control region, and is subtracted from the `do or die' cost function to reward sub-maximal control utilization in optimal control systems. A moderation potential is a function on the cotangent bundle of the state space such that the solutions of Hamilton's equations satisfying appropriate boundary conditions are solutions of the synthesis problem - the control-parametrized Hamiltonian system central to Pontryagin's Maximum Principle. A multi-parameter family of moderation incentives for affinely controlled systems with quadratic control constraints possesses simple, readily calculated moderation potentials. One member of this family is a shifted version of the kinetic energy-style control cost term frequently used in geometric optimal control. The controls determined by this family approach those determined by a logarithmic penalty function as one of the parameters approaches zero, while the cost term itself is bounded.