Propellant Consumption Optimal Adaptive Terminal Control of Launch Vehicle

Abstract

This paper provides the solution technique of propellant consumption optimal adaptive terminal control problem for launch vehicles. The initial nonlinear continuous-time model of plant is approximated by linear discrete-time dynamical system using linearization along reference trajectory and subsequent discretization. It is assumed that state vector and control vector are constrained by convex, closed and bounded polyhedral sets with finite number of vertices in corresponding finite-dimensional vector spaces. The problems of optimal open-loop and adaptive (closed-loop) control problems are formulated for approximated system. The solution of the main problem is reduced to sequential solving of auxiliary problems. An optimal adaptive terminal control algorithm is developed based on computation and analysis of forward and backward reachable sets of approximating system. The computation of polyhedral reachable sets is implemented by general recurrent algebraic method. The performance of proposed algorithms is shown at the numerical example of optimal adaptive terminal control for launch vehicle’s third stage.