Abort landing in the presence of windshear as a minimax optimal control problem, part 2: Multiple shooting and homotopy

1991 ◽  
Vol 70 (2) ◽  
pp. 223-254 ◽  
Author(s):  
R. Bulirsch ◽  
F. Montrone ◽  
H. J. Pesch
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Multiple Shooting ◽  
Abort Landing ◽  
Minimax Optimal Control

Trajectory Optimization for DDE Models of Supercavitating Underwater Vehicles

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Carlo L. Bottasso ◽  
Francesco Scorcelletti ◽  
Massimo Ruzzene ◽  
Seong S. Ahn
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Optimization ◽  
Past History ◽  
Flight Mechanics ◽  
Multiple Shooting ◽  
Supercavitating Vehicles ◽  
Delay Differential

In this study we first develop a flight mechanics model for supercavitating vehicles, which is formulated to account for the dependence of the cavity shape from the past history of the system. This mathematical model is governed by a particular class of delay differential equations, featuring time delays on the states of the system. Next, flight trajectories and maneuvering strategies for supercavitating vehicles are obtained by solving an optimal control problem, whose solution, given a cost function and general constraints and bounds on states and controls, yields the control time histories that maneuver the vehicle according to a desired strategy, together with the associated flight path. The optimal control problem is solved using a novel direct multiple shooting approach, which is formulated to properly handle conditions dictated by the delay differential equation formulation governing the dynamic behavior of the vehicle. Specifically, the new formulation enforces the state continuity line conditions in a least-squares sense using local interpolations, which supports local time stepping and drastically reduces the number of optimization unknowns. Examples of maneuvers and resulting trajectories demonstrate the effectiveness of the proposed methodology and the generality of the formulation. The results are also compared with those obtained from a previously developed model governed by ordinary differential equations to highlight the differences and demonstrate the need for the current formulation.

NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST

2002 ◽  
Vol 12 (02) ◽  
pp. 183-203 ◽  
Author(s):  
LAURA S. ARAGONE ◽  
SILVIA C. DI MARCO ◽  
ROBERTO L. V. GONZÁLEZ
Keyword(s):  
Optimal Control ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Convergence Rate ◽  
Control Problem ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Minimax Optimal Control ◽  
Continuous Problem

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.

scholarly journals MATLAB Implementation of Direct and Indirect Shooting Methods to Solve an Optimal Control Problem With State Constraints

2021 ◽  
pp. 43-50
Author(s):  
Andrzej Karbowski
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraints ◽  
General Procedure ◽  
Time Discretization ◽  
Multiple Shooting ◽  
Mathematical Programming Problem ◽  
Shooting Methods ◽  
State Equations

The paper presents a general procedure to solve numerically optimal control problems with state constraints. Itis used in the case, when the simple time discretization of the state equations and expressing the optimal control problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect.The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two Matlab codes are shown.

scholarly journals Minimax optimal control problem with state constraints

2016 ◽  
Vol 32 ◽  
pp. 24-31 ◽  
Author(s):  
Dmitry Karamzin ◽  
Valeriano de Oliveira ◽  
Fernando Pereira ◽  
Geraldo Silva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraints ◽  
Minimax Optimal Control
Sign in / Sign up

Export Citation Format

Share Document