TY - GEN
T1 - Non-Linear-Quadratic Optimal Control Problem for a Unicycle
T2 - 14th UKACC International Conference on Control, CONTROL 2024
AU - Merkulov, Gleb
AU - Turetsky, Vladimir
AU - Shima, Tal
N1 - Publisher Copyright: © 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - A finite-horizon optimal control problem for a nonlinear unicycle with constant linear velocity is considered. The cost functional consists of the squared norm of a final position and the integral penalty term for the control effort, i.e., both the miss distance and the control are soft-constrained. A finite horizon formulation arises, for instance, in coordinated guidance attack against a stationary target, in which all interceptors have to arrive at the target at the same time. The soft constraint on terminal position allows for tradeoff between the miss distance and control effort. Semi-analytical solution is derived by representing the squared norm as a maximum of a quadratic form and by changing the order of maximization and minimization. The inner minimization problem becomes a problem of calculus of variations, which Euler-Lagrange equation writes as a nonlinear pendulum equation. Based on the solution of this equation, a numerical scheme for constructing the suboptimal control is developed. As a by-product of the approach, the posterior control bounds are obtained.
AB - A finite-horizon optimal control problem for a nonlinear unicycle with constant linear velocity is considered. The cost functional consists of the squared norm of a final position and the integral penalty term for the control effort, i.e., both the miss distance and the control are soft-constrained. A finite horizon formulation arises, for instance, in coordinated guidance attack against a stationary target, in which all interceptors have to arrive at the target at the same time. The soft constraint on terminal position allows for tradeoff between the miss distance and control effort. Semi-analytical solution is derived by representing the squared norm as a maximum of a quadratic form and by changing the order of maximization and minimization. The inner minimization problem becomes a problem of calculus of variations, which Euler-Lagrange equation writes as a nonlinear pendulum equation. Based on the solution of this equation, a numerical scheme for constructing the suboptimal control is developed. As a by-product of the approach, the posterior control bounds are obtained.
UR - http://www.scopus.com/inward/record.url?scp=85194832089&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/CONTROL60310.2024.10532056
DO - https://doi.org/10.1109/CONTROL60310.2024.10532056
M3 - منشور من مؤتمر
T3 - 2024 UKACC 14th International Conference on Control, CONTROL 2024
SP - 287
EP - 292
BT - 2024 UKACC 14th International Conference on Control, CONTROL 2024
Y2 - 10 April 2024 through 12 April 2024
ER -