TY - GEN
T1 - Optimal trajectory planning via chebyshev-based state parameterization
AU - Nagurka, M.
AU - Wang, S.
N1 - Publisher Copyright:
© 1990 IEEE.
PY - 1990/1/1
Y1 - 1990/1/1
N2 - Two state parameterization methods based on finite-term Chebyshev representations are developed to determine the optimal state and control trajectories of unconstrained linear timeinvariant dynamic systems with quadratic performance indices. In one method, each state variable of a dynamic system is approximated by a shifted Chebyshev series. In the second method, each state variable is represented by the superposition of a shifted Chebyshev series and a third order polynomial. In both approaches, the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. The results of simulation studies demonstrate that the Chebyshev-pluspolynomial method offers computational advantages relative to the direct Chebyshev method, a previous Chebyshev method and a state-transition approach.
AB - Two state parameterization methods based on finite-term Chebyshev representations are developed to determine the optimal state and control trajectories of unconstrained linear timeinvariant dynamic systems with quadratic performance indices. In one method, each state variable of a dynamic system is approximated by a shifted Chebyshev series. In the second method, each state variable is represented by the superposition of a shifted Chebyshev series and a third order polynomial. In both approaches, the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. The results of simulation studies demonstrate that the Chebyshev-pluspolynomial method offers computational advantages relative to the direct Chebyshev method, a previous Chebyshev method and a state-transition approach.
UR - http://www.scopus.com/inward/record.url?scp=85067926273&partnerID=8YFLogxK
U2 - 10.1109/IMC.1990.687328
DO - 10.1109/IMC.1990.687328
M3 - Conference contribution
AN - SCOPUS:85067926273
T3 - Proceedings of the IEEE International Workshop on Intelligent Motion Control, IMC 1990
SP - 265
EP - 270
BT - Proceedings of the IEEE International Workshop on Intelligent Motion Control, IMC 1990
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1990 IEEE International Workshop on Intelligent Motion Control, IMC 1990
Y2 - 20 August 1990 through 22 August 1990
ER -