TY - GEN
T1 - A variational derivation of LQR for piecewise time-varying systems
AU - Ansari, Alex
AU - Murphey, Todd
N1 - Publisher Copyright:
© 2015 American Automatic Control Council.
PY - 2015/7/28
Y1 - 2015/7/28
N2 - This paper provides a complete derivation for LQR optimal controllers and the optimal value function using basic principles from variational calculus. As opposed to alternatives, the derivation does not rely on the Hamilton-Jacobi-Bellman (HJB) equations, Pontryagin's Maximum Principle (PMP), or the Euler Lagrange (EL) equations. Because it requires significantly less background, the approach is educationally instructive. It provides a different perspective of how and why key quantities such as the adjoint variable and Riccati equation show up in optimal control computations and their connection to the optimal value function. Additionally, the derivation presented requires fewer regularity assumptions than necessary in applying the HJB or EL equations. As with PMP, the methods in this paper apply to systems and controls that are piecewise continuous in time.
AB - This paper provides a complete derivation for LQR optimal controllers and the optimal value function using basic principles from variational calculus. As opposed to alternatives, the derivation does not rely on the Hamilton-Jacobi-Bellman (HJB) equations, Pontryagin's Maximum Principle (PMP), or the Euler Lagrange (EL) equations. Because it requires significantly less background, the approach is educationally instructive. It provides a different perspective of how and why key quantities such as the adjoint variable and Riccati equation show up in optimal control computations and their connection to the optimal value function. Additionally, the derivation presented requires fewer regularity assumptions than necessary in applying the HJB or EL equations. As with PMP, the methods in this paper apply to systems and controls that are piecewise continuous in time.
UR - http://www.scopus.com/inward/record.url?scp=84940911788&partnerID=8YFLogxK
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U2 - 10.1109/ACC.2015.7171069
DO - 10.1109/ACC.2015.7171069
M3 - Conference contribution
AN - SCOPUS:84940911788
T3 - Proceedings of the American Control Conference
SP - 2260
EP - 2265
BT - ACC 2015 - 2015 American Control Conference
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2015 American Control Conference, ACC 2015
Y2 - 1 July 2015 through 3 July 2015
ER -