Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems
Apstrakt
A recursive method for the solution of the Riccati equations that yield the matrix gains required for the Nash strategies for quasi-singularly perturbed systems is presented. This method involves solution of Lyapunov and reduced-order Riccati equations corresponding to reduced-order fast and slow subsystems. The algorithm is shown to converge, under specified assumptions, to the exact solution with error at the kth iteration being O(epsilon(k)) where epsilon is a small, positive, singular perturbation parameter.
Ključne reči:
recursive algorithm / quasi-singularly perturbed systems / Nash equilibrium / matrix algebraic Riccati equation / differential gamesIzvor:
Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm, 2002, 9, 2, 317-333Izdavač:
- Watam Press
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Koskie, S AU - Škatarić, Dobrila AU - Petrović, B PY - 2002 UR - https://machinery.mas.bg.ac.rs/handle/123456789/272 AB - A recursive method for the solution of the Riccati equations that yield the matrix gains required for the Nash strategies for quasi-singularly perturbed systems is presented. This method involves solution of Lyapunov and reduced-order Riccati equations corresponding to reduced-order fast and slow subsystems. The algorithm is shown to converge, under specified assumptions, to the exact solution with error at the kth iteration being O(epsilon(k)) where epsilon is a small, positive, singular perturbation parameter. PB - Watam Press T2 - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm T1 - Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems EP - 333 IS - 2 SP - 317 VL - 9 UR - https://hdl.handle.net/21.15107/rcub_machinery_272 ER -
@article{ author = "Koskie, S and Škatarić, Dobrila and Petrović, B", year = "2002", abstract = "A recursive method for the solution of the Riccati equations that yield the matrix gains required for the Nash strategies for quasi-singularly perturbed systems is presented. This method involves solution of Lyapunov and reduced-order Riccati equations corresponding to reduced-order fast and slow subsystems. The algorithm is shown to converge, under specified assumptions, to the exact solution with error at the kth iteration being O(epsilon(k)) where epsilon is a small, positive, singular perturbation parameter.", publisher = "Watam Press", journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm", title = "Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems", pages = "333-317", number = "2", volume = "9", url = "https://hdl.handle.net/21.15107/rcub_machinery_272" }
Koskie, S., Škatarić, D.,& Petrović, B.. (2002). Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems. in Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm Watam Press., 9(2), 317-333. https://hdl.handle.net/21.15107/rcub_machinery_272
Koskie S, Škatarić D, Petrović B. Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems. in Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm. 2002;9(2):317-333. https://hdl.handle.net/21.15107/rcub_machinery_272 .
Koskie, S, Škatarić, Dobrila, Petrović, B, "Convergence proof for recursive solution of linear-quadratic Nash games for quasi-singularly perturbed systems" in Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm, 9, no. 2 (2002):317-333, https://hdl.handle.net/21.15107/rcub_machinery_272 .