TY - JOUR
T1 - Nonstationary discrete-time deterministic and stochastic control systems
T2 - Bounded and unbounded cases
AU - Guo, Xianping
AU - Hernández-Del-Valle, Adrián
AU - Hernández-Lerma, Onésimo
N1 - Funding Information:
The first author’s research is supported by NSFC and GDUPS (2010) .
Funding Information:
The research of the third author was partially supported by the Consejo Nacional de Ciencia y Tecnología (CONACyT) grant 104001 .
PY - 2011/7
Y1 - 2011/7
N2 - This paper is about nonstationary nonlinear discrete-time deterministic and stochastic control systems with Borel state and control spaces, with either bounded or unbounded costs. The control problem is to minimize an infinite-horizon total cost performance index. Using dynamic programming arguments we show that, under suitable assumptions, the optimal cost functions satisfy optimality equations, which in turn give a procedure to find optimal control policies. We also prove the convergence of value iteration (or successive approximations) functions. Several examples illustrate our results under different sets of assumptions.
AB - This paper is about nonstationary nonlinear discrete-time deterministic and stochastic control systems with Borel state and control spaces, with either bounded or unbounded costs. The control problem is to minimize an infinite-horizon total cost performance index. Using dynamic programming arguments we show that, under suitable assumptions, the optimal cost functions satisfy optimality equations, which in turn give a procedure to find optimal control policies. We also prove the convergence of value iteration (or successive approximations) functions. Several examples illustrate our results under different sets of assumptions.
KW - Discrete-time control systems
KW - Nonlinear systems
KW - Nonstationary dynamic programming
KW - Time-nonhomogeneous systems
KW - Time-varying systems
UR - http://www.scopus.com/inward/record.url?scp=79958192115&partnerID=8YFLogxK
U2 - 10.1016/j.sysconle.2011.04.006
DO - 10.1016/j.sysconle.2011.04.006
M3 - Artículo
SN - 0167-6911
VL - 60
SP - 503
EP - 509
JO - Systems and Control Letters
JF - Systems and Control Letters
IS - 7
ER -