TY - JOUR
T1 - Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion
AU - Pan, Zigang
AU - Başar, Tamer
PY - 1999
Y1 - 1999
N2 - This paper develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of long-term average cost for a given risk-sensitivity parameter θ. Furthermore, they lead to closed-loop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics. A numerical example included in the paper illustrates the analytical results.
AB - This paper develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems under a risk-sensitive cost function criterion. The design procedure follows the integrator backstepping methodology, and the controllers obtained guarantee any desired achievable level of long-term average cost for a given risk-sensitivity parameter θ. Furthermore, they lead to closed-loop system trajectories that are bounded in probability, and in some cases asymptotically stable in the large. These results also generalize to nonlinear systems with strongly stabilizable zero dynamics. A numerical example included in the paper illustrates the analytical results.
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U2 - 10.1137/S0363012996307059
DO - 10.1137/S0363012996307059
M3 - Article
AN - SCOPUS:0344182421
SN - 0363-0129
VL - 37
SP - 957
EP - 995
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
IS - 3
ER -