Parameter-sensitivity study for a linear-quadratic control problem with random state coefficients

Optimal feedback-control laws generally cannot be obtained in closed form for stochastic control problems. The characterizations which have been obtained for several simplified problems have provided valuable insight into the properties of optimal feedback-control laws as well as providing guidance for the construction of suboptimal control laws. In this paper an analytical and computer simulated parameter-sensitivity study is presented for the optimal feedback-control law and dynamic-programming optimality equations associated with a discrete-time, finite-horizon, linear-quadratic control problem with random state coefficients. One interesting characteristic revealed by analysis is the existence of simple linear relationships between parameter sensitivities for the optimal feedback-control selections and for the corresponding cost-to-go expressions.