Khanh Dai Pham An optimal k-cost-cumulant (kCC) control problem is formulated, in which the objective is minimization of a finite linear combination of the first k cost cumulants of a finite-horizon integral quadratic cost associated with a linear stochastic system, when the controller measures the states. This problem not only defines a very general linear-quadratic Gaussian problem class, but also may be seen as an approximation in some sense to the theory of risk sensitive control. The

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... on is obtained by a more direct dynamic programming approach to the kCC initial-cost problem. Moreover, the research continues with a development of cost cumulants per unit time in infinite horizon control for the state-feedback kCC problem. A constant controller is obtained by using a Lagrange multiplier technique. The performance and stability properties of kCC controllers are discussed at length. A theory of output feedback for the linear-quadratic kCC problem class is also developed. Under linearity and Gaussian assumptions, it is reasonable to conclude that Kalman-state estimates contain all statistical information. Henceforth, the finite-horizon kCC control problem with Kalman state-estimate feedback laws is formulated. Solutions to the output-feedback kCC control problem having both standard and generalized finite-horizon integral quadratic costs are then obtained by adapting a dynamic programming technique. Furthermore, constant controllers