From the optimization point of view, an optimum solution of the unit commitment problem with reliability constraints can be achieved when all constraints are simultaneously satisfied rather than sequentially or separately satisfying them. Therefore, the reliability constraints need to be appropriately formulated in terms of the conventional unit commitment variables. In this paper, the reli...

Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research fields. Although it is not straightforward to handle probabilistic constraints in an optimization problem, several methods haven been proposed to handle probabilistic constraints. This paper examines probabilistic constrained optimal control problems for linear discrete-time sy...

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractab...

Abstract: This paper designs multi-step probabilistic sets for linear, discrete-time, stochastic systems with unbounded multiplicative noise and probabilistic constraints. Multi-step probabilistic sets strengthen IWPp by bringing more degrees of freedom to optimize the applicable region of finite-step probabilistic constraints, and extending the prediction horizon of IWPp to infinity for infini...