The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The maximum principle changes the problem of optimal control to a two point boundary value problem which can be completely solved only in special tasks. It was probably the reaso...

A two-stage stochastic program is formulated for day-ahead commitment of thermal generating units to minimize total expected cost considering uncertainties in the day-ahead load and the availability of variable generation resources. Commitments of thermal units in the stochastic reliability unit commitment (SRUC) are viewed as first-stage decisions, and dispatch is relegated to the second stage...

We provide an American version of the Geometric Dynamic Programming Principle of Soner and Touzi [22] for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0, T ]. As an example of application, we show how it can ...

This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system.Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking...

A crucial challenge in future smart energy grids is the largescale coordination of distributed energy demand and generation. The well-known PowerMatcher is a promising approach that integrates demand and supply flexibility in the operation of the electricity system through dynamic pricing and a hierarchical bidding coordination scheme. However, as the PowerMatcher focuses on short-term coordina...