We present Shrinking Horizon Model Predictive Control (SHMPC) for discrete-time linear systems with Signal Temporal Logic (STL) specification constraints under stochastic disturbances. The control objective is to maximize an optimization function under the restriction that a given STL specification is satisfied with high probability against stochastic uncertainties. We formulate a general solution, which does not require precise knowledge of the probability distributions of the (possibly dependent) stochastic disturbances; only the bounded support intervals of the density functions and moment intervals are used. For the specific case of disturbances that are independent and normally distributed, we optimize the controllers further by utilizing knowledge of the disturbance probability distributions. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for an HVAC system.
Scheduled charging offers the potential for electric vehicles (EVs) to use renewable energy more efficiently, lowering costs and improving the stability of the electricity grid. Many studies related to EV charge scheduling found in the literature assume perfect or highly accurate knowledge of energy demand for EVs expected to arrive after the scheduling is performed. However, in practice, there is always a degree of uncertainty related to future EV charging demands. In this work, a Model Predictive Control (MPC) based smart charging strategy is developed, which takes this uncertainty into account, both in terms of the timing of the EV arrival as well as the magnitude of energy demand. The objective of the strategy is to reduce the peak electricity demand at an EV parking lot with PVarrays. The developed strategy is compared with both conventional EV charging as well as smart charging with an assumption of perfect knowledge of uncertain future events. The comparison reveals that the inclusion of a 24 h forecast of EV demand has a considerable effect on the improvement of the performance of the system. Further, strategies that are able to robustly consider uncertainty across many possible forecasts can reduce the peak electricity demand by as much as 39% at an office parking space. The reduction of peak electricity demand can lead to increased flexibility for system design, planning for EV charging facilities, deferral or avoidance of the upgrade of grid capacity as well as its better utilization.
The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discreteevent systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is "linear" in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems. Keywords Max-plus linear systems • Max-plus algebra • Analysis of discrete-event systems • Model-based control of max-plus linear systems • Residuation-based control • Model predictive control • Survey
Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. In previous work we have extended MPC to a class of discrete-event systems, namely the max-plus linear systems, i.e., models that are "linear" in the maxplus algebra. Lately, the application of MPC for stochastic max-plus-linear systems has attracted a lot of attention. At each event step, an optimization problem then has to be solved that is, in general, a highly complex and computationally hard problem. Therefore, the focus of this paper is on decreasing the computational complexity of the optimization problem. To this end, we use an approximation approach that is based on the p-th raw moments of a random variable. This method results in a much lower computational complexity and computation time while still guaranteeing a good performance.
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