A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control

We present a numerical method for finite-horizon stochastic optimal control models. We derive a stochastic minimum principle (SMP) and then develop a numerical method based on the direct solution of the SMP. The method combines Monte Carlo pathwise simulation and non-parametric interpolation methods. We present results from a standard linear quadratic control model, and a realistic case study that captures the stochastic dynamics of intermittent power generation in the context of optimal economic dispatch models.National Science Foundation (U.S.) (Grant 1128147)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0005171)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0003906

Stochastic performance indices to infer deterministic indices through machine learning in the performance analysis of control loops

Control loops are the most critical components in many production processes. In this process, the economic yield is strongly linked to the performance of the control loops since aspects such as safety conditions, process quality, and energy and raw material consumption depend on this. However, experience has shown that most of the control loops can be improved by identifying and correcting the causes of the poor perfor-mance. The indices to evaluate the performance of the control loops can be divided into two groups, stochastic and deterministic. The most known of the former is the minimum variance index. Stochastic indices only require data collected under normal operating conditions and minimum knowledge of the process, making it possible to evaluate performance online. However, some disadvantages, such as scale and span problems, make performance analysis difficult. The deterministic indices (rise time, settling time, overshoot, phase and gain margins, etc.) are easy to interpret, facilitating the analysis; however, invasive plant tests are necessary to estimate them, making them impractical. Is it possible to link these two approaches? With that question in mind, in this work, it is proposed to build a model to estimate deterministic indices (to evaluate robustness and performance of control loops), considering stochastic indices and some process information as model inputs. This paper shows the procedure to build the inferential model by using machine learning techniques

Techno-Economic Analysis and Optimal Control of Battery Storage for Frequency Control Services, Applied to the German Market

Optimal investment in battery energy storage systems, taking into account degradation, sizing and control, is crucial for the deployment of battery storage, of which providing frequency control is one of the major applications. In this paper, we present a holistic, data-driven framework to determine the optimal investment, size and controller of a battery storage system providing frequency control. We optimised the controller towards minimum degradation and electricity costs over its lifetime, while ensuring the delivery of frequency control services compliant with regulatory requirements. We adopted a detailed battery model, considering the dynamics and degradation when exposed to actual frequency data. Further, we used a stochastic optimisation objective while constraining the probability on unavailability to deliver the frequency control service. Through a thorough analysis, we were able to decrease the amount of data needed and thereby decrease the execution time while keeping the approximation error within limits. Using the proposed framework, we performed a techno-economic analysis of a battery providing 1 MW capacity in the German primary frequency control market. Results showed that a battery rated at 1.6 MW, 1.6 MWh has the highest net present value, yet this configuration is only profitable if costs are low enough or in case future frequency control prices do not decline too much. It transpires that calendar ageing drives battery degradation, whereas cycle ageing has less impact.Comment: Submitted to Applied Energ

Optimal transport over a linear dynamical system

We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schroedinger bridge. As the white noise intensity tends to zero, the flow of densities converges to that of the deterministic dynamics and can serve as a way to compute the solution of its deterministic counterpart. The solution can be expressed in closed-form for Gaussian initial and final state densities in both cases