Gaussian Process Derivative at Uncertain Input for SE Kernel

Given a Gaussian Process with a zero mean and a Squared Exponential (SE) kernel. We are interested in the exact mean and covariance of the predictive distribution of the latent function f and its gradient ∂f/∂x at an uncertain input x ∼ N(μ,Σ). This technical note develops the calculations of these quantities and documents an implementation of these calculations in a Matlab function called gppred_exactmoments_se

Scalable Scheduling of Energy Control Systems

Peak power consumption is a universal problem across energy control systems in electrical grids, buildings, and industrial automation where the uncoordinated operation of multiple controllers result in temporally correlated electricity demand surges (or peaks). While there exist several different approaches to balance power consumption by load shifting and load shedding, they operate on coarse grained time scales and do not help in de-correlating energy sinks. The Energy System Scheduling Problem is particularly hard due to its binary control variables. Its complexity grows exponentially with the scale of the system, making it impossible to handle systems with more than a few variables. We developed a scalable approach for fine-grained scheduling of energy control systems that novelly combines techniques from control theory and computer science. The original system with binary control variables are approximated by an averaged system whose inputs are the utilization values of the binary inputs within a given period. The error between the two systems can be bounded, which allows us to derive a safety constraint for the averaged system so that the original system\u27s safety is guaranteed. To further reduce the complexity of the scheduling problem, we abstract the averaged system by a simple single-state single-input dynamical system whose control input is the upper-bound of the total demand of the system. This model abstraction is achieved by extending the concept of simulation relations between transition systems to allow for input constraints between the systems. We developed conditions to test for simulation relations as well as algorithms to compute such a model abstraction. As a consequence, we only need to solve a small linear program to compute an optimal bound of the total demand. The total demand is then broken down, by solving a linear program much smaller than the original program, to individual utilization values of the subsystems, whose actual schedule is then obtained by a low-level scheduling algorithm. Numerical simulations in Matlab show the effectiveness and scalability of our approach

Event-based Green Scheduling of Radiant Systems in Buildings

This paper looks at the problem of peak power demand reduction for intermittent operation of radiant systems in buildings. Uncoordinated operation of the circulation pumps of a multi-zone hydronic radiant system can cause temporally correlated electricity demand surges when multiple pumps are activated simultaneously. Under a demand-based electricity pricing policy, this uncoordinated behavior can result in high electricity costs and expensive system operation. We have previously presented Green Scheduling with the periodic scheduling approach for reducing the peak power demand of electric radiant heating systems while maintaining indoor thermal comfort. This paper develops an event-based state feedback scheduling strategy that, unlike periodic scheduling, directly takes into account the disturbances and is thus more suitable for building systems. The effectiveness of the new strategy is demonstrated through simulation in MATLAB

DR-Advisor: A Data Driven Demand Response Recommender System

A data-driven method for demand response baselining and strategy evaluation is presented. Using meter and weather data along with set-point schedule information, we use an ensemble of regression trees to learn non-parametric data-driven models for predicting the power consumption of the building. This model can be used for evaluating demand response strategies in real-time, without having to learn complex models of the building. The methods have been integrated in an open-source tool called DR-Advisor, which acts as a recommender system for the building’s facilities manager by advising on which control actions should be during a demand response event. We provide a case study using data from a large commercial vistural test-bed building to evaluate the performance of the DR-Advisor tool. Keywords: demand response, regression trees, machine learnin

IMpACT: Inverse Model Accuracy and Control Performance Toolbox for Buildings

Uncertainty affects all aspects of building performance: from the identification of models, through the implementation of model-based control, to the operation of the deployed systems. Learning models of buildings from sensor data has a fundamental property that the model can only be as accurate and reliable as the data on which it was trained. For small and medium size buildings, a low-cost method for model capture is necessary to take advantage of optimal model-based supervisory control schemes. We present IMpACT, a methodology and a toolbox for analysis of uncertainty propagation for building inverse modeling and controls. Given a plant model and real input data, IMpACT automatically evaluates the effect of the uncertainty propagation from sensor data to model accuracy and control performance. We also present a statistical method to quantify the bias in the sensor measurement and to determine near optimal sensor placement and density for accurate signal measurements. In our previous work, we considered the end-to-end propagation of uncertainty in the form of fixed bias in the sensor data. In this paper, we extend the method to work with random errors in the sensor data, which is more realistic. Using a real building test-bed, we show how performing an uncertainty analysis can reveal trends about inverse model accuracy and control performance, which can be used to make informed decisions about sensor requirements and data accuracy

Peak Power Control of Battery and Super-capacitor Energy Systems in Electric Vehicles

Hybrid energy systems consist of a load powered by a source and a form of energy storage. Systems with mixed energy supply find applications in the electric grid with renewable and non-renewable sources, in mission critical systems such as Mars rovers with rechargeable and non-rechargeable batteries and low-power monitoring systems with energy harvesting. A general problem for hybrid energy systems is the reduction of peak power consumption to ensure cost-efficient operation as peak power draws require additional resources, adversely affect the system reliability and storage lifetime. Furthermore, in some cases such as electric vehicles, the load dynamics are fast, not perfectly known a priori and the computation power available is often limited, making the implementation of traditional optimal control difficult. This paper aims to develop a control scheme to reduce the peak power drawn from the source for hybrid energy systems with limited computation power and limited load forecasts. We propose a scheme with two control levels and provide a sufficient condition for control of the different energy storage/generation components to meet the instantaneous load while satisfying a peak power threshold. The scheme provides performance comparable to Model Predictive Control, while requiring less computation power and only coarse-grained load predictions. As a case study we implement the scheme for a battery-supercapacitor system in an electric vehicle with real world drive cycles to demonstrate the low execution time and effective reduction of the battery power (hence temperature), which is crucial to the lifetime of the battery

ADMM-based Adaptive Sampling Strategy for Nonholonomic Mobile Robotic Sensor Networks

This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at unmeasured positions, which enables the sampling optimization problem to be formulated by the use of the log determinant of a predicted covariance matrix at next sampling locations. The control, movement and nonholonomic dynamics constraints of the mobile sensors are also considered in the adaptive sampling optimization problem. In order to tackle the nonlinearity and nonconvexity of the objective function in the optimization problem we first exploit the linearized alternating direction method of multipliers (L-ADMM) method that can effectively simplify the objective function, though it is computationally expensive since a nonconvex problem needs to be solved exactly in each iteration. We then propose a novel approach called the successive convexified ADMM (SC-ADMM) that sequentially convexify the nonlinear dynamic constraints so that the original optimization problem can be split into convex subproblems. It is noted that both the L-ADMM algorithm and our SC-ADMM approach can solve the sampling optimization problem in either a centralized or a distributed manner. We validated the proposed approaches in 1000 experiments in a synthetic environment with a real-world dataset, where the obtained results suggest that both the L-ADMM and SC- ADMM techniques can provide good accuracy for the monitoring purpose. However, our proposed SC-ADMM approach computationally outperforms the L-ADMM counterpart, demonstrating its better practicality.Comment: submitted to IEEE Sensors Journal, revised versio

Peak Power Reduction in Hybrid Energy Systems with Limited Load Forecasts

Hybrid energy systems, which consist of a load powered by a source and a form of energy storage, find applications in many systems, e.g., the electric grid and electric vehicles. A key problem for hybrid energy systems is the reduction of peak power consumption to ensure cost-efficient operation as peak power draws require additional resources and adversely affect the system reliability and lifetime. Furthermore, in some cases such as electric vehicles, the load dynamics are fast, not perfectly known in advance and the on-board computation power is often limited, making the implementation of traditional optimal control difficult. We aim to develop a control scheme to reduce the peak power drawn from the source for hybrid energy systems with limited computation power and limited load forecasts. We propose a scheme with two control levels and provide a sufficient condition for control of the different energy storage/generation components to meet the instantaneous load while satisfying a peak power threshold. The scheme provides performance comparable to Model Predictive Control, while requiring less computation power and only coarse-grained load predictions. For a case study, we implement the scheme for a battery-supercapacitor-powered electric vehicle with real world drive cycles to demonstrate the low execution time and effective reduction of the battery power (hence temperature), which is crucial to the lifetime of the battery

Robust Model Predictive Control with Anytime Estimation

With an increasing autonomy in modern control systems comes an increasing amount of sensor data to be processed, leading to overloaded computation and communication in the systems. For example, a vision-based robot controller processes large image data from cameras at high frequency to observe the robot’s state in the surrounding environment, which is used to compute control commands. In real-time control systems where large volume of data is processed for feedback control, the data-dependent state estimation can become a computation and communication bottleneck, resulting in potentially degraded control performance. Anytime algorithms, which offer a trade-off between execution time and accuracy of computation, can be leveraged in such systems. We present a Robust Model Predictive Control approach with an Anytime State Estimation Algorithm, which computes both the optimal control signal for the plant and the (time-varying) deadline/accuracy constraint for the anytime estimator. Our approach improves the system’s performance (concerning both the control performance and the estimation cost) over conventional controllers, which are designed for and operate at a fixed computation time/accuracy setting. We numerically evaluate our approach in an idealized motion model for navigation with both state and control constraints