arXiv subjects

Draguna Vrabie

Publications and source records attributed to Draguna Vrabie.

29 records · Page 2Linked to original sources

arXiv2022

Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees

We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model. We demonstrate that the proposed method can learn parametric constrained control policies to stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. In contrast with imitation learning-based approaches, our method does not depend on a supervisory controller. Most importantly, we demonstrate that, without losing performance, our method is scalable and computationally more efficient than implicit, explicit, and approximate MPC. Under review at IEEE Transactions on Automatic Control.

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arXiv2021

Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems

We present differentiable predictive control (DPC) as a deep learning-based alternative to the explicit model predictive control (MPC) for unknown nonlinear systems. In the DPC framework, a neural state-space model is learned from time-series measurements of the system dynamics. The neural control policy is then optimized via stochastic gradient descent approach by differentiating the MPC loss function through the closed-loop system dynamics model. The proposed DPC method learns model-based control policies with state and input constraints, while supporting time-varying references and constraints. In embedded implementation using a Raspberry-Pi platform, we experimentally demonstrate that it is possible to train constrained control policies purely based on the measurements of the unknown nonlinear system. We compare the control performance of the DPC method against explicit MPC and report efficiency gains in online computational demands, memory requirements, policy complexity, and construction time. In particular, we show that our method scales linearly compared to exponential scalability of the explicit MPC solved via multiparametric programming.

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arXiv2021

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from the observed system's dynamics, and the neural control law is optimized offline by leveraging the differentiable closed-loop system model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. The control performance of the proposed DPC method is demonstrated in simulation using learned model of multi-zone building thermal dynamics.

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arXiv2021

Sparse Control Synthesis for Uncertain Responsive Loads with Stochastic Stability Guarantees

Recent studies have demonstrated the potential of flexible loads in providing frequency response services. However, uncertainty and variability in various weather-related and end-use behavioral factors often affect the demand-side control performance. This work addresses this problem with the design of a demand-side control to achieve frequency response under load uncertainties. Our approach involves modeling the load uncertainties via stochastic processes that appear as both multiplicative and additive to the system states in closed-loop power system dynamics. Extending the recently developed mean square exponential stability (MSES) results for stochastic systems, we formulate multi-objective linear matrix inequality (LMI)-based optimal control synthesis problems to not only guarantee stochastic stability, but also promote sparsity, enhance closed-loop transient performance, and maximize allowable uncertainties. The fundamental trade-off between the maximum allowable (\textit{critical}) uncertainty levels and the optimal stochastic stabilizing control efforts is established. Moreover, the sparse control synthesis problem is generalized to the realistic power systems scenario in which only partial-state measurements are available. Detailed numerical studies are carried out on IEEE 39-bus system to demonstrate the closed-loop stochastic stabilizing performance of the sparse controllers in enhancing frequency response under load uncertainties; as well as illustrate the fundamental trade-off between the allowable uncertainties and optimal control efforts.

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arXiv2021

Occupancy-Driven Stochastic Decision Framework for Ranking Commercial Building Loads

For effective integration of building operations into the evolving demand response programs of the power grid, real-time decisions concerning the use of building appliances for grid services must excel on multiple criteria, ranging from the added value to occupants' comfort to the quality of the grid services. In this paper, we present a data-driven decision-support framework to dynamically rank load control alternatives in a commercial building, addressing the needs of multiple decision criteria (e.g. occupant comfort, grid service quality) under uncertainties in occupancy patterns. We adopt a stochastic multi-criteria decision algorithm recently applied to prioritize residential on/off loads, and extend it to i) complex load control decisions (e.g. dimming of lights, changing zone temperature set-points) in a commercial building; and ii) systematic integration of zonal occupancy patterns to accurately identify short-term grid service opportunities. We evaluate the performance of the framework for curtailment of air-conditioning, lighting, and plug-loads in a multi-zone office building for a range of design choices. With the help of a prototype system that integrates an interactive \textit{Data Analytics and Visualization} frontend, we demonstrate a way for the building operators to monitor the flexibility in energy consumption and to develop trust in the decision recommendations by interpreting the rationale behind the ranking.

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arXiv2021

Constrained Block Nonlinear Neural Dynamical Models

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.

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arXiv2020

Constrained Neural Ordinary Differential Equations with Stability Guarantees

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches require domain expertise and are often difficult to tune or adapt to new systems. In this paper, we show how to model discrete ordinary differential equations (ODE) with algebraic nonlinearities as deep neural networks with varying degrees of prior knowledge. We derive the stability guarantees of the network layers based on the implicit constraints imposed on the weight's eigenvalues. Moreover, we show how to use barrier methods to generically handle additional inequality constraints. We demonstrate the prediction accuracy of learned neural ODEs evaluated on open-loop simulations compared to ground truth dynamics with bi-linear terms.

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arXiv2020

Model Predictive Control of Discrete-Continuous Energy Systems via Generalized Disjunctive Programming

Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete decisions in the continuous space, and logical propositions to denote algebraic constraints in the discrete space. Compared to traditional mixed-integer programming (MIP), the inherent logic structure in GDP yields tighter relaxations that are exploited by global branch and bound algorithms to improve solution quality. In this paper, we present a general GDP model for optimal control of hybrid systems that exhibit both discrete and continuous dynamics. Specifically, we use GDP to formulate a model predictive control (MPC) model for piecewise-affine systems with implicit switching logic. As an example, the GDP-based MPC approach is used as a supervisory control to improve energy efficiency in residential buildings with binary on/off, relay-based thermostats. A simulation study is used to demonstrate the validity of the proposed approach, and the improved solution quality compared to existing MIP-based control approaches.

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arXiv2018

Generative Adversarial Network based Autoencoder: Application to fault detection problem for closed loop dynamical systems

Fault detection problem for closed loop uncertain dynamical systems, is investigated in this paper, using different deep learning based methods. Traditional classifier based method does not perform well, because of the inherent difficulty of detecting system level faults for closed loop dynamical system. Specifically, acting controller in any closed loop dynamical system, works to reduce the effect of system level faults. A novel Generative Adversarial based deep Autoencoder is designed to classify datasets under normal and faulty operating conditions. This proposed network performs significantly well when compared to any available classifier based methods, and moreover, does not require labeled fault incorporated datasets for training purpose. Finally, this aforementioned network's performance is tested on a high complexity building energy system dataset.

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arXiv2018

Prioritized Threshold Allocation for Distributed Frequency Response

Higher penetration of renewable generation will increase the demand for adequate (and cost-effective) controllable resources on the grid that can mitigate and contain the contingencies locally before it can cause a network-wide collapse. However, end-use constraints can potentially lead to load unavailability when an event occurs, leading to unreliable demand response services. Sensors measurements and knowledge of the local load dynamics could be leveraged to improve the performance of load control algorithms. In the context of hierarchical frequency response using ensemble of switching loads, we present a metric to evaluate the fitness of each device in successfully providing the ancillary service. Furthermore a fitness-based assignment of control set-points is formulated which achieves reliable performance under different operating conditions. Monte Carlo simulations of ensembles of electric water heaters and residential air-conditioners are performed to evaluate the proposed control algorithm.

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arXiv2018

Optimal Energy Consumption Forecast for Grid Responsive Buildings: A Sensitivity Analysis

It is envisioned that building systems will become active participants in the smart grid operation by controlling their energy consumption to optimize complex criteria beyond ensuring local end-use comfort satisfaction. A forecast of the building energy consumption will be necessary to enable integration between building and grid operation. Such forecast will be affected by parametric and measurement uncertainty. In this paper we develop a methodology for quantifying the sensitivity of optimal hourly energy consumption forecasts to various sources model and measurement uncertainty. We demonstrate the approach for a building heating ventilation and air conditioning (HVAC) system use-case.

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