Anil Aswani

Reducing Transient and Steady State Electricity Consumption in HVAC Using Learning-Based Model-Predictive Control

Heating, ventilation, and air conditioning (HVAC) systems are an important target for efficiency improvements through new equipment and retrofitting because of their large energy footprint. One type of equipment that is common in homes and some offices is an electrical, single-stage heat pump air conditioner (AC). To study this setup, we have built the Berkeley Retrofitted and Inexpensive HVAC Testbed for Energy Efficiency (BRITE) platform. This platform allows us to actuate an AC unit that controls the room temperature of a computer laboratory on the Berkeley campus that is actively used by students, while sensors record room temperature and AC energy consumption. We build a mathematical model of the temperature dynamics of the room, and combining this model with statistical methods allows us to compute the heating load due to occupants and equipment using only a single temperature sensor. Next, we implement a control strategy that uses learning-based model-predictive control (MPC) to learn and compensate for the amount of heating due to occupancy as it varies throughout the day and year. Experiments on BRITE show that our techniques result in a 30%-70% reduction in energy consumption as compared to two-position control, while still maintaining a comfortable room temperature. The energy savings are due to our control scheme compensating for varying occupancy, while considering the transient and steady state electrical consumption of the AC. Our techniques can likely be generalized to other HVAC systems while still maintaining these energy saving features.

Provably safe and robust learning-based model predictive control

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

Expression-level optimization of a multi-enzyme pathway in the absence of a high-throughput assay

Engineered metabolic pathways often suffer from flux imbalances that can overburden the cell and accumulate intermediate metabolites, resulting in reduced product titers. One way to alleviate such imbalances is to adjust the expression levels of the constituent enzymes using a combinatorial expression library. Typically, this approach requires high-throughput assays, which are unfortunately unavailable for the vast majority of desirable target compounds. To address this, we applied regression modeling to enable expression optimization using only a small number of measurements. We characterized a set of constitutive promoters in Saccharomyces cerevisiae that spanned a wide range of expression and maintained their relative strengths irrespective of the coding sequence. We used a standardized assembly strategy to construct a combinatorial library and express for the first time in yeast the five-enzyme violacein biosynthetic pathway. We trained a regression model on a random sample comprising 3% of the total library, and then used that model to predict genotypes that would preferentially produce each of the products in this highly branched pathway. This generalizable method should prove useful in engineering new pathways for the sustainable production of small molecules.

Learning-based model predictive control on a quadrotor: Onboard implementation and experimental results

In this paper, we present details of the real time implementation onboard a quadrotor helicopter of learning-based model predictive control (LBMPC). LBMPC rigorously combines statistical learning with control engineering, while providing levels of guarantees about safety, robustness, and convergence. Experimental results show that LBMPC can learn physically based updates to an initial model, and how as a result LBMPC improves transient response performance. We demonstrate robustness to mis-learning. Finally, we show the use of LBMPC in an integrated robotic task demonstration-The quadrotor is used to catch a ball thrown with an a priori unknown trajectory.

Identifying models of HVAC systems using semiparametric regression

Heating, ventilation, and air-conditioning (HVAC) systems use a large amount of energy, and so they are an interesting area for efficiency improvements. The focus here is on the use of semiparametric regression to identify models, which are amenable to analysis and control system design, of HVAC systems. This paper briefly describes two testbeds that we have built on the Berkeley campus for modeling and efficient control of HVAC systems, and we use these testbeds as case studies for system identification. The main contribution of this work is that the use of semiparametric regression allows for the estimation of the heating load from occupancy, equipment, and solar heating using only temperature measurements. These estimates are important for building accurate models as well as designing efficient control schemes, and in our other work we have been able to achieve a reduction in energy consumption on a single room testbed using heating load estimation in conjunction with the learning-based model predictive control (LBMPC) technique. Furthermore, this framework is not restrictive to modeling nonlinear HVAC behavior, because we have been able to use this methodology to create hybrid system models that incorporate such nonlinearities.

Extensions of learning-based model predictive control for real-time application to a quadrotor helicopter

A new technique called learning-based model predictive control (LBMPC) rigorously combines statistics and learning with control engineering, while providing levels of guarantees about safety, robustness, and convergence. This paper describes modifications of LBMPC that enable its realtime implementation on an ultra-low-voltage processor that is onboard a quadrotor helicopter testbed, and it also discusses the numerical algorithms used to implement the control scheme on the quadrotor. Experimental results are provided that demonstrate the improvement to dynamic response that the learning in LBMPC provides, as well as the robustness of LBMPC to mis-learning.

Energy-Efficient Building HVAC Control Using Hybrid System LBMPC

Improving the energy-efficiency of heating, ventilation, and air-conditioning (HVAC) systems has the potential to realize large economic and societal benefits. This paper concerns the system identification of a hybrid system model of a building-wide HVAC system and its subsequent control using a hybrid system formulation of learning-based model predictive control (LBMPC). Here, the learning refers to model updates to the hybrid system model that incorporate the heating effects due to occupancy, solar effects, outside air temperature (OAT), and equipment, in addition to integrator dynamics inherently present in low-level control. Though we make significant modeling simplifications, our corresponding controller that uses this model is able to experimentally achieve a large reduction in energy usage without any degradations in occupant comfort. It is in this way that we justify the modeling simplifications that we have made. We conclude by presenting results from experiments on our building HVAC testbed, which show an average of 1.5MWh of energy savings per day (p = 0.002) with a 95% confidence interval of 1.0MWh to 2.1MWh of energy savings.

Inverse Optimization with Noisy Data

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions of a convex optimization problem are corrupted by noise. We first provide a formulation for inverse optimization and prove it to be NP-hard. In contrast to existing methods, we show that the parameter estimates produced by our formulation are statistically consistent. Our approach involves combining a new duality-based reformulation for bilevel programs with a regularization scheme that smooths discontinuities in the formulation. Using epi-convergence theory, we show the regularization parameter can be adjusted to approximate the original inverse optimization problem to arbitrary accuracy, which we use to prove our consistency results. Next, we propose two solution algorithms based on our duality-based formulation. The first is an enumeration algorithm that is applicable to settings where the dimensionality of the parameter space is modest, and the second is a semiparametric approach that combines nonparametric statistics with a modified version of our formulation. These numerical algorithms are shown to maintain the statistical consistency of the underlying formulation. Lastly, using both synthetic and real data, we demonstrate that our approach performs competitively when compared with existing heuristics.

Game-theoretic routing of GPS-assisted vehicles for energy efficiency

Congestion on roads and highways is an issue that leads to reductions in the energy-efficiency of travel. Current GPS navigation devices include features which provide turn-by turn directions to vehicles based on real-time traffic conditions, and these features provide an opportunity to improve average fuel consumption. Routing strategies in these devices optimize individual travel times, but theoretical (e.g., Braesss paradox) and empirical results show that this can actually increase congestion and average travel times. We model traffic routing in the game-theoretic framework of Stackelberg games, which is a simplification of the true information patterns, and then use this model to provide an algorithm for turn-by-turn directions. One advantage of our algorithm is that it can be easily incorporated into existing GPS devices by modifying the traffic information sent to them. Our framework is used to qualitatively study the effectiveness of traffic routing on a specific road network topology. If roughly 60% of users follow GPS directions implementing our strategy, then the average delay will be close to the optimal average delay for the road network. This poses social and technological challenges for reduction in congestion through routing. The situation is not hopeless though, because our qualitative results indicate that having a small percentage of compliant users may still lead to large reductions in congestion.

Statistics for sparse, high-dimensional, and nonparametric system identification

Local linearization techniques are an important class of nonparametric system identification. Identifying local linearizations in practice involves solving a linear regression problem that is ill-posed. The problem can be ill-posed either if the dynamics of the system lie on a manifold of lower dimension than the ambient space or if there are not enough measurements of all the modes of the dynamics of the system. We describe a set of linear regression estimators that can handle data lying on a lower-dimension manifold. These estimators differ from previous estimators, because these estimators are able to improve estimator performance by exploiting the sparsity of the system - the existence of direct interconnections between only some of the states - and can work in the “large p, small n” setting in which the number of states is comparable to the number of data points. We describe our system identification procedure, which consists of a presmoothing step and a regression step, and then we apply this procedure to data taken from a quadrotor helicopter. We use this data set to compare our procedure with existing procedures.