John Baillieul

Zhaodan Kong, Kayhan Özcimder, Nathan Fuller et al.

The movements of birds, bats, and other flying species are governed by complex sensorimotor systems that allow the animals to react to stationary environmental features as well as to wind disturbances, other animals in nearby airspace, and a wide variety of unexpected challenges. The paper and talk will describe research that analyzes the three-dimensional trajectories of bats flying in a habitat in Texas. The trajectories are computed with stereoscopic methods using data from synchronous thermal videos that were recorded with high temporal and spatial resolution from three viewpoints. Following our previously reported work, we examine the possibility that bat trajectories in this habitat are governed by optical flow sensing that interpolates periodic distance measurements from echolocation. Using an idealized geometry of bat eyes, we introduce the concept of time-to-transit, and recall some research that suggests that this quantity is computed by the animals' visual cortex. Several steering control laws based on time-to-transit are proposed for an idealized flight model, and it is shown that these can be used to replicate the observed flight of what we identify as typical bats. Although the vision-based motion control laws we propose and the protocols for switching between them are quite simple, some of the trajectories that have been synthesized are qualitatively bat-like. Examination of the control protocols that generate these trajectories suggests that bat motions are governed both by their reactions to a subset of key feature points as well by their memories of where these feature points are located.

Bowen Zhang, John Baillieul

Electricity peaks can be harmful to grid stability and result in additional generation costs to balance supply with demand. By developing a network of smart appliances together with a quasi-decentralized control protocol, direct load control (DLC) provides an opportunity to reduce peak consumption by directly controlling the on/off switch of the networked appliances. This paper proposes a packetized DLC (PDLC) solution that is illustrated by an application to air conditioning temperature control. Here the term packetized refers to a fixed time energy usage authorization. The consumers in each room choose their preferred set point, and then an operator of the local appliance pool will determine the comfort band around the set point. We use a thermal dynamic model to investigate the duty cycle of thermostatic appliances. Three theorems are proposed in this paper. The first two theorems evaluate the performance of the PDLC in both transient and steady state operation. The first theorem proves that the average room temperature would converge to the average room set point with fixed number of packets applied in each discrete interval. The second theorem proves that the PDLC solution guarantees to control the temperature of all the rooms within their individual comfort bands. The third theorem proposes an allocation method to link the results in theorem 1 and assumptions in theorem 2 such that the overall PDLC solution works. The direct result of the theorems is that we can reduce the consumption oscillation that occurs when no control is applied. Simulation is provided to verify theoretical results.

Wing Shing Wong, John Baillieul

Recent papers have treated {\em control communication complexity} in the context of information-based, multiple agent control systems including nonlinear systems of the type that have been studied in connection with quantum information processing. The present paper continues this line of investigation into a class of two-agent distributed control systems in which the agents cooperate in order to realize common goals that are determined via independent actions undertaken individually by the agents. A basic assumption is that the actions taken are unknown in advance to the other agent. These goals can be conveniently summarized in the form of a {\em target matrix}, whose entries are computed by the control system responding to the choices of inputs made by the two agents. We show how to realize such target matrices for a broad class of systems that possess an input-output mapping that is bilinear. One can classify control-communication strategies, known as {\em control protocols}, according to the amount of information sharing occurring between the two agents. Protocols that assume no information sharing on the inputs that each agent selects and protocols that allow sufficient information sharing for identifying the common goals are the two extreme cases. Control protocols will also be evaluated and compared in terms of cost functionals given by integrated quadratic functions of the control inputs. The minimal control cost of the two classes of control protocols are analyzed and compared. The difference in the control costs between the two classes reflects an inherent trade-off between communication complexity and control cost.

Kenneth Sebesta, John Baillieul

There is evidence that flying animals such as pigeons, goshawks, and bats use optical flow sensing to enable high-speed flight through forest clutter. This paper discusses the elements of a theory of controlled flight through obstacle fields in which motion control laws are based on optical flow sensing. Performance comparison is made with feedback laws that use distance and bearing measurements, and practical challenges of implementation on an actual robotic air vehicle are described. The related question of fundamental performance limits due to clutter density is addressed.

Dimitar Baronov, John Baillieul

Research into several aspects of robot-enabled reconnaissance of random fields is reported. The work has two major components: the underlying theory of information acquisition in the exploration of unknown fields and the results of experiments on how humans use sensor-equipped robots to perform a simulated reconnaissance exercise. The theoretical framework reported herein extends work on robotic exploration that has been reported by ourselves and others. Several new figures of merit for evaluating exploration strategies are proposed and compared. Using concepts from differential topology and information theory, we develop the theoretical foundation of search strategies aimed at rapid discovery of topological features (locations of critical points and critical level sets) of a priori unknown differentiable random fields. The theory enables study of efficient reconnaissance strategies in which the tradeoff between speed and accuracy can be understood. The proposed approach to rapid discovery of topological features has led in a natural way to to the creation of parsimonious reconnaissance routines that do not rely on any prior knowledge of the environment. The design of topology-guided search protocols uses a mathematical framework that quantifies the relationship between what is discovered and what remains to be discovered. The quantification rests on an information theory inspired model whose properties allow us to treat search as a problem in optimal information acquisition. A central theme in this approach is that "conservative" and "aggressive" search strategies can be precisely defined, and search decisions regarding "exploration" vs. "exploitation" choices are informed by the rate at which the information metric is changing.

John Baillieul

This paper discusses elements of a control theory of systems comprised of networks of simple agents that collectively achieve sensing and actuation goals despite having strictly limited capability when acting alone. The goal is to understand {\em neuromorphic} feedback control in which streams of data come from large arrays of sensors (e.g. photo-receptors in the eye) and actuation requires coordination of large numbers of actuators (e.g. motor neurons). The context for this work is set by consideration of a stylized problem of robot navigation that uses optical flow as sensed by two idealized and precise photoreceptors. A robust steering law in this setting establishes a foundation for exploiting optical flow based on averaged noisy inputs from large numbers of imprecise sensing elements. Seeking inspiration in neurobiology, the challenges of actuator and sensor intermittency are discussed as are learning actuator coordination strategies. It is shown that there are advantages to having large numbers of control inputs and outputs. The results will be shown to make contact with ideas from control communication complexity and the standard parts problem.

Bowen Zhang, John Baillieul

Demand side management has gained increasing importance as the penetration of renewable energy grows. Based on a Markov jump process modelling of a group of thermostatic loads, this paper proposes a two level feedback system design between the independent system operator (ISO) and the regulation service provider such that two objectives are achieved: (1) the ISO can optimally dispatch regulation signals to multiple providers in real time in order to reduce the requirement for expensive spinning reserves, and (2) each regulation provider can control its thermostatic loads to respond the ISO signal. It is also shown that the amount of regulation service that can be provided is implicitly restricted by a few fundamental parameters of the provider itself, such as the allowable set point choice and its thermal constant. An interesting finding is that the regulation provider's ability to provide a large amount of long term accumulated regulation and short term signal tracking restrict each other. Simulation results are presented to verify and illustrate the performance of the proposed framework.

Reka Albert, John Baillieul, Adilson E. Motter

The emerging field at the intersection of quantitative biology, network modeling, and control theory has enjoyed significant progress in recent years. This Special Issue brings together a selection of papers on complementary approaches to observe, identify, and control biological and biologically inspired networks. These approaches advance the state of the art in the field by addressing challenges common to many such networks, including high dimensionality, strong nonlinearity, uncertainty, and limited opportunities for observation and intervention. Because these challenges are not unique to biological systems, it is expected that many of the results presented in these contributions will also find applications in other domains, including physical, social, and technological networks.

Shuai Wang, John Baillieul

It is well known that the reserves/redundancies built into the transmission grid in order to address a variety of contingencies over a long planning horizon may, in the short run, cause economic dispatch inefficiency. Accordingly, power grid optimization by means of short term line switching has been proposed and is typically formulated as a mixed integer programming problem by treating the state of the transmission lines as a binary decision variable, i.e. in-service or out-of-service, in the optimal power flow problem. To handle the combinatorial explosion, a number of heuristic approaches to grid topology reconfiguration have been proposed in the literature. This paper extends our recent results on the iterative heuristics and proposes a fast grid decomposition algorithm based on vertex cut sets with the purpose of further reducing the computational cost. The paper concludes with a discussion of the possible relationship between vertex cut sets in transmission networks and power trading.

Shuai Wang, John Baillieul

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using using IEEE 118- bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched.

Shuai Wang, John Baillieul

The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental node voltages and fundamental edge currents. Every steady-state DC circuit can be decomposed into a voltage controlled subcircuit and a current controlled subcircuit. In terms of such a decomposition, the I^2R losses of a mixed source circuit are always the sum of losses on the voltage controlled subcircuit and the current controlled subcircuit. The paper concludes by showing that the total power flowing in a mixed source circuit can be found as critical points of the power expressed in terms of the key voltage and current variables mentioned above. The possible relationship to topology control of electric grid operations is discussed.

Zexin Sun, Mingyu Chen, John Baillieul

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In this paper, we present a novel data-driven linear estimator based on Koopman operator theory to extract meaningful finite-dimensional representations of complex non-linear systems. The Koopman model is used together with deep reinforcement networks that learn the optimal stepwise actions to predict future states of nonlinear systems. Our estimator is also adaptive to a diffeomorphic transformation of the estimated nonlinear system, which enables it to compute optimal state estimates without re-learning.

Zexin Sun, John Baillieul

Building on our recent research on neural heuristic quantization systems, results on learning quantized motions and resilience to channel dropouts are reported. We propose a general emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved by model predictive control (MPC), but because the optimization step involves integer programming, the approach suffers from combinatorial complexity when the number of input channels becomes large. Even if we collect data points to train a neural network simultaneously, collection of training data and the training itself are still time-consuming. Therefore, we propose a general Deep Q Network (DQN) algorithm that can not only learn the trajectory but also exhibit the advantages of resilience to channel dropout. Furthermore, to transfer the model to other emulation problems, a mapping-based transfer learning approach can be used directly on the current model to obtain the optimal direction for the new emulation problems.

Chiara Boretti, Philippe Bich, Yanyu Zhang et al.

Drawing inspiration from biology, we describe the way in which visual sensing with a monocular camera can provide a reliable signal for navigation of mobile robots. The work takes inspiration from a classic paper by Lee and Reddish (Nature, 1981, https://doi.org/10.1038/293293a0) in which they outline a behavioral strategy pursued by diving sea birds based on a visual cue called time-to-contact. A closely related concept of time-to-transit, tau, is defined, and it is shown that idealized steering laws based on monocular camera perceptions of tau can reliably and robustly steer a mobile vehicle within a wide variety of spaces in which features perceived to lie on walls and other objects in the environment provide adequate visual cues. The contribution of the paper is two-fold. It provides a simple theory of robust vision-based steering control. It goes on to show how the theory guides the implementation of robust visual navigation using ROS-Gazebo simulations as well as deployment and experiments with a camera-equipped Jackal robot. As far as we know, the experiments described below are the first to demonstrate visual navigation based on tau.

Bowen Zhang, Michael C. Caramanis, John Baillieul

We propose and solve a stochastic dynamic programming (DP) problem addressing the optimal provision of regulation service reserves (RSR) by controlling dynamic demand preferences in smart buildings. A major contribution over past dynamic pricing work is that we pioneer the relaxation of static, uniformly distributed utility of demand. In this paper we model explicitly the dynamics of energy service preferences leading to a non-uniform and time varying probability distribution of demand utility. More explicitly, we model active and idle duty cycle appliances in a smart building as a closed queuing system with price-controlled arrival rates into the active appliance queue. Focusing on cooling appliances, we model the utility associated with the transition from idle to active as a non-uniform time varying function. We (i) derive an analytic characterization of the optimal policy and the differential cost function, and (ii) prove optimal policy monotonicity and value function convexity. These properties enable us to propose and implement a smart assisted value iteration (AVI) algorithm and an approximate DP (ADP) that exploits related functional approximations. Numerical results demonstrate the validity of the solution techniques and the computational advantage of the proposed ADP on realistic, large-state-space problems.

Zhaodan Kong, Kayhan Ozcimder, Nathan W. Fuller et al.

Animals within groups need to coordinate their reactions to perceived environmental features and to each other in order to safely move from one point to another. This paper extends our previously published work on the flight patterns of Myotis velifer that have been observed in a habitat near Johnson City, Texas. Each evening, these bats emerge from a cave in sequences of small groups that typically contain no more than three or four individuals, and they thus provide ideal subjects for studying leader-follower behaviors. By analyzing the flight paths of a group of M. velifer, the data show that the flight behavior of a follower bat is influenced by the flight behavior of a leader bat in a way that is not well explained by existing pursuit laws, such as classical pursuit, constant bearing and motion camouflage. Thus we propose an alternative steering law based on virtual loom, a concept we introduce to capture the geometrical configuration of the leader-follower pair. It is shown that this law may be integrated with our previously proposed vision-enabled steering laws to synthesize trajectories, the statistics of which fit with those of the bats in our data set. The results suggest that bats use perceived information of both the environment and their neighbors for navigation.