arXiv subjects

John Baillieul

Publications and source records attributed to John Baillieul.

At least 19 recordsLinked to original sources

arXiv2025

Structure and Control of Biology-inspired Networks

There is increasing interest in developing the theoretical foundations of networked control systems that illuminate how brain networks function so as to enable sensory perception, control of movement, memory and all the operations that are needed for animals to survive. The present paper proposes a biologically inspired network model featuring dynamic connections regulated by Hebbian learning. Drawing on the machinery of graph theory and classical control we show that our novel nonlinear model exhibits such biologically plausible features as bounded evolution, stability, resilience, and a kind of structural stability -- meaning that perturbations of the model parameters leave the essential properties of the model in tact. The proposed network model involves generalized cactus graphs with multiple control input nodes, and it is shown that the properties of the network are resilient to various changes in network topology provided these changes preserve the generalized cactus structure. A particular example described in what follows is an idealized network model of the visual system of a macaque monkey. The model displays resilience to network disruptions such as might occur in a living organism due to disease or injury. A different model of the same type provides an example of a system that can perform data classification.

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arXiv2024

Koopman-based Deep Learning for Nonlinear System Estimation

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.

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arXiv2023

Neuromimetic Dynamic Networks with Hebbian Learning

Leveraging recent advances in neuroscience and control theory, this paper presents a neuromimetic network model with dynamic symmetric connections governed by Hebbian learning rules. Formal analysis grounded in graph theory and classical control establishes that this biologically plausible model exhibits boundedness, stability, and structural controllability given a generalized sym-cactus structure with multiple control nodes. We prove the necessity of this topology when there are distributed control inputs. Simulations using a 14-node generalized sym-cactus network with two input types validate the model's effectiveness in capturing key neural dynamics.

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arXiv2023

On the complexity of linear systems: an approach via rate distortion theory and emulating systems

We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a Gaussian source of uncertainty in those increments. The complexity of a linear system has relevance in control-communications contexts requiring local and dynamic decision-making based on sampled data representations. We relate this notion of complexity to the design of attention-varying controllers, and demonstrate a novel methodology for constructing source codes via the endpoint maps of so-called emulating systems, with potential for non-parametric, data-based simulation and analysis of unknown dynamical systems.

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arXiv2023

Model Predictive Control for Neuromimetic Quantized Systems

Based on our recent research on neural heuristic quantization systems, we propose an emulation problem consistent with the neuromimetic paradigm. This optimal quantization problem can be solved with model predictive control (MPC) by deriving the conditions under which the quantized system can guarantee (asymptotic) stability during emulation by optimizing a Lyapunov-like objective function. The neuromimetic model features large numbers of discrete inputs, and the optimization involves integer variables. The approach in the paper begins by solving an optimization using model predictive control (MPC) and then using a neural network to train the data generated in this process and applying Fincke and Pohst's sphere decoding algorithm to narrow down the search for the optimal solution.

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arXiv2023

Emulation Learning for Neuromimetic Systems

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.

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arXiv2022

Neuromimetic Linear Systems -- Resilience and Learning

Building on our recent work on {\em neuromimetic control theory}, new results on resilience and neuro-inspired quantization are reported. The term neuromimetic refers to the models having features that are characteristic of the neurobiology of biological motor control. As in previous work, the focus is on what we call {\em overcomplete} linear systems that are characterized by larger numbers of input and output channels than the dimensions of the state. The specific contributions of the present paper include a proposed {\em resilient} observer whose operation tolerates output channel intermittency and even complete dropouts. Tying these ideas together with our previous work on resilient stability, a resilient separation principle is established. We also propose a {\em principled quantization} in which control signals are encoded as simple discrete inputs which act collectively through the many channels of input that are the hallmarks of the overcomplete models. Aligned with the neuromimetic paradigm, an {\em emulation} problem is proposed and this in turn defines an optimal quantization problem. Several possible solutions are discussed including direct combinatorial optimization, a Hebbian-like iterative learning algorithm, and a deep Q-learning (DQN) approach. For the problems being considered, machine learning approaches to optimization provide valuable insights regarding comparisons between optimal and nearby suboptimal solutions. These are useful in understanding the kinds of resilience to intermittency and channel dropouts that were earlier demonstrated for continuous systems.

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arXiv2021

Visual Navigation Using Sparse Optical Flow and Time-to-Transit

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.

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arXiv2021

Neuromimetic Control -- A Linear Model Paradigm

Stylized models of the neurodynamics that underpin sensory motor control in animals are proposed and studied. The voluntary motions of animals are typically initiated by high level intentions created in the primary cortex through a combination of perceptions of the current state of the environment along with memories of past reactions to similar states. Muscle movements are produced as a result of neural processes in which the parallel activity of large multiplicities of neurons generate signals that collectively lead to desired actions. Essential to coordinated muscle movement are intentionality, prediction, regions of the cortex dealing with misperceptions of sensory cues, and a significant level of resilience with respect to disruptions in the neural pathways through which signals must propagate. While linear models of feedback control systems have been well studied over decades, this paper proposes and analyzes a class of models whose aims are to capture some of the essential features of neural control of movement. Whereas most linear models of feedback systems entail a state component whose dimension is higher than the number of inputs or outputs, the work that follows will treat models in which the numbers of input and output channels greatly exceed the state dimension. While we begin by considering continuous time systems, the aim will be to treat systems whose evolution involves classes of inputs that emulate neural spike trains. Within the proposed class of models, the paper will study resilience to channel dropouts, the ways in which noise and uncertainty can be mitigated by an appropriate notion of consensus among noisy inputs, and finally, by a simple model in which binary activations of a multiplicity of input channels produce a dynamic response that closely approximates the dynamics of a prescribed linear system whose inputs are continuous functions of time.

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arXiv2021

Visual Navigation with a 2-pixel Camera---Possibilities and Limitations

Borrowing terminology from fluid mechanics, the concepts of {\em Eulerian} and {\em Lagrangian optical flow sensing} are introduced. Eulerian optical flow sensing assumes that each photoreceptor in the camera or eye can instantaneously detect feature image points and their velocities on the retina. If this assumption is satisfied, even a two pixel imaging system can provide a moving agent with information about its movement along a corridor that is sufficiently precise as to be used as a robustly reliable steering signal. Implementing Eulerian optical flow sensing poses significant challenges, however. Lagrangian optical flow, on the other hand, tracks feature image points as they move on the retina. This form of visual sensing is the basis for many standard computer vision implementations, including Lukas-Kanade and Horn-Schunck. Lagrangian optical flow has its own challenges, not least of which is that it is badly confounded by rotational components of motion. Combined steering and sensing strategies for mitigating the effects of rotational motions are considered.

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arXiv2019

Perceptual Control with Large Feature and Actuator Networks

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.

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arXiv2018

Introduction to the Special Issue on Approaches to Control Biological and Biologically Inspired Networks

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.

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arXiv2018

Power Grid Decomposition Based on Vertex Cut Sets and Its Applications to Topology Control and Power Trading

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.

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arXiv2018

Paradigm and Paradox in Topology Control of Power Grids

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.

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arXiv2017

A Novel Decomposition for Control of DC Circuits and Grid Models with Heterogeneous Energy Sources

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.

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arXiv2017

Optimal Provision of Regulation Service Reserves Under Dynamic Energy Service Preferences

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.

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arXiv2015

The Kirchhoff-Braess Paradox and Its Implications for Smart Microgrids

Well known in the theory of network flows, Braess paradox states that in a congested network, it may happen that adding a new path between destinations can increase the level of congestion. In transportation networks the phenomenon results from the decisions of network participants who selfishly seek to optimize their own performance metrics. In an electric power distribution network, an analogous increase in congestion can arise as a consequence Kirchhoff's laws. Even for the simplest linear network of resistors and voltage sources, the sudden appearance of congestion due to an additional conductive line is a nonlinear phenomenon that results in a discontinuous change in the network state. It is argued that the phenomenon can occur in almost any grid in which they are loops, and with the increasing penetration of small-scale distributed generation it suggests challenges ahead in the operation of microgrids.

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arXiv2015

Control and Communication Protocols that Enable Smart Building Microgrids

Recent communication, computation, and technology advances coupled with climate change concerns have transformed the near future prospects of electricity transmission, and, more notably, distribution systems and microgrids. Distributed resources (wind and solar generation, combined heat and power) and flexible loads (storage, computing, EV, HVAC) make it imperative to increase investment and improve operational efficiency. Commercial and residential buildings, being the largest energy consumption group among flexible loads in microgrids, have the largest potential and flexibility to provide demand side management. Recent advances in networked systems and the anticipated breakthroughs of the Internet of Things will enable significant advances in demand response capabilities of intelligent load network of power-consuming devices such as HVAC components, water heaters, and buildings. In this paper, a new operating framework, called packetized direct load control (PDLC), is proposed based on the notion of quantization of energy demand. This control protocol is built on top of two communication protocols that carry either complete or binary information regarding the operation status of the appliances. We discuss the optimal demand side operation for both protocols and analytically derive the performance differences between the protocols. We propose an optimal reservation strategy for traditional and renewable energy for the PDLC in both day-ahead and real time markets. In the end we discuss the fundamental trade-off between achieving controllability and endowing flexibility.

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