Control-theoretic Perspective Research Articles

Shortest-path recovery from signature with an optimal control approach

AbstractIn this paper, we consider the signature-to-path reconstruction problem from the control-theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $$L^2$$ L 2 -norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $$\Gamma $$ Γ -converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.

Controlled gradient descent: A control theoretical perspective for optimization

The Gradient Descent (GD) paradigm is a foundational principle of modern optimization algorithms. The GD algorithm and its variants, including accelerated optimization algorithms, geodesic optimization, natural gradient, and contraction-based optimization, to name a few, are used in machine learning and the system and control domain. Here, we proposed a new algorithm based on the control theoretical perspective, labeled as the Controlled Gradient Descent (CGD). Specifically, this approach overcomes the challenges of the abovementioned algorithms, which rely on the choice of a suitable geometric structure, particularly in machine learning. The proposed CGD approach visualizes the optimization as a Manifold Stabilization Problem (MSP) through the notion of an invariant manifold and its attractivity. The CGD approach leads to an exponential contraction of trajectories under the influence of a pseudo-Riemannian metric generated through the control procedure as an additional outcome. The efficacy of the CGD is demonstrated with various test objective functions like the benchmark Rosenbrock function, objective function with a lack of flatness, and semi-contracting objective functions often encountered in machine learning applications.

How to regulate pattern formations for malware propagation in cyber-physical systems.

Malware propagation can be fatal to cyber-physical systems. How to detect and prevent the spatiotemporal evolution of malware is the major challenge we are facing now. This paper is concerned with the control of Turing patterns arising in a malware propagation model depicted by partial differential equations for the first time. From the control theoretic perspective, the goal is not only to predict the formation and evolution of patterns but also to design the spatiotemporal state feedback scheme to modulate the switch of patterns between different modes. The Turing instability conditions are obtained for the controlled malware propagation model with cross-diffusion. Then, the multi-scale analysis is carried out to explore the amplitude equations near the threshold of Turing bifurcation. The selection and stability of pattern formations are determined based on the established amplitude equations. It is proved that the reaction-diffusion propagation model has three types of patterns: hexagonal pattern, striped pattern, and mixed pattern, and selecting the appropriate control parameters can make the pattern transform among the three patterns. The results of the analysis are numerically verified and provide valuable insights into dynamics and control of patterns embedded in reaction-diffusion systems.

Modeling Theory of Mind in Dyadic Games Using Adaptive Feedback Control

A major challenge in cognitive science and AI has been to understand how intelligent autonomous agents might acquire and predict the behavioral and mental states of other agents in the course of complex social interactions. How does such an agent model the goals, beliefs, and actions of other agents it interacts with? What are the computational principles to model a Theory of Mind (ToM)? Deep learning approaches to address these questions fall short of a better understanding of the problem. In part, this is due to the black-box nature of deep networks, wherein computational mechanisms of ToM are not readily revealed. Here, we consider alternative hypotheses seeking to model how the brain might realize a ToM. In particular, we propose embodied and situated agent models based on distributed adaptive control theory to predict the actions of other agents in five different game-theoretic tasks (Harmony Game, Hawk-Dove, Stag Hunt, Prisoner’s Dilemma, and Battle of the Exes). Our multi-layer control models implement top-down predictions from adaptive to reactive layers of control and bottom-up error feedback from reactive to adaptive layers. We test cooperative and competitive strategies among seven different agent models (cooperative, greedy, tit-for-tat, reinforcement-based, rational, predictive, and internal agents). We show that, compared to pure reinforcement-based strategies, probabilistic learning agents modeled on rational, predictive, and internal phenotypes perform better in game-theoretic metrics across tasks. The outlined autonomous multi-agent models might capture systems-level processes underlying a ToM and suggest architectural principles of ToM from a control-theoretic perspective.

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems Based on Sample Identifying Complexity and Deciphering Time

In the state-of-the-art literature on cryptography and control theory, there has been no systematic methodology of constructing cyber–physical systems that can achieve the desired control performance while being protected against eavesdropping attacks. In this article, we tackle this challenging problem. We first propose two novel notions referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sample identifying complexity</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sample deciphering time</i> in an encrypted control framework. The former explicitly captures the relation between the dynamical characteristics of control systems and the level of identifiability of the systems while the latter shows the relation between the computation time for the identification and the key length of a cryptosystem. Based on these two tractable new notions, we propose a systematic method for designing both of an optimal key length to prevent system identification with a given precision within a given life span of systems and of an optimal controller to maximize both of the control performance and the difficulty of the identification. The efficiency of the proposed method in terms of security level and realtime-ness is investigated through numerical simulations. To the best of our knowledge, this article first connects the relationship between the security of cryptography and dynamical systems from a control-theoretic perspective.

WiEdge: Edge Computing for Audio Sensing Applications With Accurate Wireless Link Prediction

Audio sensing applications on embedded and mobile devices have recently enjoyed increasing popularity. Their performance can be significantly improved by edge computing which offloads computation-intensive tasks to edge servers through wireless links. The quality of wireless links is essential to offloading performance. However, existing edge computing solutions can hardly predict the link quality accurately and efficiently in a dynamic wireless environment, resulting in less optimal offloading decisions and unsatisfied user-perceived Quality of Experience (QoE). In this article, we present WiEdge, a distributed edge computing framework for audio sensing applications with accurate wireless link prediction. By combining cross-layer information extracted from recently received WiFi beacons, TCP-level statistics, and the past throughput observations, WiEdge can predict the throughput of wireless links accurately and efficiently in the near future. Based on the prediction, WiEdge makes optimal offloading decisions for QoE maximization. We formulate the offloading decision problem as a stochastic optimal control problem and propose an efficient solution based on model predictive control from the control-theoretic perspective. We implement WiEdge and evaluate its performance extensively in three representative real-world scenarios. Results show that WiEdge achieves high prediction accuracy and improves average normalized QoE by 2%, 11%, and 40% in three different scenarios, compared with state-of-the-art approaches.

Gender-based differences in abstention and desistance from drug use among American Indian adolescents

Informed by the social control theoretical perspective, this study intends to identify the factors more likely to differentiate American Indian (AI) adolescents who never used illicit drugs (abstainers) and those who used drugs in the past but did not report recent drug usage (desisters) from their peers who reported lifetime and recent drug usage (persisters). This secondary analysis is based on data from a multi-site study conducted between 2009 and 2013. It is based on a gender-balanced sample (N = 3,380) of AI adolescents (50.50% male; Mean age = 14.75; SD = 1.69) representing the major AI languages and cultural groups in the U.S. Half of the AI adolescents reported lifetime drug use (50.40%), 37.50% never used drugs, and 12.10% stopped using drugs. When controlling for the variables included in the analysis, AI boys were significantly more likely than AI girls to desist from drug use. Both boys and girls who never used drugs tended to be younger, were less likely to have delinquent friends and a lower level of self-control, had stronger bonds to school, but lower levels of family attachment, and reported increased parental supervision. Compared to drug users, desisters associated significantly less with delinquent peers. While school attachment, self-control, and parental monitoring did not differentiate female desisters from female drug users, adolescent boys who desisted from drug use were more likely to report higher levels of school attachment and parental monitoring and their level of self-control was less likely to be low.

Shallow water waves generated by a floating object: A control theoretical perspective

&lt;p style='text-indent:20px;'&gt;We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a vertical force acting on the floating body. We first derive the full governing equations of the fluid-body system in a water tank and reformulate them as an initial boundary value problem of a first-order evolution system. We then linearize the equations around the equilibrium state and we study its well-posedness. Finally we focus on the reachability and stabilizability of the linear system. Our main result asserts that, provided that the floating body is situated in the middle of the tank, any symmetric waves with appropriate regularity can be obtained from the equilibrium state by an appropriate control force. This implies, in particular, that we can project this system on the subspace of states with appropriate symmetry properties to obtain a reduced system which is approximately controllable and strongly stabilizable. Note that, in general, this system is not controllable (even approximately).&lt;/p&gt;

Input-to-State Stability of a Bilevel Proximal Gradient Descent Algorithm*

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized in the outer loop and a discrete-time control trajectory is optimized in the inner loop, but also arise in other domains including machine learning. In the paper, an interconnection of proximal gradient algorithms is proposed to solve the inner loop and outer loop optimization problems in the setting of control-aware design optimization, and its robustness is analyzed from a control-theoretic perspective. By employing input-to-state stability arguments, conditions are derived that ensure convergence of the interconnected scheme to the optimal solution for a class of the bilevel optimization problems.

Brain modeling for control: A review

Neurostimulation technologies have seen a recent surge in interest from the neuroscience and controls communities alike due to their proven potential to treat conditions such as epilepsy, Parkinson’s Disease, and depression. The provided stimulation can be of different types, such as electric, magnetic, and optogenetic, and is generally applied to a specific region of the brain in order to drive the local and/or global neural dynamics to a desired state of (in)activity. For most neurostimulation techniques, however, an underlying theoretical understanding of their efficacy is still lacking. From a control-theoretic perspective, it is important to understand how each stimulus modality interacts with the inherent complex network dynamics of the brain in order to assess the controllability of the system and develop neurophysiologically relevant computational models that can be used to design the stimulation profile systematically and in closed loop. In this paper, we review the computational modeling studies of 1) deep brain stimulation, 2) transcranial magnetic stimulation, 3) direct current stimulation, 4) transcranial electrical stimulation, and 5) optogenetics as five of the most popular and commonly used neurostimulation technologies in research and clinical settings. For each technology, we split the reviewed studies into 1) theory-driven biophysical models capturing the low-level physics of the interactions between the stimulation source and neuronal tissue, 2) data-driven stimulus-response models which capture the end-to-end effects of stimulation on various biomarkers of interest, and 3) data-driven dynamical system models that extract the precise dynamics of the brain’s response to neurostimulation from neural data. While our focus is particularly on the latter category due to their greater utility in control design, we review key works in the former two categories as the basis and context in which dynamical system models have been and will be developed. In all cases, we highlight the strength and weaknesses of the reviewed works and conclude the review with discussions on outstanding challenges and critical avenues for future work.

Pitchfork-bifurcation-based competitive and collaborative control of an E-bike system

This paper is concerned with the design of a human-in-the-loop system for deployment on a smart pedelec (e-bike). From the control-theoretic perspective, the goal is not only to use the power assistance of the e-bike to reject disturbances along the route but also to manage the possibly competitive interactions between a human and the motor intervention. Managing the competitive/cooperative nature of the interactions is crucial for applications in which we wish to control physical aspects of the cycling behavior (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, modeling the interactions, augmented using ideas from gain-scheduling. In vivo experiments have been conducted, showing the effectiveness of the proposed control strategy.

Convexity and Feedback in Approximate Dynamic Programming for Delivery Time Slot Pricing

We consider the revenue management problem of finding profit-maximizing prices for delivery time slots in the context of attended home delivery. This multistage optimal control problem admits a dynamic programming (DP) formulation that is intractable for realistic problem sizes due to the so-called “curse of dimensionality.” We therefore study three approximate DP algorithms both from a numerical and control-theoretical perspective. Our analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests indicate that one of these algorithms, namely gradient-bounded DP, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.

Impact of VR Technology on a Human in Semi-autonomous Multi-robot Navigation: Control-Theoretic Perspective

In this paper, we investigate a scenario of one-human-multiple-robot navigation in three dimensions, and examine the impacts of the VR (Virtual Reality) technology on human properties from a control-theoretic perspective. We start by reviewing a passivity-based distributed control architecture that takes complementary interactions such that motion synchronization is autonomously completed by a distributed robot controller while the operator is dedicated to robot navigation. Due to the limited human capability of 3-D recognition and limited dimensionality on the real-time manipulability, 3-D navigation is completely different from that of the one- or two-dimensional case and we need to carefully design both feedback and command interfaces between the operator and robots. Specifically, we employ two different pairs of the interfaces, traditional joystick controller with 2-D display monitor and HMD (Head Mounted Display) with VR controller. We then build human models from the operation data with these interfaces on a human-in-the-loop simulator. Through the human modeling, we present two novel findings: (i) VR interfaces improve the accuracy of the human model with about 25∼45% of fitting ratio, which must drastically eases the design of human-robot collaboration systems, (ii) VR interfaces enhance human passivity, which is a key to ensuring closed-loop stability for the human-in-the-loop system.

Behavior Trees in Robot Control Systems

In this article, we provide a control-theoretic perspective on the research area of behavior trees in robotics. The key idea underlying behavior trees is to make use of modularity, hierarchies, and feedback in order to handle the complexity of a versatile robot control system. Modularity is a well-known tool to handle software complexity by enabling the development, debugging, and extension of separate modules without detailed knowledge of the entire system. A hierarchy of such modules is natural, since robot tasks can often be decomposed into a hierarchy of subtasks. Finally, feedback control is a fundamental tool for handling uncertainties and disturbances in any low-level control system, but in order to enable feedback control on the higher level, where one module decides what submodule to execute, information regarding the progress and applicability of each submodule needs to be shared in the module interfaces. We describe how these three concepts can be used in theoretical analysis, practical design, and extensions and combinations with other ideas from control theory and robotics.

A control-theoretic perspective on optimal high-order optimization

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function varPhi : {mathbb {R}}^d rightarrow {mathbb {R}} that is convex and twice continuously differentiable, we study a closed-loop control system that is governed by the operators nabla varPhi and nabla ^2 varPhi together with a feedback control law lambda (cdot ) satisfying the algebraic equation (lambda (t))^pVert nabla varPhi (x(t))Vert ^{p-1} = theta for some theta in (0, 1). Our first contribution is to prove the existence and uniqueness of a local solution to this system via the Banach fixed-point theorem. We present a simple yet nontrivial Lyapunov function that allows us to establish the existence and uniqueness of a global solution under certain regularity conditions and analyze the convergence properties of trajectories. The rate of convergence is O(1/t^{(3p+1)/2}) in terms of objective function gap and O(1/t^{3p}) in terms of squared gradient norm. Our second contribution is to provide two algorithmic frameworks obtained from discretization of our continuous-time system, one of which generalizes the large-step A-HPE framework of Monteiro and Svaiter (SIAM J Optim 23(2):1092–1125, 2013) and the other of which leads to a new optimal p-th order tensor algorithm. While our discrete-time analysis can be seen as a simplification and generalization of Monteiro and Svaiter (2013), it is largely motivated by the aforementioned continuous-time analysis, demonstrating the fundamental role that the feedback control plays in optimal acceleration and the clear advantage that the continuous-time perspective brings to algorithmic design. A highlight of our analysis is that we show that all of the p-th order optimal tensor algorithms that we discuss minimize the squared gradient norm at a rate of O(k^{-3p}), which complements the recent analysis in Gasnikov et al. (in: COLT, PMLR, pp 1374–1391, 2019), Jiang et al. (in: COLT, PMLR, pp 1799–1801, 2019) and Bubeck et al. (in: COLT, PMLR, pp 492–507, 2019).

Sampled-data-based fault-tolerant consensus control for multi-agent systems: A data privacy preserving scheme

This paper is concerned with the fault-tolerant consensus control problem for a general class of linear continuous-time multi-agent systems (MASs) with the data privacy preserving (DPP) constraints. Rather than employing the traditional cryptographic mechanism, we develop a novel dynamic-quantization-based DPP scheme from a control-theoretic perspective. Under our developed DPP scheme, the sampled, quantized, released, received and recovered data is used to design a fault-tolerant controller. With the adopted controller structure, the consensus of the MASs is guaranteed where the size of the data transmitted among agents can be made finite. A series of numerical examples are given and the comparative analysis is carried out to illustrate the effectiveness of the developed consensus control scheme.

Structural Differences Between Healthy Subjects and Patients With Schizophrenia or Schizoaffective Disorder: A Graph and Control Theoretical Perspective.

The coordinated dynamic interactions of large-scale brain circuits and networks have been associated with cognitive functions and behavior. Recent advances in network neuroscience have suggested that the anatomical organization of such networks puts fundamental constraints on the dynamical landscape of brain activity, i.e., the different states, or patterns of regional activation, and transition between states the brain can display. Specifically, it has been shown that densely connected, central regions control the transition between states that are “easily” reachable (in terms of expended energy), whereas weakly connected areas control transitions to states that are hard-to-reach. Changes in large-scale brain activity have been hypothesized to underlie many neurological and psychiatric disorders. Evidence has emerged that large-scale dysconnectivity might play a crucial role in the pathophysiology of schizophrenia, especially regarding cognitive symptoms. Therefore, an analysis of graph and control theoretic measures of large-scale brain connectivity in patients offers to give insight into the emergence of cognitive disturbances in the disorder. To investigate these potential differences between patients with schizophrenia (SCZ), patients with schizoaffective disorder (SCZaff) and matched healthy controls (HC), we used structural MRI data to assess the microstructural organization of white matter. We first calculate seven graph measures of integration, segregation, centrality and resilience and test for group differences. Second, we extend our analysis beyond these traditional measures and employ a simplified noise-free linear discrete-time and time-invariant network model to calculate two complementary measures of controllability. Average controllability, which identifies brain areas that can guide brain activity into different, easily reachable states with little input energy and modal controllability, which characterizes regions that can push the brain into difficult-to-reach states, i.e., states that require substantial input energy. We identified differences in standard network and controllability measures for both patient groups compared to HCs. We found a strong reduction of betweenness centrality for both patient groups and a strong reduction in average controllability for the SCZ group again in comparison to the HC group. Our findings of network level deficits might help to explain the many cognitive deficits associated with these disorders.

Adaptive distributed synchronization of heterogeneous multi-Agent systems over directed graphs with time-Varying edge weights

Time-varying edge weights represent dynamical interactions between any two nodes in multi-agent systems (MASs). In this paper, we consider a synchronization problem for heterogeneous MASs over directed graphs with time-varying edge weights from a control-theoretic perspective. We seek for an adaptive control protocol that drives the synchronization error in the presence of time-varying edge weights to converge in terms of asymptotic stability. We propose a class of observer networks for estimating leaders and output regulation equation solvers built on directed graphs with time-varying edge weights. Finally, we use a simulation study to verify the effectiveness of the proposed protocol.

Modeling and control of epidemics through testing policies

Testing is a crucial control mechanism in the beginning phase of an epidemic when the vaccines are not yet available. It enables the public health authority to detect and isolate the infected cases from the population, thereby limiting the disease transmission to susceptible people. However, despite the significance of testing in epidemic control, the recent literature on the subject lacks a control-theoretic perspective. In this paper, an epidemic model is proposed that incorporates the testing rate as a control input and differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. After estimating the model on the data corresponding to the beginning phase of COVID-19 in France, two testing policies are proposed: the so-called best-effort strategy for testing (BEST) and constant optimal strategy for testing (COST). The BEST policy is a suppression strategy that provides a minimum testing rate that stops the growth of the epidemic when implemented. The COST policy, on the other hand, is a mitigation strategy that provides an optimal value of testing rate minimizing the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France.

Actor-Critic Reinforcement Learning for Control With Stability Guarantee

Reinforcement Learning (RL) and its integration with deep learning have achieved impressive performance in various robotic control tasks, ranging from motion planning and navigation to end-to-end visual manipulation. However, stability is not guaranteed in model-free RL by solely using data. From a control-theoretic perspective, stability is the most important property for any control system, since it is closely related to safety, robustness, and reliability of robotic systems. In this paper, we propose an actor-critic RL framework for control which can guarantee closed-loop stability by employing the classic Lyapunov's method in control theory. First of all, a data-based stability theorem is proposed for stochastic nonlinear systems modeled by Markov decision process. Then we show that the stability condition could be exploited as the critic in the actor-critic RL to learn a controller/policy. At last, the effectiveness of our approach is evaluated on several well-known 3-dimensional robot control tasks and a synthetic biology gene network tracking task in three different popular physics simulation platforms. As an empirical evaluation on the advantage of stability, we show that the learned policies can enable the systems to recover to the equilibrium or way-points when interfered by uncertainties such as system parametric variations and external disturbances to a certain extent.