Control Theoretic Approach Research Articles

A unified framework for the analysis of accuracy and stability of a class of approximate Gaussian filters for the Navier–Stokes equations

Abstract Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

A control theoretic approach to evaluate and inform ecological momentary interventions.

Ecological momentary interventions (EMI) are digital mobile health interventions administered in an individual's daily life to improve mental health by tailoring intervention components to person and context. Experience sampling via ecological momentary assessments (EMA) furthermore provides dynamic contextual information on an individual's mental health state. We propose a personalized data-driven generic framework to select and evaluate EMI based on EMA. We analyze EMA/EMI time-series from 10 individuals, published in a previous study. The EMA consist of multivariate psychological Likert scales. The EMI are mental health trainings presented on a smartphone. We model EMA as linear dynamical systems (DS) and EMI as perturbations. Using concepts from network control theory, we propose and evaluate three personalized data-driven intervention delivery strategies. Moreover, we study putative change mechanisms in response to interventions. We identify promising intervention delivery strategies that outperform empirical strategies in simulation. We pinpoint interventions with a high positive impact on the network, at low energetic costs. Although mechanisms differ between individuals - demanding personalized solutions - the proposed strategies are generic and applicable to various real-world settings. Combined with knowledge from mental health experts, DS and control algorithms may provide powerful data-driven and personalized intervention delivery and evaluation strategies.

Newton's cradle: Cell cycle regulation by two mutually inhibitory oscillators

The cell division cycle is a fundamental physiological process displaying a great degree of plasticity during the course of multicellular development. This plasticity is evident in the transition from rapid and stringently-timed divisions of the early embryo to subsequent size-controlled mitotic cycles. Later in development, cells may pause and restart proliferation in response to myriads of internal or external signals, or permanently exit the cell cycle following terminal differentiation or senescence. Beyond this, cells can undergo modified cell division variants, such as endoreplication, which increases their ploidy, or meiosis, which reduces their ploidy. This wealth of behaviours has led to numerous conceptual analogies intended as frameworks for understanding the proliferative program. Here, we aim to unify these mechanisms under one dynamical paradigm. To this end, we take a control theoretical approach to frame the cell cycle as a pair of arrestable and mutually-inhibiting, doubly amplified, negative feedback oscillators controlling chromosome replication and segregation events, respectively. Under appropriate conditions, this framework can reproduce fixed-period oscillations, checkpoint arrests of variable duration, and endocycles. Subsequently, we use phase plane and bifurcation analysis to explain the dynamical basis of these properties. Then, using a physiologically realistic, biochemical model, we show that the very same regulatory structure underpins the diverse functions of the cell cycle control network. We conclude that Newton's cradle may be a suitable mechanical analogy of how the cell cycle is regulated.

Modeling Reliability-Driven Software Release Strategy Considering Testing Effort with Fault Detection and Correction Processes: A Control Theoretic Approach

In this paper, we have introduced a software reliability growth model (SRGM) that integrates a Weibull testing effort function (TEF) within the software fault detection process (FDP) and fault correction process (FCP), effectively capturing the intricacies of software testing. Leveraging the least squared estimation method, we estimated both model parameters and the TEF, leading to a notably improved fit with the dataset and enhancing our comprehension of software reliability dynamics. Our approach also involved employing a reliability-based method to identify the optimal time for software release, further reinforcing the robustness of our model. Subsequently, we devised an optimal control model to minimize testing efforts throughout the software development life cycle. This work provides a comprehensive methodological framework for computing the total cost while ensuring debugging costs follow a learning curve pattern. Through numerical simulations involving hypothetical values and the Weibull TEF, we observed that once the software achieves the desired reliability for release, subsequent costs gradually decline to zero. In essence, both testing and future costs converge to zero post-release, reducing instantaneous expenses.

A Trustworthy and Responsible Decision-Making Framework for Resource Management in Food-Energy-Water Nexus: A Control-Theoretical Approach

This paper introduces a hybrid framework for trustworthy and responsible natural resource management, aimed at building bottom-up trust to enhance cooperation among decision makers in the Food, Energy, and Water sectors. Cooperation is highly critical for the adoption and application of resource management alternatives (solutions), including those generated by AI-based recommender systems, in communities due to significant impact of these sectors on the environment and the economic productivity of affected communities. While algorithms can recommend solutions, effectively communicating and gaining community acceptance of these solutions is crucial. Our research stands out by emphasizing the collaboration between humans and machines, which is essential for addressing broader challenges related to climate change and the need for expert trade-off handling in the management of natural resources. To support future decision-making, we propose a successful control-theory model based on previous decision-making and actor behavior. We utilize control theory to depict how community decisions can be affected by how much individuals trust and accept proposed solutions on irrigation water rights and crop operations in an iterative and interactive decision support environment. This model interacts with stakeholders to collect their feedback on the acceptability of solutions, while also examining the influence of consensus levels, trust sensitivities, and the number of decision-making rounds on the acceptance of proposed solutions. Furthermore, we investigate a system of multiple decision-making and explore the impact of learning actors who adjust their trust sensitivities based on solution acceptance and the number of decision-making rounds. Additionally, our approach can be employed to evaluate and refine potential policy modifications. Although we assess potential outcomes using hypothetical actions by individuals, it is essential to emphasize our primary objective of developing a tool that accurately captures real human behavior and fosters improved collaboration in community decision-making. Ultimately, our aim is to enhance the harmony between AI-based recommender systems and human values, promoting a deeper understanding and integration between the two.

Strategizing Against Q-Learners: A Control-Theoretical Approach

Strategizing Against Q-Learners: A Control-Theoretical Approach

Sonnet: A control-theoretic approach for resource allocation in cluster management

Cluster users expect to minimize the resource costs while ensuring target performance for different applications. It is particularly difficult to reach such a goal, because the applications are diverse with dynamic load changes, and interference exists between them. In addition, the performance of the applications depends on heterogeneous resources with different costs. However, existing works either use simplistic and generalized heuristics that disregard resource-specific characteristics or need suspending service to get expert knowledge to optimize the resource cost for a brand-new application or runtime, which fails to optimize the resource allocation finely.In this paper, we propose Sonnet, a control-theoretic approach to perform efficient resource allocation. Sonnet can efficiently optimize the cost of resources while satisfying the SLO by quickly establishing new application performance models through only online profiling and without affecting service. Experiments on Docker Swarm using various open-source benchmarks demonstrate that Sonnet can decrease the SLO violation rate by 91% while reducing resource costs up to 47% compared with the state-of-the-arts.

A stochastic control perspective on term structure models with roll-over risk

In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control-theoretic approach of Gombani and Runggaldier (Math. Finance23 (2013) 659–686) and derive representations of spot/forward spreads as value functions of suitable stochastic optimal control problems, formulated under the real-world probability and with power-type objective functionals. We determine endogenously the funding–liquidity spread by relating it to the risk-sensitive optimisation problem of a representative investor.

A greedy Galerkin method to efficiently select sensors for linear dynamical systems

A key challenge in inverse problems is the selection of sensors to gather the most effective data. In this paper, we consider the problem of inferring the initial condition to a linear dynamical system and develop an efficient control-theoretical approach for greedily selecting sensors. Our method employs a Galerkin projection to reduce the size of the inverse problem, resulting in a computationally efficient algorithm for sensor selection. As a byproduct of our algorithm, we obtain a preconditioner for the inverse problem that enables the rapid recovery of the initial condition. We analyze the theoretical performance of our greedy sensor selection algorithm as well as the performance of the associated preconditioner. Finally, we verify our theoretical results on various inverse problems involving partial differential equations.

Congestion Control for Datacenter Networks: A Control-Theoretic Approach

In this paper, we present <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> , a robust congestion control approach for datacenter networks based on RDMA. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> leverages switch queue size as an input to a PI controller, which computes the fair data rate of flows in the queue. The PI parameters are self-tuning to guarantee stability, rapid convergence, and fair and near-optimal throughput in a wide range of congestion scenarios. Our simulation and DPDK implementation results show that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> can achieve up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$7\times$</tex-math></inline-formula> reduction in PFC frames generated under high load levels, compared to DCQCN. At the same time, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> can achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.7 - 4.5\times$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.4 - 3.9\times$</tex-math></inline-formula> lower tail latency for long flows and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.1-7\times$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3.5-8.2\times$</tex-math></inline-formula> lower tail latency for short flows, compared to DCQCN and HPCC, respectively. We also find that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> does not require PFC. The functional components of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RoCC</i> can be efficiently implemented in P4 and FPGA-based switch hardware.

Editorial for the special issue “Control‐theoretic approaches for systems in the life sciences”

Editorial for the special issue “Control<scp>‐theoretic</scp> approaches for systems in the life sciences”

Effects of emission reduction and rework policy in a production system of green products: An interval valued optimal control theoretic approach

Over the last few decades, the implementation of emission regulation by the government due to the impact of emissions from the industrial sector on the environment has included a rough demotivation among the small and moderate manufacturing industries. In the recent market situation, it is observed that, consumers much prefer to purchase eco-friendly products. Further, in the highly imprecise competitive market, it is rather a complicated task for a competent authority/operator of every manufacturing company to make an appropriate decision regarding marketing policy of the firm. Taking these three factors into account, this work aims to formulate the model of a production system that can benefit such manufacturers who are dealing with these three issues. This model is developed using interval modelling technique, and it is solved by using optimal control in interval uncertainty. Regarding emission tax estimation, two distinct cases appear to the manufacturer, which are explained separately. After the numerical analysis of the proposed model, it contemporarily observed that for a small/moderate manufacturing sector, adoption of emission reduction technology appears to be more beneficiary rather than paying emission tax free of reduction technology. Further, greenness index for the manufactured items imposes considerably-sensitive impact on the revenue of the system. Therefore the major contribution of the model is to investigate an emergent business policy for a manufacturing firm of green products under emission taxation regulation so that it may influence small and moderate manufacturers to set up their best-found marketing policies.

An optimal software enhancement and customer growth model: a control-theoretic approach

PurposeRecently, the popularity of software has grown significantly in the market. Enhancement of software is needed to decrease the burden of getting high-quality and reliable software. To achieve this, the software is upgraded by adding new features to the previous version. Therefore, adding new features in the last version to be consistent with the earlier version is challenging. This paper aims to discuss the optimal software enhancement and customer growth model.Design/methodology/approachThis paper discusses a model when new features are added to the software, and the customers' adoption of the software is presented as a customer growth model. An optimal control problem is introduced to maximize the profit obtained from the software system over the system's lifetime period. Total gain is calculated by the value generated from selling the software over the total expenditure during the software development process. The closed-form solution and some theoretical results are presented using the optimal control-theoretic approach. The theoretical results are supported by a numerical example.FindingsThis paper gives several substantive insights during sensitivity analysis and provides essential results. The results discussed here are compatible with the actual scenario and useful in software enhancement.Originality/valueThe authors have proposed a new feature growth and customer growth model to maximize the total profit using optimal control theory.

Stability Analysis in Mixed-Autonomous Traffic With Deep Reinforcement Learning

The emergence of autonomous driving vehicles on roads has increased the importance of research on autonomous driving in mixed-autonomous traffic. In mixed-autonomous traffic scenarios, it is necessary to comprehend the instability of autonomous vehicles and traffic flow corresponding to the uncertainty level in human-driven behaviors. However, studies of stability analysis in deep reinforcement learning are limited. This study focuses on the impact of deep reinforcement learning based autonomous vehicles in mixed-autonomous traffic from the stability perspective. We define the policy instability and traffic flow instabilities using the entropy of the velocity distributions to quantitatively measure the instability of an autonomous vehicle. Subsequently, we provide mathematical analyses to explain logarithmic growth patterns of instability. Moreover, we propose a novel deep reinforcement learning approach that jointly determines discrete and continuous actions under partial observation. To verify the proposed solution, we perform extensive simulations of various traffic scenarios (e.g., increasing traffic volumes, increasing the number of autonomous vehicles on the road, and setting the multiple uncertainty levels for human-driven behaviors) with ablation studies on reward function. Moreover, we analyze instabilities when human-driven vehicles are modeled using the human-like noisy controller and a policy that imitates actual human-driving data based on imitation learning. The simulation results support the theoretical analysis and confirm that the proposed method is stabler compared to a conventional control-theoretic approach.

On asymptotic log-optimal portfolio optimization

In this paper, we consider a frequency-dependent portfolio optimization problem with multiple assets using a control-theoretic approach. The expected logarithmic growth (ELG) rate of wealth is used as the objective performance metric. It is known that if the portfolio contains a special asset, the so-called dominant asset, then the optimal ELG level is achieved by investing all available funds in that asset. However, this “all-in” strategy is arguably too risky to implement. As a result, we study the case where the portfolio weights are chosen in a rather ad-hoc manner, and a linear buy-and-hold strategy is subsequently used. We show that if the underlying portfolio contains a dominant asset, buy and hold on that specific asset is asymptotically log-optimal with a logarithmic convergence rate. This result also extends to the scenario when a trader does not have a probabilistic model for returns or does not trust a model based on historical data. Specifically, we prove a version of the one fund theorem, which states that if a market contains a dominant asset, buying and holding a market portfolio with nonzero weights for each asset is asymptotically log-optimal. Additionally, we extend an existing result regarding the property called high-frequency maximality of an ELG-based portfolio from a single asset to a multi-asset portfolio case. This means that, in the absence of transaction costs, high-frequency rebalancing is unbeatable in terms of ELG. This result enables us to further improve the log-optimality obtained previously. Finally, we provide a result on the issue of how often a portfolio should be rebalanced, if needed. Examples using simulations with high-frequency historical trading data are included throughout to illustrate the theory.

Impact of Goodwill on Consumer Buying through Advertising in a Segmented Market: An Optimal Control Theoretic Approach

Market segmentation is one of the key marketing activities to target the potential market for a product, which allows the firm to have a better understanding of their customers. This paper considers an optimal control problem to determine the dynamic price and advertising policies of a new product introduction in a segment-specific market incorporating advertising-based goodwill. Under differentiated advertising and single-channel advertising, advertising efforts increase the stock of goodwill in each segment. Single-channel advertising starts in all segments with a fixed segment spectrum, while the differentiated advertising process deals with each segment independently. The explicit optimal dynamic advertising effort and price strategies are obtained by applying Pontryagin’s maximum principle, and local stability of equilibria have also been examined. The effectiveness of the proposed method is validated through numerical examples, and a local sensitivity analysis is performed to find the sensitive parameters that can affect the optimal values of price and advertising effort rates.

A control-theoretic approach for input saturated linear systems: Integration of phase-shaping and gain-scheduling

Saturation is mainly characterized by its passivity and magnitude bound. But most of the saturation control methods only make use of either of these features. To enhance the performance of saturated systems, this paper develops a novel method capable of fully using both of these two features. This method is a two-stage design scheme which integrates the phase-shaping technique with the gain-scheduled control. The phase-shaping fully uses the passivity of saturation while the gain-scheduling actively utilizes the magnitude bound of saturation. In this way, the design conservatism associated with existing methods is reduced substantially. Specifically, a matrix-type phase-shaping method is developed through the placement of systems’ frequency loci, and a meta-heuristic method is devised for the design of the phase-shaping function. Furthermore, the gain-scheduled control is transformed into the robust performance problem of a passive uncertain system, and designed by the passivity-based robust control method of the authors. Application to two practical control systems validates the effectiveness of the proposed method. The superiority is demonstrated via comparisons with typical saturation control methods.

An Observer-Based Key Agreement Scheme for Remotely Controlled Mobile Robots

Remotely controlled mobile robots are important examples of Cyber–Physical Systems (CPSs) that are being deployed in many safety critical applications. Different control schemes that have been proposed to secure such systems against sophisticated cyber-attacks require the exchange of secret messages between their smart actuators and the remote controller. Thus, these schemes require pre-shared secret keys, or an established Public Key Infrastructure that allows for key agreement. Such cryptographic approaches might not always be suitable for the deployment environments of such remotely mobile robots. To address this problem, in this paper, we consider a control theoretic approach for establishing a secret key between the remotely controlled robot and the networked controller without resorting to traditional cryptographic techniques. Our key agreement scheme leverages a nonlinear unknown input observer and an error correction code mechanism to allow the robot to securely agree on a secret key with its remote controller. The effectiveness of the proposed solution is shown by mean of experimental results obtained using a Khepera-IV robot.

Adaptive Coexistence of Delay-Sensitive and Delay-Tolerant MTC Devices: A Control-Theoretic Approach

We consider future cellular networks and study the coexistence of delay-sensitive (DS) and delay-tolerant (DT) devices in machine-type communication (MTC). DS devices require to minimize access delay for their low delay requirements; in contrast, DT devices have flexible delay constraints. For reducing access delay, we extend fast retrial idea in the data transmissions when a group of preambles is divided into two subsets to support the time-varying nature of the traffic from DS devices. We focus on the stability dynamics by design—we derive convergence conditions by using a control-theoretic approach in terms of variation in the 1) arrival rates; 2) buffer sizing at the devices; 3) number of preambles; and 4) number of DS devices. More importantly, we discover a novel adaptive algorithm that dynamically allocates the number of preambles for DS, thus guaranteeing stability by design. We validate our findings with extensive simulations. Besides, we develop a novel framework that describes how the control theory idea can be applied to address the issue of tracking the buffers and handling coexistence in such a diverse network environment under realistic application constraints. Our extension to the control-theoretic idea predicts whether the overall system is stable, i.e., whether data flows are desynchronized. Given the data flows are desynchronized, small buffers are always sufficient. Our approach shows that a smaller DS buffer often promotes desynchronization—a virtuous cycle.

A Key-Agreement Scheme for Cyber–Physical Systems

Traditional cryptographic approaches may not always be suitable for cyber–physical systems (CPSs). In this correspondence, we present a control-theoretic approach allowing a networked controller and a smart actuator of a stochastic CPS to agree on a common secret key without resorting to classical cryptographic approaches. More precisely, by utilizing the asymmetry in the system model knowledge available to the control system defender and to the eavesdropper, we propose a key-agreement scheme utilizing a simultaneous input and state estimation algorithm. The validity of the proposed solution is shown through a numerical example.