Input-output Behavior Research Articles

Model order reduction for the input–output behavior of a geothermal energy storage

In this article, we consider a geothermal energy storage system in which the spatio-temporal temperature distribution is modeled by a heat equation with a time-dependent convection term. Such storage systems are often embedded in residential heating systems. The control and management of such systems requires knowledge of aggregated characteristics of the temperature distribution in the storage. These describe the input–output behavior of the storage, the associated energy flows, and their response to charging and discharging processes. Our aim is to derive an efficient, approximate description of these characteristics by using low-dimensional systems of ordinary differential equations (ODEs). This leads to a model order reduction problem for a large-scale linear system of ODEs resulting from the semidiscretization of the heat equation combined with a linear algebraic output equation. In a first step, we approximated the nonautonomous system of ODEs by a linear time-invariant system. Then, we applied Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system that has only a few state equations but almost the same input–output behavior. The results of our extensive numerical experiments show the efficiency of the applied model order reduction method. We found that only a few suitably chosen ODEs are sufficient to achieve good approximations of the input–output behavior of the storage.

An Integrated Dynamic and Quality Modeling Framework for Batch Processes

This manuscript considers batch process operations and addresses the challenge of identifying a model that synergistically captures the dynamic input–output behavior of continuously measured variables along with the quality variables measured only at batch termination. To this end, an optimization-based framework is developed to identify one model that captures both the dynamics between the inputs and the continuously measured output variables, measurements of which are available at every time step, and the relation between the dynamic “state” information and the terminal quality measurements. Existing approaches either do not identify the dynamic and the quality model simultaneously, or they simply connect the whole trajectory of the process variables with the qualities and do not address the dynamic relationship between the inputs and the process variables. The improved modelling performance of the model obtained from this approach is demonstrated using data from a Uni-axial Rotational Molding process, and compared with existing modelling approaches.

Monotone One-Port Circuits

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped to periodic output signals, and these input-output behaviors can be efficiently computed using a maximal monotone splitting algorithm, which decomposes the computation according to the circuit topology. A new splitting algorithm is presented, which applies to any monotone one-port circuit defined as a port interconnection of monotone elements.

Fuzzy Coordinated Control of TCSCs to Improve Power System Stability

This paper presents the application of a coordinated fuzzy logic controller for the Thyristor Controlled Series Capacitors (TCSC) to improve the stability of the power system. The nonlinear fuzzy logic controller is used to overcome the problems generated by modeling and different uncertainties existing in power systems during design stage of controllers to damp electromechanical oscillations. To facilitate the design process, neural network is used to model the system input-output behavior. Proposed method is implemented on the 9 Bus IEEE power system and simulation results are presented to confirm the performance of the proposed controller. It is shown that this controller can increase the damping of the system

A Study on Communication Behaviour of Wheat Growers in Reasi Distt. of Jammu & Kashmir, India

Introduction of latest interactive communication technology among the rural population has opened a new vista of researchers to find out viability, acquaintance, accessibility, satisfaction, constraints and many more issues of the launched electronic communication technology and systems. There exists a gap between the information available and its dissemination. There is a need to find out better and faster means of communication which will bridge the gap between the researches and their applicability. The information technology revolution has provided huge opportunities to make easy access to information with interactive distance learning. The mechanism of internet and T.V. aided information technology help to reach the unreach.
 Wheat is an important crop grown in hilly Distt. Reasi of Union Territory of Jammu and Kashmir where different varieties of wheat are grown. Keeping in mind the importance of communication behaviour in the transfer of wheat production technology, a study on “Communication Behaviour of Wheat Growers in Reasidistt. Reasi of Jammu &Kashmir, India” was conducted in hilly District Reasi of Union Territory of Jammu and Kashmir which was selected purposively. Out of 12 C.D. Blocks 4C.D.Blocks namely Reasi, Pouni, Katra and Thuroo were selected randomly. A sample of 20 per cent villages was selected randomly from selected Gram Panchayats. A sample of 20 per cent Gram Panchayats from each selected block was selected randomly. A sample of 20 per cent villages from the selected Gram Panchayats was selected randomly. A sample of 20 per cent (150) wheat growers was selected randomly from selected villages. Hence, a total of 150 respondents were finally selected for recording their responses for study purpose. Communication behaviour of wheat growers has been operationalised as information input, information processing and information output behaviour of the respondents. An index was prepared for studying the communication behaviour of wheat growers, wherein information input was studied in terms of sources of information, processing of information was studied in terms of evaluation, storage and transfer of information and information output was studied in terms of dissemination of information.
 It was found that the majority of respondents were using Extension Personnel of KVK, Extension Personnel of Departments of Agriculture, progressive farmers, television, relatives and friends and radio as arranged rank wise 1, 2, 3,4, 5 and 6respectively as the main sources of information on wheat production technologies referred as the information input behaviour of the vegetables growers.
 A large number of farmers used to evaluate (processing) the information by discussing with the elder family members, progressive farmers, neighbourers and local leaders/key communicators as arranged rankwise 1, 2, 3 and 4 respectively. Majority of wheat growers stored the information by memorization and writing in general notebooks as arranged rankwise 1 and 2 respectively. A large number of wheat growers transformed the information by rearranging the important information as per their needs and rearranging the information in local dialect. Majority of wheat growers disseminated the information (information output) to their family members, neighbourers and those who cultivate in their lands as arranged rank wise 1, 2 and 3 respectively. It was found that majority of wheat growers had medium communication behaviour towards different wheat production information sources.

Novel Gramian-Based Structure-Preserving Model Order Reduction for Power Systems With High Penetration of Power Converters

Renewable energy and high voltage direct current connections increase the number of power electronic devices in the grid, changing how power systems operate and introducing new dynamic behavior. For this reason, it is fundamental to understand what modeling details are needed to represent the system in this new context. This paper proposes a novel model reduction approach using frequency-limited controllability and observability Gramians that preserves the link between the physical structure of the system and the state variables. This method allows understanding and analytically determining how vital each state is to the input-output behavior in different frequency ranges. The primary contribution of this paper is an algorithm that can provide intuitive results to help power system experts understand the simulation tools and minimum modeling details needed to perform different stability studies. Two case studies supported the applicability of the developed method, and a tool for MATLAB/Simulink was developed based on the findings, allowing visualization and immediate identification of the model components that are most relevant for the system dynamics under study. This tool can analyze dynamic behaviors where the cause is poorly understood and provide clarity around modeling detail requirements in converter-rich power systems.

Adaptive control of a linear first-order discrete-time system providing linear-like behaviour and asymptotic tracking

Adaptive control is an approach used to deal with systems having uncertain and/or time-varying parameters. In this paper, we consider the problem of designing an adaptive controller for a discrete-time first-order plant. Recently, Shahab et.al. considered this problem and proposed an approach which provides linear-like behaviour: exponential stability and a convolution bound on the input–output behaviour, together with robustness to slow time-variations and unmodelled dynamics. However, asymptotic tracking of a general reference signal was not provided. Here, we extend the aforementioned work with the aim to achieve asymptotic tracking while retaining linear-like closed-loop behaviour. We replace this uncertainty set with a pair of convex sets, one for each sign of the input gain, which enables us to use two parameter estimators — one for each convex set. We design these estimators using the modified version of the original projection algorithm. For each estimator, there is the corresponding one-step-ahead control law. A dynamic performance signal based switching rule is then adopted that decides which controller should be used at each time step. It is shown that the proposed approach preserves linear-like behaviour. In addition to that, we also have shown asymptotic trajectory tracking for two different circumstances: when the reference signal is asymptotically strongly persistently exciting of order two, and for a fairly general reference signal but the plant is unstable. Numerical simulations are presented to demonstrate the efficacy of the proposed approach.

Modeling and simulation of the input–output behavior of a geothermal energy storage

This paper investigates mathematical modeling and numerical methods for simulations of the input–output behavior of a geothermal energy storage. Such simulations are needed for the optimal control and management of residential heating systems equipped with an underground thermal storage. There, a given volume under or aside of a building is filled with soil and insulated to the surrounding ground. The thermal energy is stored by raising the temperature of the soil inside the storage. It is charged and discharged via pipe heat exchangers filled with a moving fluid. Simulations of geothermal energy storages aim to determine how much energy can be stored in or taken from the storage within a given period of time. The latter depends on the dynamics of the spatial temperature distribution in the storage, which is governed by a linear heat equation with convection and appropriate boundary and interface conditions. We consider semidiscretization and full discretization of that PDE using finite difference schemes and study associated stability problems. Finally, we present numerical results.

Centralized performance of a 2-rate decentralized controller for a class of two-channel systems

Given a two-channel, discrete linear time-invariant (LTI) plant, this paper investigates whether a 2-rate decentralized controller can achieve identical input–output behaviour as set by a centralized LTI controller designed for an augmented version of the two-channel plant. It is shown that the problem is solvable for stable plants with subsystems of equal sizes and minimum-phase strongly connected channel transfer functions, if the above centralized LTI controller is stable, minimum-phase and satisfies some relative degree condition. A suitable example is considered to illustrate the results.

Liquidity analysis in resource-aware programming

Liquidity is a liveness property of programs managing resources that pinpoints those programs not freezing any resource forever. We consider a simple stateful language whose resources are assets (digital currencies, non fungible tokens, etc.). Then we define a type system that tracks in a symbolic way the input-output behavior of functions with respect to assets. These types and their composition, which define types of computations, allow us to design two algorithms for liquidity that have different precisions and costs. We also demonstrate the correctness of the algorithms.

Position Control of a Fully Constrained Planar Cable-Driven Parallel Robot With Unknown or Partially Known Dynamics

In this article, we propose an intelligent proportional-integral-derivative (iPID) controller to control the position of a planar cable-driven parallel robot (CDPR). The proposed control method is based on ultralocal model estimation in short time intervals using only the system input–output behavior. We first employed the reference model-free iPID control, which requires the complete system dynamics estimation for the robot. Then, we modified the controller to utilize the partially known system dynamics represented in the feedback linearized form of the nonlinear model. Only the remaining unmodeled dynamics are estimated with the modified controller. We experimentally investigated the classical model-free intelligent proportional and derivative (iPD) controller and the modified iPD controller performances on the planar CPDR. The results show that significant performance improvement is achieved with the modified iPD controller.

First three years of the international verification of neural networks competition (VNN-COMP)

AbstractThis paper presents a summary and meta-analysis of the first three iterations of the annual International Verification of Neural Networks Competition (VNN-COMP), held in 2020, 2021, and 2022. In the VNN-COMP, participants submit software tools that analyze whether given neural networks satisfy specifications describing their input-output behavior. These neural networks and specifications cover a variety of problem classes and tasks, corresponding to safety and robustness properties in image classification, neural control, reinforcement learning, and autonomous systems. We summarize the key processes, rules, and results, present trends observed over the last three years, and provide an outlook into possible future developments.

Contrastive counterfactual visual explanations with overdetermination

A novel explainable AI method called CLEAR Image is introduced in this paper. CLEAR Image is based on the view that a satisfactory explanation should be contrastive, counterfactual and measurable. CLEAR Image seeks to explain an image’s classification probability by contrasting the image with a representative contrast image, such as an auto-generated image obtained via adversarial learning. This produces a salient segmentation and a way of using image perturbations to calculate each segment’s importance. CLEAR Image then uses regression to determine a causal equation describing a classifier’s local input–output behaviour. Counterfactuals are also identified that are supported by the causal equation. Finally, CLEAR Image measures the fidelity of its explanation against the classifier. CLEAR Image was successfully applied to a medical imaging case study where it outperformed methods such as Grad-CAM and LIME by an average of 27% using a novel pointing game metric. CLEAR Image also identifies cases of causal overdetermination, where there are multiple segments in an image that are sufficient individually to cause the classification probability to be close to one.

Reduced realization for switched linear systems with known mode sequence

We consider switched linear systems with mode-dependent state-dimensions and/or state jumps and propose a method to obtain a switched system of reduced size with identical input–output behavior. A key feature of our method is that only the mode sequence of the switching signal needs to be known and not the exact switching times. Since simple examples show that a minimal realization will depend on the switching times, our algorithm cannot result in a minimal realization in general, but we conjecture that it results in a minimal realization for almost all switching times. Our approach is based on considering time-dependent reachability and unobservability spaces as well as suitable extended reachability and restricted unobservability spaces together with the notion of a weak Kalman decomposition.

Data-Driven Inference on Optimal Input–Output Properties of Polynomial Systems With Focus on Nonlinearity Measures

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to determine nonlinearity measures and other optimal input-output properties for nonlinear polynomial systems without explicitly identifying a model but from a finite number of input-state measurements which are subject to noise. To this end, we deduce from data for the unidentified ground-truth system three possible set-membership representations, compare their accuracy, and prove that they are asymptotically consistent with respect to the amount of samples. Moreover, we leverage these representations to compute guaranteed upper bounds on nonlinearity measures and the corresponding optimal linear approximation model via semi-definite programming. Furthermore, we extend the established framework to determine optimal input-output properties described by time domain hard integral quadratic constraints.

Analysis of the optimization landscape of Linear Quadratic Gaussian (LQG) control

This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: (1) Connectivity of the set of stabilizing controllers $$\mathcal {C}_n$$ ; and (2) Structure of stationary points. It is known that similarity transformations do not change the input-output behavior of a dynamic controller or LQG cost. This inherent symmetry by similarity transformations makes the landscape of LQG very rich. We show that (1) The set of stabilizing controllers $$\mathcal {C}_n$$ has at most two path-connected components and they are diffeomorphic under a mapping defined by a similarity transformation; (2) There might exist many strictly suboptimal stationary points of the LQG cost function over $$\mathcal {C}_n$$ that are not controllable and not observable; (3) All controllable and observable stationary points are globally optimal and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.

On the Rational Design of Cooperative Receptors.

Cooperativity (homotropic allostery) is the primary mechanism by which evolution steepens the binding curves of biomolecular receptors to produce more responsive input-output behavior in biomolecular systems. Motivated by the ubiquity with which nature employs this effect, over the past 15 years we, together with other groups, have engineered this mechanism into several otherwise noncooperative receptors. These efforts largely aimed to improve the utility of such receptors in artificial biotechnologies, such as synthetic biology and biosensors, but they have also provided the first quantitative, experimental tests of longstanding ideas about the mechanisms underlying cooperativity. In this article, we review the literature on the design of this effect, paying particular attention to the design strategies involved, the extent to which each can be rationally applied to (and optimized for) new receptors, and what each teaches us about the origins and optimization of this important phenomenon.

Inductive Synthesis of Structurally Recursive Functional Programs from Non-recursive Expressions

We present a novel approach to synthesizing recursive functional programs from input-output examples. Synthesizing a recursive function is challenging because recursive subexpressions should be constructed while the target function has not been fully defined yet. We address this challenge by using a new technique we call block-based pruning. A block refers to a recursion- and conditional-free expression (i.e., straight-line code) that yields an output from a particular input. We first synthesize as many blocks as possible for each input-output example, and then we explore the space of recursive programs, pruning candidates that are inconsistent with the blocks. Our method is based on an efficient version space learning, thereby effectively dealing with a possibly enormous number of blocks. In addition, we present a method that uses sampled input-output behaviors of library functions to enable a goal-directed search for a recursive program using the library. We have implemented our approach in a system called Trio and evaluated it on synthesis tasks from prior work and on new tasks. Our experiments show that Trio outperforms prior work by synthesizing a solution to 98% of the benchmarks in our benchmark suite.

Minimal Realizations of Input–Output Behaviors by LPV State-Space Representations With Affine Dependence

The paper makes the first steps towards a behavioral theory of LPV state-space representations with only affine dependence on the scheduling signal, by characterizing minimality of such state-space representations. We show that minimality is equivalent to observability, and that minimal realizations of the same behavior are isomorphic. Finally, we establish a formal relationship between minimality of LPV state-space representations with an affine dependence on the scheduling signal and minimality of LPV state-space representations with a dynamic and meromorphic dependence on the scheduling signal.

Tube-Based Control Barrier Function With Integral Quadratic Constraints for Unknown Input Delay

This paper proposes a Control Barrier Function (CBF)-based controller design to achieve safety for systems subjecting to unknown input delay and additive disturbance. Integral quadratic constraints characterizing the input-output behavior of the unmodeled dynamics caused by the unknown input delay are used to generate a bound of the error between the nominal model and the true uncertain system. The bound is incorporated into a tube-based CBF formulation to ensure robust system safety. The proposed method guarantees that the constraints are input affine, so the safe controller can be implemented by solving a quadratic programming problem in real-time. A simple example demonstrates the effectiveness of the tube-based CBF approach.