Hybrid System Framework Research Articles

Closed-Form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems

This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">status updates</i> to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">freshness</i> of status updates when they reach the destination using the concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Age of Information (AoI)</i> . Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distributional properties</i> of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.

Age of Information in Multi-source Updating Systems Powered by Energy Harvesting

This paper considers a multi-source updating system in which a transmitter node powered by energy harvesting (EH) sends status updates about multiple sources of information to a destination, where the freshness of status updates is measured in terms of Age of Information (AoI). The status updates of each source and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. Further, the transmitter can harvest energy only when its server is idle. Unlike most of the existing queueing-theoretic analyses of AoI that focus on characterizing its average when the transmitter has a reliable energy source and is hence not powered by EH (referred henceforth as a non-EH transmitter), our analysis is focused on understanding the distributional properties of AoI in multi-source systems through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the average/MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and source-agnostic/source-aware preemptive in service strategies. The generality of our results is demonstrated by recovering several existing results as special cases.

Input-to-state Stability for Hybrid Kalman Filters

In this article, we propose a Lyapunov-based characterization of exponential input-to-state stability (ISS) for hybrid systems. We propose a new formulation of the continuous-discrete Kalman filter algorithm Särkkä (2006) using the hybrid systems framework Goebel et al. (2012) where we consider continuous-time system dynamics and discrete-time observations. We prove exponential input-to-state stability on the estimation error of the hybrid Kalman filter under mild assumptions on the system's model.

A novel reset control approach to leader-following consensus of second-order nonlinear multi-agent systems

This paper investigates the leader-following consensus problem of second-order nonlinear multi-agent systems with directed graph. A novel reset control approach is proposed for the aim of improving transient consensus performance, e.g., settling time. By introducing consensus error into reset conditions, the output of reset integrator will keep the same sign with the consensus error, thus, the desired states can be compensated preferentially and the system transient performance is improved accordingly. To appropriately describe the closed-loop system with reset-induced jump dynamics, a hybrid system model consisting of both flow dynamics and jump dynamics is constructed. Based on this model, and combined with backstepping method, Lyapunov-based consensus analysis is presented under hybrid system framework. Finally, a numerical example is provided to show the effectiveness of the obtained results.

Investigation of Optimal Hybrid Energy Systems Using Available Energy Sources in a Rural Area of Bangladesh

The aims of this paper are to develop hybrid energy systems considering biomass energy sources as well as a framework and optimal configuration of hybrid systems of energy for a southern sub-urban area of Bhola district in Bangladesh, named Kukri Mukri island, and analyse the feasibility of the techno-economic prospects of these systems. In this work, electrification for the rural area is analysed for different configurations of the hybrid systems. The estimation of available resources with optimal sizing and analysis of techno-economic aspects is done through HOMER Pro software to satisfy the demand of peak load. Different configurations of hybrid energy systems, including PV/diesel, PV/wind, PV/diesel/wind, PV/wind/diesel/biomass, and wind/diesel, are analysed and compared through optimization of different energy sources in HOMER. The size of the system and components are optimized and designed depending on the net present cost (NPC) and the levelized cost of energy (LCOE). Due to the lower availability and rising cost of wind energy, the outcome of this work shows a solar-based photovoltaic (PV) as the main energy source, battery as the storage media, and diesel generator as an energy source for backup. The results indicate that LCOE is much lower for PV/wind/diesel/biomass (0.142 USD/kWh) than PV/diesel (0.199 USD/kWh), PV/wind (0.239 USD/kWh), PV/diesel/wind (0.167 USD/kWh), PV/diesel (0.343 USD/kWh), and wind/diesel (0.175 USD/kWh). Additionally, it is demonstrated from the research that the genetic algorithm (GA) process gives sustainable and cost-effective outcomes compared to HOMER.

A reliable and cost-effective planning framework of rural area hybrid system considering intelligent weather forecasting

The use of hybrid systems for electrification of remote areas has been increased dramatically in recent years, and the optimal sizing of these systems is a significant challenge for cost-effectiveness and reliability. This paper aims to propose a predictable planning framework that increases the renewable energy penetration (REP) rate and minimizes the annualized cost of the system (ACS) considering CO2 emission and different loss of power supply probability (LPSP). Due to the unavailability of precise weather data in remote areas, an intelligent weather forecasting scheme is developed using an adaptive neuro-fuzzy process based on fuzzy c-means clustering technique to estimate the solar radiation, wind speed, and ambient temperature. This paper also examines various evolutionary algorithms and compare the collected result of the proposed Multi-Verse Optimizer (MVO) with other meta-heuristic methods in terms of total annualized cost with different LPSP, and REP amounts. Moreover, to assess the impact of wind speed, solar irradiation, the lifespan of battery energy storage systems, and the fuel price of diesel engine generators on optimal sizing problem, a sensitivity analysis is performed for different values of REP and LPSP. The effectiveness of the proposed approach is verified using a realistic case study in the Sistan & Balouchestan province of Iran. Simulation results illustrate that using photovoltaic panels, wind turbine generators, battery energy storage systems, and diesel engine generators (PV/WTG/BESS/DEG) is the most cost-effective strategy resulting in a 96.13% decrease of CO2 emission compared to DEG system at REPmin=97% and LPSPmax=1%. Moreover, the growth of fuel cost causes an increase in the production of renewable energy resources (RESs) and a decrease in the usage of diesel engine generators. Consequently, for LPSPmax=10% and REPmin=91%, and 50% rise in the price of fuel, the number of DEG drops to zero, and the optimal number of PV and BESS increase from 311 and 172 to 411 and 228, respectively.

Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems

Abstract This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple one-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online.

Cooperative Output Regulation With Asynchronous Transmissions and Time-Varying Delays

This article revisits the sampled-data cooperative output regulation problem in a hybrid system framework. Due to the inevitable network-induced imperfections caused by communication among agents, we consider the problem under asynchronous transmissions and time-varying delays. A hybrid system model is introduced to incorporate the aforementioned communication imperfections and facilitate the analysis on internal stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_2$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_\infty$</tex-math></inline-formula> ) performance of closed-loop systems. A novel Lyapunov functional candidate is proposed to establish the stability condition in terms of maximally allowable transmission intervals (MATIs) and maximally allowable delays (MADs). Compared with some existing results, the proposed Lyapunov functional candidate provides clearer physical significance. As a result, more straightforward computations and tradeoff designs on MATIs and MADs can be provided. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the obtained results.

Event-triggered controller design for linear systems with saturated input and bounded disturbance

This paper deals with the stabilisation problem of linear systems subject to saturated input and bounded disturbance via event-triggered control strategy. In a hybrid systems framework, both a state feedback law and a static output feedback law are proposed to design the event-triggered controllers, which provide solutions to the event-triggered control collaborative design problem. For the case of using static output feedback, an iterative linear matrix inequality algorithm is proposed to obtain the feedback gain. In addition, the local uniform ultimate boundedness of the closed-loop system is ensured. Finally, two examples are given to illustrate the effectiveness of the proposed controllers.

Quantized Dynamic Output Feedback Control and $L_2$-Gain Analysis for Networked Control Systems: A Hybrid Approach

In this article, the problems of stabilization and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain performance analysis for continuous-time networked control systems (NCSs) with quantization effects are addressed. The plant output and control input are quantized respectively by two different dynamic quantizers before being transmitted over networks. In order to deal with the dynamic behavior resulting from the dynamic quantizers, a hybrid system framework is adopted to remodel the NCSs. The hybrid model is flexible to the joint design of dynamic output feedback controller, nonequidistant samplers and dynamic quantizers. Furthermore, our method can effectively prevent the Zeno phenomenon on the instants of sampling and the updates of quantizer variables. By constructing a novel Lyapunov function, new sufficient conditions guaranteeing the uniformly globally asymptotic stability (UGAS) and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain performance are presented in terms of matrix inequalities, respectively. Finally, two numerical examples illustrate the effectiveness of our proposed method.

A Hybrid Dynamic Event-Triggered Approach to Consensus of Multiagent Systems With External Disturbances

This article addresses the event-triggered consensus problem of multiagent systems (MAS) with disturbances. Model-based control protocols are designed, and a hybrid dynamic event-triggering mechanism (HDETM) is proposed. Based on the proposed event-triggered control protocol, continuous communication between neighboring agents is not needed, and a prespecified strictly positive minimum ETI is guaranteed, i.e., Zeno behavior is excluded. A timer variable with jump dynamics is introduced to describe the HDETM in the closed-loop system. Then, a novel hybrid model is constructed for the closed-loop MAS, which contains both flow dynamics, and jump dynamics. Lyapunov-based stability analysis and HDETM design are presented based on hybrid systems framework, and matrix inequality conditions are given to verify the consensus and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Finally, a spacecraft formation example is provided to show the effectiveness of the proposed methods.

Modelling drugs interaction in treatment-experienced patients on antiretroviral therapy

Understanding pharmacology and drug resistance patterns plus appropriate use of laboratory testing is vital for managing treatment-experienced patients with new agents. While we acknowledge that patients with extensive drug resistance now have multiple options for suppressive therapy, and expert care is essential to avoid the rapid emergence of resistance to these new agents, clinicians are unaware of the inherent (hidden) patterns created by combined drug regimens that could trigger adverse drug reactions. This paper proposes a novel hybrid system framework that combines soft computing techniques, for drugs interaction modelling and precise patient response optimisation. A Fuzzy Logic system was developed to address the uncertainty in treatment change episodes (TCEs). A weighted least-squares cost function was then employed to auto-tune hyperparameters for training the neural network. After acceptable tuning, the final hyperparameters served the neural network—to efficiently learn the ensuing patterns for precice drug interaction classification. The proposed framework was experimented with clinical data of TCEs from two disparate sources: a publicly available HIV database (the Stanford HIV database: https://hivdb.stanford.edu ), and clinical data collected from 13 health centers managing HIV cases in Akwa Ibom State of Nigeria (the Akwa-Ibom HIV database). In both databases, a correlation of prognostic markers suggests strong association between first line CD4 and follow-up CD4 counts; while a moderately weak association was observed for first line and follow-up viral loads. Correlation of physiological feature gave very strong association between first line and follow-up body mass index in Akwa-Ibom database. Analysis of the patients progress explains the decreased potency of CD4 count and body mass index as HIV predictors. The root mean square error (RMSE) and classification accuracy were used as performance metrics for measuring the precision of our hybrid framework. Results obtained showed improved RMSE and classification accuracy for both databases, when compared with existing works.

A Decision-Making Framework of Hybrid System Based on Modified Hybrid Stochastic Timed Petri Net and Deep Learning

For designing the decision model of hybrid systems, there are sophisticated quantitative and qualitative attributes such as discrete events, continuous processes, stochasticity, and time delay. Meanwhile, the inherent heterogeneity and concurrency existing in hybrid systems trigger multiple decision challenges, including behavior uncertainty and states consistency. It is difficult to express the complicated nonlinear mapping relationship between decision results and hybrid situations. This proposes the decision-making scheme M-HSTPN-DL with a three-tier architecture based on modified hybrid stochastic timed Petri net (M-HSTPN) and deep learning (DL). Among them, M-HSTPN describes the various hybrid situations, and DL models are taken as the decision model to express the nonlinear relationship between decision results and hybrid situations. Then the training and calling mechanism of decision models is introduced. Taking the hybrid system of bearing fault diagnosis as an example, we compare the decision-making ability of multiple decision models and analyze the advantage of M-HSTPN-DL. It has proven to be that the M-HSTPN-DL architecture can adequately represent the hybrid situation and solves the complex decision- making problem of hybrid systems.

Explicit Construction of Stabilizing Robust Avoidance Controllers for Linear Systems With Drift

We propose a constructive design method for linear systems with a nontrivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, is investigated via numerical examples.

Model-Based Dynamic Event-Triggered Control for Systems With Uncertainty: A Hybrid System Approach

In this article, the event-triggered control problem for linear systems with uncertainties is addressed. A model-based dynamic event-triggered transmission strategy is proposed for linear systems, and for systems that can be decomposed into interconnected subsystems, a distributed model-based dynamic event-triggered transmission strategy is also proposed with transmission delays and transmission protocols in the networks. The whole systems are modeled into a hybrid system framework by introducing storage variables. Using stability theorems of hybrid systems, explicit designs of the transmission strategies are presented and asymptotic stability is guaranteed. Finally, an example is given to show that the transmissions are significantly reduced by the transmission strategy in this article compared with the transmission strategy by zero-order-hold.

A Hybrid Event-Triggered Approach to Consensus of Multiagent Systems With Disturbances

This article investigates the event-triggered consensus problem for multiagent systems (MAS) with external disturbances. A hybrid event-triggering mechanism (ETM) is proposed, which utilizes time regularization to force the minimum interevent time to be strictly positive, such that Zeno freeness is ensured in the presence of disturbances. Model-based control protocol is used to avoid continuous communication between neighboring agents. With the proposed hybrid ETM, the closed-loop MAS contains both flow dynamics and jumping dynamics, which cannot be described by the existing MAS models. By means of hybrid system framework and auxiliary variables, a hybrid model of the MAS is constructed to describe the flow dynamics and jumping dynamics. Based on this model, the Lypuanov-based consensus analysis and hybrid ETM design are developed, and the finite-gain L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stability property is guaranteed. An example of spacecraft formation is provided to show the effectiveness of the proposed approach.

Reset PID Design for Motion Systems With Stribeck Friction

We present a reset control approach to achieve setpoint regulation of a motion system with a proportional-integral-derivative (PID)-based controller, subject to Coulomb friction and a velocity-weakening (Stribeck) contribution. While classical PID control results in persistent oscillations (hunting), the proposed reset mechanism induces asymptotic stability of the setpoint and significant overshoot reduction. Moreover, robustness to an unknown static friction level and an unknown Stribeck contribution is guaranteed. The closed-loop dynamics are formulated in a hybrid systems framework, using a novel hybrid description of the static friction element, and the asymptotic stability of the setpoint is proven accordingly. The working principle of the controller is demonstrated experimentally on a motion stage of an electron microscope, showing superior performance over classical PID control.

Hybrid modelling and predictive control of utility-scale variable-speed variable-pitch wind turbines

Wind energy has proven to be the highest reliable source of renewables due to the maturity of the technology. Wind turbine (WT) systems are complex systems with undergoing development process that requires innovative methods of design and control. In this paper, WTs are studied through hybrid systems framework. Hybrid models of WT are extracted with representable dynamics from nonlinear complex design code. The WT model is formulated into a mixed-logical dynamical model (MLD) and a piecewise affine (PWA) model. Then, a receding horizon control strategy is applied to WT hybrid model resulting in a hybrid model predictive control (HMPC) with mixed-integer programming (MIP) problem. The performance of the proposed controller is compared against the baseline controller within a simulation environment for the National Renewable Energy Laboratory (NREL) 5MW benchmark WT as a case study. The analysis and investigation of HMPC highlight its capability as a potential tool for exploiting the control objectives of WT systems.

Lyapunov-based Singular Perturbation Results in the Framework of Hybrid Systems

Abstract Stability properties of singularly perturbed hybrid systems are investigated via Lyapunov functions with assistance from the invariance principle. Both continuously differentiable Lyapunov functions and non-smooth Lyapunov functions are considered. In each case, under appropriate assumptions, uniform asymptotic stability and uniform global asymptotic stability are established. An estimate of the basin of attraction is given for the former property. Two examples are given to illustrate the proposed theoretical results based on continuously differentiable Lyapunov functions. In addition, one example for switched learning inclusions with unstable modes is given to show the effectiveness of the results obtained based on non-smooth Lyapunov functions.

An Adaptive Hybrid Control Algorithm for Sender-Receiver Clock Synchronization

Abstract This paper presents an innovative hybrid systems approach to the sender-receiver synchronization of timers. Via the hybrid systems framework, we unite the traditional sender-receiver algorithm for clock synchronization with an online, adaptive strategy to achieve synchronization of the clock rates to exponentially synchronize a pair of clocks connected over a network. Following the conventions of the algorithm, clock measurements of the nodes are given at periodic time instants, and each node uses these measurements to achieve synchronization. For this purpose, we introduce a hybrid system model of a network with continuous and impulsive dynamics that captures the sender-receiver algorithm as a state-feedback controller to synchronize the network clocks. Moreover, we provide sufficient design conditions that ensure attractivity of the synchronization set.