State Jumps Research Articles

Practical exponential stability and applications of switched homogeneous nonlinear systems with external inputs and impulses

The practical exponential stability of switched homogeneous nonlinear systems (SHNS) with external inputs and impulses is studied in this paper, which includes two types of continuous-time systems and discrete-time systems. Specifically, we add a kind of nonnegative impulses which is consistent with the switching behaviours for the systems. We first study switched homogeneous positive nonlinear systems (SHPNS) case, then we extend the SHPNS to a time-varying SHNS case. The primary difficulty of this research is the estimation of Lyapunov function value at switching-impulse points under the coupling effects of synchronous switches and state jumps. By employing the max-separable Lyapunov function approach, we present new sufficient stability criteria and design new switching-impulse signals, and successfully establish the new relation between the average dwell time parameter and impulse strength. Then, we apply the obtained results to the time-varying vehicle formation model with impulses. At last, four examples are given to demonstrate the feasibility of our results, which includes the specific algorithm verification process.

A Hybrid Controller Enhancing Transient Performance for an Aerial Manipulator Extracting a Wedged Object

Autonomous aerial manipulation requires the capability to handle inevitable dynamic changes during physical interaction. Previously, very few studies have addressed the stability and transient performance of the scenarios involving abrupt changes in dynamics. This paper proposes a hybrid controller enhancing transient performance for an aerial manipulator extracting an object wedged in a static structure. This task incurs a significant jump in the interaction force on the end-effector so that the analysis using the concept of hybrid dynamical systems is required. To demonstrate the dynamic characteristics of the object-extracting aerial manipulator, we derive the dynamic equations for two flight modes, i.e., free-flight and object-extracting, and the rule of state jumps. Also, we design control strategies which enhance the transient performance during flight mode transition. Then, the stability of the proposed control law is proven, and the overshoot reduction after the object extraction is analyzed. To show the improved performance, we conduct plug-pulling experiments with a quadrotor-based aerial manipulator using the proposed controller and two different existing controllers. The comparative results confirm that our controller enables the aerial manipulator to maintain its stability after the flight mode transition and shows the best transient performance in overshoot minimization among three controllers. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation for this article is the desire to prevent unexpected collisions between obstacles and an aerial manipulator after the vehicle extracts a wedged object from a static structure. To resolve this problem, we present a hybrid control method for such tasks while avoiding an excessive overshoot after the extraction. This method can be utilized in tasks involving abrupt changes in the dynamic model such as retrieving a device attached to a tall structure, reclaiming an object in disaster recovery, or pulling a plug out of a socket. Unlike existing methods, the proposed method simultaneously considers the stability <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> the initial overshoot right after pulling the object out of the structure, by employing a disturbance observer (DOB) in a hybrid control structure. It can be utilized for the aerial manipulator to avoid collision in a narrow space or to keep it in a safe operation envelope even though the task requires producing a relatively large pulling force.

FESD-J: Finite Elements with Switch Detection for numerical optimal control of rigid bodies with impacts and Coulomb friction

The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method (Nurkanović et al., 2022) to the dynamic equations of multiple rigid bodies that exhibit state jumps due to impacts and Coulomb friction. This new method is referred to as FESD with Jumps (FESD-J). Starting from the standard Runge–Kutta equations, we let the integration step sizes be degrees of freedom. Additional constraints are introduced to ensure exact switch detection and to remove spurious degrees of freedom if no switches occur. Moreover, at the boundaries of each integration interval (finite element), we impose the impact equations in their complementarity form, at both the position and velocity level. They compute the normal and tangential impulses in case of contact making. Otherwise, they are reduced to the continuity conditions for the velocities. FESD-J treats multiple contacts, where each contact can have a different coefficient of restitution and friction. All methods introduced in this paper are implemented in the open-source software package NOSNOC (Nurkanović and Diehl, 2022). We illustrate the use of FESD-J in both simulation and optimal control examples.

Averaging for switched impulsive systems with pulse width modulation

Linear switched impulsive systems (SIS) are characterized by ordinary differential equations as modes dynamics and state jumps at the switching time instants. The presence of possible jumps in the state makes nontrivial the application of classical averaging techniques. In this paper we consider SIS with pulse width modulation (PWM) and we propose an averaged model whose solution approximates the moving average of the SIS solution with an error which decreases with the multiple of the switching period and by decreasing the PWM period. The averaging result requires milder assumptions on the system matrices with respect to those needed by the previous averaging techniques for SIS. The interest of the proposed model is strengthened by the fact that it reduces to the classical averaged model for PWM systems when there are no jumps in the state. The theoretical results are verified through simulations obtained by considering a switched capacitor electrical circuit.

Senior official speeches and severe price discontinuities in the foreign exchange market

Purpose This study aims to better understand the effects of speeches as a valuable communication tool for central banks. It extends the analysis of the effects of public speeches on jumps to determine whether individual speakers matter partly because of their name, position or institution. Design/methodology/approach This study detects intraday jumps using a robust-to-jump volatility estimator that accounts for deterministic seasonality. As a result, this study removes spurious jumps that occur when volatility is high and consider the relatively small jumps that occur when volatility is low. After identifying jumps, this study examines their reactions to senior official speeches and macroeconomic news surrounding the US and European Union (EU) financial crises. Findings Despite having the most influential individual speakers, this study finds that the impact of the Federal Reserve (Fed) and European Central Bank (ECB) is mitigated because the two institutions have a relatively small impact on currency jumps. This finding shows that the speaker’s name is more important than his or her institution affiliation. While the Federal Reserve Bank President and Chief Executive, as well as ECB board members, significantly reduce jump sizes, particularly during the EU crisis period, both the Fed Chairman and the ECB President increase the magnitude of the jump in both the US crisis and noncrisis periods, contributing to market instability. Practical implications The implications of the results include international portfolio management, currency derivatives pricing and hedging, risk management and market efficiency. Originality/value The findings contribute to a better understanding of the effects of senior official speech attributes on currency jumps in various economic states. The results raise questions about the speaker’s name, institution and position’s effectiveness in calming markets and reducing uncertainty.

The time-freezing reformulation for numerical optimal control of complementarity Lagrangian systems with state jumps

This paper introduces a novel time-freezing reformulation and numerical methods for optimal control of complementarity Lagrangian systems (CLS) with state jumps. We cover the difficult case when the system evolves on the boundary of the dynamic’s feasible set after the state jump. In nonsmooth mechanics, this corresponds to inelastic impacts. The main idea of the time-freezing reformulation is to introduce a clock state and an auxiliary dynamical system whose trajectory endpoints satisfy the state jump law. When the auxiliary system is active, the clock state is not evolving, hence by taking only the parts of the trajectory when the clock state was active, we can recover the original solution. The resulting time-freezing system is a Filippov system that has jump discontinuities only in the first time derivative instead of the trajectory itself. This enables one to use the recently proposed Finite Elements with Switch Detection (Nurkanović et al., 2022), which makes high accuracy numerical optimal control of CLS with impacts and friction possible. We detail how to recover the solution of the original system and show how to select appropriate auxiliary dynamics. The theoretical findings are illustrated on a nontrivial numerical optimal control example of a hopping one-legged robot.

Quantized H∞$$ {H}_{\infty } $$ output feedback control for uncertain impulsive switched systems via a hybrid control approach

SummaryThis article investigates the quantized dynamical output feedback (DOF) control problem for uncertain impulsive switched systems (ISSs) with multiple state impulsive jumps, where the static quantization strategy is applied to quantize the control input to improve the signal transmission capacity of ISSs. First, to correspond the abrupt changes for states of ISSs at switching moments, the controller states are also allowed to jump besides the system state jumps of ISSs, which increases the universality of the impulsive behavior in ISSs. Second, the multiple Lyapunov functions approach and the average dwell time switching strategy are applied to derive the sufficient conditions that guarantee the stability and weighted performance of the closed‐loop uncertain ISSs. The desired hybrid controllers comprising of DOF controllers for every subsystem and controller state update rules at switching instants can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example is provided to verify the effectiveness of the obtained results.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes.

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

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.

Auto–Transition in RADG based on chaotic System

The RADG (Reaction Automata Direct Graph) cryptosystem is the automata direct graph and reaction states combination. The classical RADG does not require key exchange (keyless), or agreement between users just the design of RADG, which is static. The RADG algorithm with keys has two agreements between users, one is on the keys, and other is a design of RADG. The RADG design depends on states and transitions between them, since transitions between states are static transitions, or dynamic transitions have agreement between users to determine the type of state (Jump state, Reaction state) of RADG algorithm with keys, and the transition between states must cover each states scenario of RADG design .This article presents algorithm called (Auto- Transition Function (ATF)), which merge properties of RADG algorithm with chaotic system to obtain on transitions between states are automatic. The parameters of ATF are chaotic initial value, parameter of chaotic function, and characteristics of RADG, then ATF is an auto creation of transitions among all states in RADG, and it satisfies each scenario of RADG design.

A Gaian habitable zone

ABSTRACTWhen searching for inhabited exoplanets, understanding the boundaries of the habitable zone around the parent star is the key. If life can strongly influence its global environment, then we would expect the boundaries of the habitable zone to be influenced by the presence of life. Here, using a simple abstract model of ‘tangled-ecology’ where life can influence a global parameter, labelled as temperature, we investigate the boundaries of the habitable zone of our model system. As with other models of life-climate interactions, the species act to regulate the temperature. However, the system can also experience ‘punctuations’, where the system’s state jumps between different equilibria. Despite this, an ensemble of systems still tends to sustain or even improve conditions for life on average, a feature we call Entropic Gaia. The mechanism behind this is sequential selection with memory which is discussed in detail. With this modelling framework we investigate questions about how Gaia can affect and ultimately extend the habitable zone to what we call the Gaian habitable zone. This generates concrete predictions for the size of the habitable zone around stars, suggests directions for future work on the simulation of exoplanets and provides insight into the Gaian bottleneck hypothesis and the habitability/inhabitance paradox.

Robust stability and fuzzy controller synthesis for a class of hybrid re-entrant manufacturing systems

This paper addresses the problem of stability analysis and state feedback fuzzy control design for multi-line re-entrant manufacturing systems (RMSs) with impulse-type state jumps. Under the impulse effect, the RMS is modeled as a hyperbolic impulsive partial differential equation (IPDE) that possesses hybrid characteristics. Then, a matrix inequality condition depending on the discrete dynamic information is presented to deal with the jump behavior of the IPDE at impulse instants. Moreover, a robust fuzzy controller based on the parallel distributed compensation scheme is derived to render the RMS to a desired producing mode with steady feeding and output rates. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed robust fuzzy controller.

Finite-Time Stability of Switched Nonlinear Systems With State Jumps: A Dwell-Time Method

This article investigates the finite-time stability (FTS) of switched nonlinear systems (SNSs) with state jumps. Our main concerns are twofold. One is that the SNS only consists of FTS subsystems. The other is that the SNS has both FTS subsystems and exponentially stable (ES) subsystems. Due to the switches and state jumps, the main challenge of the study comes from the estimation of settling time and the synthesis of different Lyapunov functions for FTS/ES subsystems. Based on the analytical-inductive method and the initial-value-dependent dwell-time approach, several FTS criteria for the SNSs are established. Then, we provide the estimation of settling time which is explicitly dependent on the dwell time and initial value. Our results can be applied to the finite-time control problem of switched systems with/without state jumps, even when some subsystems can only be exponentially stabilized through linear feedback control and others are finite-time stabilized by discontinuous/nonlinear controls. Finally, three examples are given to illustrate the proposed results. The finite-time stabilization of a continuous stirred tank reactor and the finite-time consensus of a multiagent system are both adopted as potential applications.

Event-triggered control for switched singular systems with asynchronous switching and state jumps

This work discusses the event-triggered control (ETC) issue for switched singular systems (SSS) with asynchronous switching and state jumps. Firstly, a modified consistency projector is presented to describe the transient state jumps at switching moments, which shows that the state jumps are caused by switching law and algebraic constraint. Then, a discontinuous multiple Lyapunov function is presented under the event-triggered state feedback control, and several sufficient conditions are derived to ensure that the closed-loop systems are regular, impluse-free and globally uniformly exponentially stable (GUES). Then, a Luenberger-like observer is constructed to estimate continuous and jumping states, some new sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained by using matrix decoupling techniques under the observer-based ETC. Furthermore, a lower bound for the event-triggered time interval to exclude the Zeno phenomenon is given. Finally, two examples and an application are presented to demonstrate the validity of the results.

Global exponential stability of impulsive switched positive nonlinear systems with mode-dependent impulses

The global exponential stability for a type of continuous-time impulsive switched positive nonlinear systems (ISPNSs) with average dwell time (ADT) switching and mode-dependent impulsive effects is explored in this research. Where we consider a type of nonnegative impulses, which do not need to be in step with the switching behaviors in the constructed systems. The main challenge of this study comes from the estimation of Lyapunov functions within any time interval under the coupling effect of asynchronous switches and state jumps. To solve this difficulty, based on the multiple max-separable Lyapunov functions (MSLFs) method involving mode-dependent average impulsive interval (MDAII) approach, we consider two special cases in which switching and impulses are completely asynchronous and synchronous respectively, and successfully establish the relation of impulse strength, system modes, ADT and MDAII. Subsequently, several stability criteria are presented for ISPNSs with unstable and/or stable modes. In particular, the impact of various sorts of impulses on stability are also analysed in depth. Then, the obtained results are applied to the ISPNSs with synchronous impulses and switching. Moreover, the stability conditions of the considered systems without switches are gained directly, which enshrouds the existing results.

Output Regulation State Bumpless Transfer Control for Switched Descriptor Systems

This brief is concerned with the state bumpless transfer control problem for switched descriptor systems with output regulation performance. Firstly, in order to alleviate state jumps at the switching instants while ensuring the solvability of the output regulation problem, a definition of the output regulation state bumpless transfer performance of switched descriptor systems is proposed for the first time. Then, sufficient conditions are put forward to ensure the output regulation performance and state bumpless transfer performance for the closed-loop switched descriptor systems based on the co-design scheme of switching rule and controller. Meanwhile, the co-design scheme gets rid of the requirement that each subsystem satisfies output regulation performance. In the end, a simulation example certifies that the given control technique is effective.

ANS-based compression and encryption with 128-bit security

The bulk of Internet interactions is highly redundant and also security sensitive. To reduce communication bandwidth and provide a desired level of security, a data stream is first compressed to squeeze out redundant bits and then encrypted using authenticated encryption. This generic solution is very flexible and works well for any pair of (compression, encryption) algorithms. Its downside, however, is the fact that the two algorithms are designed independently. One would expect that designing a single algorithm that compresses and encrypts (called compcrypt) should produce benefits in terms of efficiency and security. The work investigates how to design a compcrypt algorithm using the ANS entropy coding. First, we examine basic properties of ANS and show that a plain ANS with a hidden encoding table can be broken by statistical attacks. Next, we study ANS behavior when its states are chosen at random. Our compcrypt algorithm is built using ANS with randomized state jumps and a sponge MonkeyDuplex encryption. Its security and efficiency are discussed. The design provides 128-bit security for both confidentiality and integrity/authentication. Our implementation experiments show that our compcrypt algorithm processes symbols with a rate up to 269 MB/s (with a slight loss of compression rate) 178 MB/s.

An Elastic Resource Allocation Algorithm Based on Dispersion Degree for Hybrid Requests in Satellite Optical Networks

The satellite-assisted Internet of Things (IoT) communication is considered a key component of the 6G network, and low Earth orbit (LEO) satellite is the leading choice of IoT-related satellites due to its minimum delay. Hybrid requests, including immediate reservation (IR) and advanced reservation (AR) services in LEO satellite netoworks cause the occurrence of resource fragments (RFrags), which adversely affect the network performance. To alleviate the degradation of network performance caused by resource fragmentation, a routing, wavelength, and time-slots assignment algorithm, which is named elastic resource allocation algorithm based on the dispersion degree (ERA-DD), is proposed in this article. Possible resource fragmentation types are analyzed and a fragmentation description named dispersion degree (DD) is designed. In the DD, the number of free resource blocks is accurately described by the state jumps (SJs) of adjacent resource slots, and the numerical relationship between SJs and free resource blocks is proposed and proved. Besides, restrictions on the selection priority of candidate schemes in the ERA-DD algorithm are analyzed. Finally, the traffic blocking rate, the wavelength utilization, the average communication delay, and the average initial delay are evaluated by simulation. The results demonstrate that RFrags are more fully utilized compared with the maximum total link spectrum consecutiveness (MTLSC) algorithm. The traffic blocking rate can be reduced by 32.5% and wavelength utilization can be increased by 1.6%.

Almost surely exponential stability of semi‐Markovian switched singular stochastic systems with mode‐dependent ranks

This paper investigated the almost surely exponential stability (ES a.s.) for semi‐Markovian switched singular stochastic systems (SSSSs) with mode‐dependent ranks, in which the derivative matrices Ei have different ranks. Due to the constraint of consistent initial conditions, state jumps may occur at switching instants in switched singular systems. Some more general conditions for the existence and uniqueness of the solution of semi‐Markovian SSSSs with mode‐dependent ranks are given together with a detailed analysis of state jumps. Based on the equivalent systems transformation and multiple Lyapunov functions method, novel conditions of ES a.s. are presented for addressed systems. An example is given to explain the effectiveness of developed results.

Multiple event‐triggered schemes for a class of switched descriptor systems with asynchronous switching

AbstractThis article studies asynchronous switching for a class of switched descriptor systems (SDSs) under multiple event‐triggered schemes (ETSs). First, by using a mode‐dependent coordinates transformation, a SDS is equivalently transformed into a reduced‐order ordinary switched linear system with state jumps. Then, multiple ETSs are used to transmit the state and switching signal information. The asynchronism between system modes and controller modes inevitably happens in a switching interval. Next, by constructing a controller‐mode‐dependent Lyapunov functional and using the asynchronous switching strategy, an exponential stability criterion is presented for the closed‐loop system with average dwell time switching signals. Meanwhile, the state feedback controller and multiple ETSs are codesigned. Besides, the Zeno behavior is avoided. In the end, the validity of the proposed method is demonstrated by a numerical example.