State-dependent Switching Research Articles

Mating reconciles fitness and fecundity by switching diet preference in flies.

Protein-rich diets shorten lifespan but increase fecundity in many organisms. Animals actively adjust their feeding behavior to meet their nutritional requirements. However, the neural mechanisms underlying the dynamic regulation of protein consumption remain unclear. Here we find that both sexes of fruit flies exhibit a preference for protein food before mating to prepare for reproduction. Mated female flies display an increased appetite for yeast to benefit their offspring, albeit at the cost of stress resistance and lifespan. In contrast, males show a momentarily reduced yeast appetite after mating likely to restore their fitness. This mating state-dependent switch between sexes is mediated by a sexually dimorphic neural circuit labeled with leucokinin in the anterior brain. Furthermore, intermittent yeast consumption benefits both the lifespan and fecundity of males, while maximizing female fecundity without compromising lifespan.

Bumpless transfer control of switched systems: A dynamic event-triggering switching control approach

This paper studies the bumpless transfer (BT) control issue for switched systems with event-triggered (ET) control input. The aim is to reduce the jumps in control input at both switching and triggering points, while capturing the stability of the switched systems. First, a dynamic ET program is constructed with the triggering condition based on the level of suppression of input signal jumps. This not only reduces input jumps at triggering points, but also prevents Zeno behavior caused by triggering within the operation time interval of subsystems. Second, a sampled state-dependent switching signal is designed to ensure a dwell time for subsystems to prevent Zeno phenomenon induced by switching. Further, a switched ET controller with alleviated jumps is designed. Third, conditions are obtained to simultaneously reach both stabilization and BT of switched systems. Finally, the effectiveness of the theoretical results is demonstrated through a simulation of an engine model.

Bounded and Saturation Control-Based Fixed-Time Synchronization of Discontinuous Fuzzy Competitive Networks With State-Dependent Switching

Bounded and Saturation Control-Based Fixed-Time Synchronization of Discontinuous Fuzzy Competitive Networks With State-Dependent Switching

Non-fragile event-triggered control for switched positive linear systems using state-dependent switching method

This article is concerned with the issues of stability and L1-gain characteristic for switched positive linear systems utilizing bumpless transfer (BT) technique and event-triggered (ET) strategy. Under the state-driven switching policy, a regulatory approach that couples BT and ET is introduced to attenuate the hybrid bumps stemming from switching and triggering moments. Compared with traditional state-driven switching, the proposed hysteresis switching can delay the occurrence of switching. Based on multiple copositive Lyapunov functions, a state feedback controller with an ET mechanism is constructed for positive systems, which reduces the update frequency of the actuator, and this control strategy is extended to the case of actuator faults. It is confirmed that the proposed control scheme can assure the positivity, stability, and L1-gain performance of the system. Additionally, the Zeno phenomenon is addressed via establishing a positive lower bound for the ET interval. Ultimately, simulation examples containing a turbofan engine model are provided to demonstrate the effectiveness of the proposed approach.

Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy.

This article investigates the finite-time control problem of the switched affine systems via an event-triggered strategy. It is well known that the existence of affine terms brings great difficulties in analysis of the finite-time property of such systems. Furthermore, the design of the globally feasible event-triggered mechanism (ETM) under a finite-time control framework is challenging. Thus, a two-step hybrid control scheme is proposed in this article. The first step focuses on the event-triggered finite-time control for practical stability, while the second step aims to achieve finite-time stabilization. Particularly, in step one, by constructing the intersection between the affine term's threshold and feasible state region of the established ETM, it is verified that the Zeno behavior can be excluded. Thereafter, an affine state-dependent switching law and sufficient conditions are provided for achieving practical stability. Meanwhile, an estimation for the practical settling time to enter the bounded set is provided. In step two, the criteria for finite-time stabilization of the considered systems are further presented, and an overall settling-time upper bound is derived. Finally, a numerical example is illustrated to demonstrate the effectiveness of our proposed method.

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Bumpless transfer control for switched time-delay systems with application to aero-engine control

For switched time-delay systems, the bumpless transfer control issue is investigated by utilizing the multiple piecewise Lyapunov–Krasovskii function approach. First, a time-delay-dependent bumpless transfer concept is put forward to depict the transient performance of switched time-delay systems, which restricts the bumps in the amplitude of the present state and the time-delay state, simultaneously. Second, a state-dependent switching signal with a prescribed time is designed to avoid switching frequently. A time-varying switching controller is developed to decrease control bumps. Third, under the premise of achieving asymptotic stability, a solvability condition ensuring a satisfactory bumpless transfer performance is derived through relaxing the traditional bumpless transfer condition. Finally, an instance of the aero-engine control system is used for exhibiting the validity of the presented method.

[formula omitted] security control for 2-D switched time delay systems under arbitrary delay time-variation rate and stochastic cyber attacks

This study focuses on H∞ security control for 2-D switched time delay systems subject to stochastic cyber attacks by the Roesser model, where the delay time-variation rate can be arbitrary. First, the time-delay system is modeled as the feedback interconnection of the delay-less system. To guarantee the security of the system under stochastic cyber attacks, a state-dependent switching signal and an anti-deception attack controller are constructed. Stability conditions of 2-D delay-less feedback interconnection systems are given for the first time. Then, for the considered system, some criteria based on bilinear matrix inequalities (BMIs) are established via the Lyapunov function technology such that the mean-square asymptotic stability with H∞ performance is guaranteed under arbitrary delay time-variation rate. Moreover, a cone-complement linearization (CCL) method is proposed to compute the optimized controller gains for BMIs. The effectiveness of the proposed method is validated via two numerical simulations.

Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules

This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of 3n exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are 3n synchronization manifolds, wherein n is the number of neurons. Additionally, an estimation for the settling time required for drive–response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.

Robust Guaranteed Cost Composite Anti-bump $$L_2$$-Gain Control for a Class of Switched Systems Under Mixed State-Dependent Switching

Robust Guaranteed Cost Composite Anti-bump $$L_2$$-Gain Control for a Class of Switched Systems Under Mixed State-Dependent Switching

Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching

This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.

Stability and stabilization of discrete-time linear compartmental switched systems via Markov chains

The stabilizing switching signal design of discrete-time linear compartmental switched systems (DT-LCSSs) has been heretofore unsolved. It has been proven that a DT-LCSS is stabilizable if and only if it is stabilizable by a periodic switching signal. However, it still needs to be determined whether the period of a stabilizing switching signal can be confined within a bound. Moreover, the existing design method for stabilizing periodic switching signals requires the diagonal entries of system matrices of all subsystems to be strictly positive. In this study, we propose a novel approach to solve this problem completely. We construct a discrete-time Markov chain for a given DT-LCSS, termed the associated Markov chain, and prove the equivalence of stability and stabilizability between the DT-LCSS and the associated Markov chain. Based on this, verifiable necessary and sufficient conditions for stability and stabilizability are derived. Especially, the period of a stabilizing switching signal for an n-dimensional DT-LCSS can always be chosen within the bound n2−n+1. We propose a state-independent stabilizing switching signal design method for general stabilizable DT-LCSSs. We also prove the equivalence between stabilizability by state-independent switching laws and stabilizability by state-dependent switching laws. A state-dependent global stabilizing switching signal design method is also proposed. Additionally, the proposed results are applied to the consensus analysis of discrete-time leader–follower multi-agent systems with switching communication digraphs. The effectiveness of the theoretical results is demonstrated by examples.

Bumpless transfer control for switched positive time-delay systems with linear-type dissipative inequalities

In this paper, a family of amplitude limited controllers and a hysteresis switching paradigm, for switched positive systems with time-varying delays, are simultaneously determined to achieve strict (q,r) -α-dissipativity. The concept of strictly (q,r)-α-dissipative, induced by linear-type dissipative inequalities, is introduced. The main feature of the presented method lies in two aspects. The first one is that the magnitude of controller discontinuities, at the occurrence of switching, is here restricted. The other one is that the high switching frequency is refrained commonly the appearance of in state-dependent switching schemes. Moreover, dissipativity analysis as well as feedback dissipativity are taken into account. Novel criteria are derived for the considered systems to be dissipativity by resorting to multi-linear copositive storage functionals. Eventually, the validity and superiority of the presented control strategy are demonstrated through two illustrative examples.

How the brain can be trained to achieve an intermittent control strategy for stabilizing quiet stance by means of reinforcement learning

The stabilization of human quiet stance is achieved by a combination of the intrinsic elastic properties of ankle muscles and an active closed-loop activation of the ankle muscles, driven by the delayed feedback of the ongoing sway angle and the corresponding angular velocity in a way of a delayed proportional (P) and derivative (D) feedback controller. It has been shown that the active component of the stabilization process is likely to operate in an intermittent manner rather than as a continuous controller: the switching policy is defined in the phase-plane, which is divided in dangerous and safe regions, separated by appropriate switching boundaries. When the state enters a dangerous region, the delayed PD control is activated, and it is switched off when it enters a safe region, leaving the system to evolve freely. In comparison with continuous feedback control, the intermittent mechanism is more robust and capable to better reproduce postural sway patterns in healthy people. However, the superior performance of the intermittent control paradigm as well as its biological plausibility, suggested by experimental evidence of the intermittent activation of the ankle muscles, leaves open the quest of a feasible learning process, by which the brain can identify the appropriate state-dependent switching policy and tune accordingly the P and D parameters. In this work, it is shown how such a goal can be achieved with a reinforcement motor learning paradigm, building upon the evidence that, in general, the basal ganglia are known to play a central role in reinforcement learning for action selection and, in particular, were found to be specifically involved in postural stabilization.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov–Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Practical stabilisation of discrete-time switched nonlinear systems without a common equilibrium and using hybrid switching functions

This paper presents a new practical stabilization method for discrete-time switched nonlinear systems without a common equilibrium point among all modes. The proposed method has two main features. First, the number of nonlinear terms in the stability conditions is independent of the number of switched system modes. The result is that the computational cost is reduced, and it can be applied to switched systems with a large number of subsystems. Second, using switched Lyapunov functions, hybrid switching laws are designed to preserve the practical stability property in both the closed-loop state-dependent switching function and the open-loop time-dependent one. As a result, when the state data is lost during sensor or communication failures, the controller can change the control scheme from a closed-loop state-dependent switching function to an open-loop time-dependent one without loss of stability property. Numerical examples are presented to illustrate the validity and efficiency of the proposed method.

Design of a Switching Strategy for Output Voltage Tracking Control in a DC-DC Buck Power Converter

This work proposes the design of a commutation function to solve the output voltage trajectory tracking problem in the DC-DC Buck power electronic converter. Through a Lyapunov-type analysis, sufficient conditions are established, taking into account the discontinuous model, to ensure asymptotic convergence to the desired trajectories. Based on this analysis, a state-dependent switching function was designed to guarantee the closed-loop stability of the tracking error. To validate the control performance, circuit numerical simulations were carried out under abrupt disturbances in the source and load of the converter. The results demonstrate that the voltage tracking at the output of the converter is satisfactorily achieved.

Finite-time H∞ rate anti-bump control for a class of switched systems under state-dependent switching

This paper mainly investigates the finite-time rate anti-bump switching (RABS) control problem for switched systems. A novel multiple convex Lyapunov function is first proposed by constructing a convex combination of positive definite matrices for the RABS control problem of switched systems. By imposing a prespecified dwell time on state-dependent switching, a combined switching law is devised based on the new Lyapunov function to ensure that Zeno phenomenon is prevented. Then, a bumpless control scheme is proposed to reduce the big and undesired jump in the rate of system at switching instants while achieving the disturbance suppression in finite time. In the end, through an ingenious Simulink model to characterize the combined switching law and finite-time H∞ rate anti-bump controller, an actual engine model is used to demonstrate the validity of the proposed approach.

Stability analysis for stochastic nonlinear systems with state-dependent switching and time-delay

The stability of stochastic nonlinear systems with time-delay and state-dependent switching is studied in this paper. Firstly, system maximal solution is constructed and further extended as the global solution under certain mild conditions. Secondly, several Krasovskii-type stability and Razumikhin-type theorems are proposed by uniformly asymptotically stable functions (UASFs). These stability criteria overcome some stringent constraints associated with Lyapunov functional/functions. Finally, the theoretical findings are validated through two simulation examples.

Event-Triggered State-Dependent Switching for Adaptive Fuzzy Control of Switched Nonlinear Systems

Event-Triggered State-Dependent Switching for Adaptive Fuzzy Control of Switched Nonlinear Systems