Switching Rule Research Articles

Synthesis and L2‐gain analysis for switched systems under event‐triggered switching

AbstractIn this paper, we solve the stabilization problem of linear switched systems subject to external disturbances via an event‐based state‐dependent switching strategy. The proposed event‐triggered switching rule can relax the conditions which guarantee the stability of switched systems so as to attain more feasible solutions than the previous work. As a result, a better bound of L2 gain performance of the system is obtained over the set of admissible disturbances. The elimination of Zeno behavior for state‐dependent switched system is also proven. Finally, numerical simulations illustrate the validity of the proposed theoretical results.

Robust adaptive control for a class of nonlinear switched systems using state-dependent switching

This paper presents a novel adaptive control for a class of nonlinear switched systems by introducing a sufficient condition for stabilization. Based on the possible instability of all sub-systems, a variable structure (VS) switching rule with an adaptive approach and sliding sector was offered. Moreover, the stability condition of the system can be determined by solving linear matrix inequalities (LMIs) to ensure asymptotic stability. The application of H∞ analysis of nonlinear switched systems was also investigated through the design of the mentioned adaptive control system and defining a VS switching rule. Finally, simulation results were presented to validate the novelty of the proposed method.

3 Phase Inverter Switching Algorithm for Industrial Needs

3 phase inverter is needed, besides to change the dc to ac voltage as needed, in the industry every CNC or NC machine needs an inverter to regulate the rotation speed of the motor, constant motor rotation requires for cutting in certain a variety of speeds feeding processes, wherein conventional machines gear is used to change the rotation speed of the motor, here the AC voltage is changed to DC and returned to AC according to the required frequency. For this reason, the researchers tried to research switching the 3 phase inverter algorithm with the principle of space vector pulse wide modulation. Here the switching theory follows the SVPWM switching rule, where the resultant vector is the result of each sector of each phase. The microcontroller accepts the input data, that will be used to generate frequency, the required PWM calculation, the sector, estimates the switching process per sector, the switching sector according to the algorithm results rule. These results will generate inter-phase voltage greater than conventional switching methods, reducing noise, switching steps shorter only 6 steps, improve the power factor. The switching algorithm is ready to be used to make 3 phase inverters.

Interval Type-2 Fuzzy Passive Filtering for Nonlinear Singularly Perturbed PDT-Switched Systems and Its Application

The problem of designing a passive filter for nonlinear switched singularly perturbed systems with parameter uncertainties is explored in this paper. Firstly, the multiple-time-scale phenomenon is settled effectively by introducing a singular perturbation parameter in the plant. Secondly, the interval type-2 fuzzy set theory is employed where parameter uncertainties are expressed in membership functions rather than the system matrices. It is worth noting that interval type-2 fuzzy sets of the devised filter are different from the plant, which makes the design of the filter more flexible. Thirdly, the persistent dwell-time switching rule, as a kind of time-dependent switching rules, is used to manage the switchings among nonlinear singularly perturbed subsystems, and this rule is more general than dwell-time and average dwell-time switching rules. Next, sufficient conditions are provided for guaranteeing that the filtering error system is globally uniformly exponentially stable with a passive performance. Furthermore, on the basis of the linear matrix inequalities, the explicit expression of the designed filter can be obtained. Finally, a tunnel diode electronic circuit is rendered as an example to confirm the correctness and the validity of the developed filter.

A predictive approach to adaptive fuzzy sliding-mode control of under-actuated nonlinear systems with input saturation

In this paper, a computationally efficient robust predictive control method is proposed for continuous-time under-actuated SISO systems in the presence of actuator saturation and state-dependent uncertainties. The proposition of this research is to employ the idea of model prediction together with the Adaptive Fuzzy Sliding-Mode Control (AFSMC) for tuning the sliding surface parameters by predicting the anticipated effects of uncertainties. In the proposed scheme, only after the trigger conditions are met, the coefficients of the sliding surface are updated and the AFSMC is applied. Hence, computational complexity can be controlled by adjusting the switching rule. In the AFSMC, a fuzzy system is used to approximate a nonlinear function, and a robust term to compensate for any possible mismatches. An adaptively tuned gain is also applied to the control signal to prevent instability caused by the actuator saturation. Based on the updating sliding surface, fuzzy singletons, the upper bound of the fuzzy approximation error, and the saturation gain are adaptively tuned. Closed-loop stability is shown to be guaranteed using the multiple Lyapunov functions theorem and the Barbalat’s lemma. Finally, the method is applied for the depth control of an Autonomous Underwater Vehicle (AUV), depicting the excellent performance of the proposed method.

ℋ ∞ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61873002, 61703004, 61973199, 61573008, and 61973200).

We investigate the problem of ℋ ∞ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule, as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously. Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an ℋ ∞ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.

Quantized passive filtering for switched delayed neural networks

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

Event-Triggered Communication and Annular Finite-Time H∞ Filtering for Networked Switched Systems.

Event-triggered communication mechanism (ETCM) provides an efficient way to reduce unwanted network traffic. This article studies the co-design of an ETCM and an annular finite-time (AFT) H∞ filter for networked switched systems (NSSs). First, the AFT definition and ETCM are presented. Second, a set of mode-dependent average dwell-time (MADT) switching rules is given. By resorting to a delay-dependent Lyapunov functional approach, some feasible AFT H∞ filters are designed. Third, it is proved that the filtering error system (FES) has a good performance in attenuating the external disturbances. Finally, the feasibility of the developed method is verified via simulation.

Intelligent switching control of hybrid electromagnetic active suspension based on road identification

The hybrid electromagnetic actuator integrates a magnetorheological damper, and a linear motor can effectively reduce the energy consumption of linear electromagnetic active suspension by switching the control parameters with the same dynamic performances. Thus, the intelligent switching control of hybrid electromagnetic active suspension (HEMAS) is investigated with a fast–slow switching method for full road conditions for the first time, which uses the road level and system state variables as the switching rules. First, the intelligent switching control system architecture of HEMAS is designed, and the switching logic is refined. Then, the modified skyhook control strategy is adopted, and the control parameters (including overfull and transient objective control parameters) are optimized for different driving conditions. Then, the simultaneous estimation method of road profile and system state variables and the identification method of road level are studied. The identification result is used as a prerequisite for intelligent switching of system control parameters. Last, a road adaptive intelligent switching control system is designed, and the stability of the switching system is analyzed. Furthermore, a hardware-in-the-loop bench test is performed. The test results verify the effectiveness of the intelligent switching control system in improving the comprehensive performances (dynamic and energy-saving performances) of HEMAS.

Optimal monetary policy regime switches

An economy that switches between high and low growth regimes creates incentives for the monetary authority to change the parameters in its simple rule. As lower growth tends to produce lower real interest rates, the monetary authority has an incentive to increase the inflation target and increase the degree of inertia in setting rates in an attempt to keep the nominal rate away from the zero lower bound. An optimal simple rule therefore responds to permanently lower growth by slightly increasing both the inflation target and inertia; focusing solely on the inflation target ignores a key margin of adjustment. With repeated growth rate regime switches, an optimal simple rule that switches at the same time internalizes both the direct effects of growth regime change and the indirect expectation effects generated by switching in policy. The switching rule improves economic outcomes relative to a constant rule. A constant rule may be preferred if the monetary authority attempts a switching rule but implements the wrong rule with high enough frequency.

Finite-Time H∞ State Estimation for PDT-Switched Genetic Regulatory Networks With Randomly Occurring Uncertainties.

This article is concerned with the problem of finite-time H∞ state estimation for switched genetic regulatory networks with randomly occurring uncertainties. The persistent dwell-time switching rule, as a more versatile class of switching rules, is considered in this paper. Besides, several random variables that obey the Bernoulli distribution are used to represent randomly occurring uncertainties. The overriding purpose of this article is to design an estimator to ensure that the estimation error system is stochastically finite-time bounded and satisfies the H∞ performance. Based on this, sufficient conditions for the explicit form of the estimator gains can be obtained by the Lyapunov method. Finally, a numerical example is given to verify the correctness and feasibility of the proposed method.

Capacity Gain of Full Duplex Self-Backhauling and Opportunistic Full Duplex Self-Backhauling

This paper investigates the capacity gain of full duplex (FD) self-backhauling over the half duplex (HD) counterpart in downlink cellular systems, and then proposes an opportunistic FD scheme. The first step is to derive the capacity gain of FD self-backhauling over the HD counterpart as a function of the system parameters in a computationally tractable form. Unlike previous studies on the capacity of FD self-backhauling, a practical constraint is imposed so that the end-to-end link achieves a target signal-to-interference-plus-noise ratio (SINR) for a successful link connection. Also, a condition under which FD is more beneficial than HD is derived. Specifically, the minimum allowable self interference cancellation factor and the maximum allowable cell radius for the benefit of FD are derived as an explicit function of system parameters. Their dependencies on the system parameters are investigated and compared with counterparts derived for single-hop point-to-point links. Lastly, to overcome the weak points of FD and HD, this paper proposes a user-wise opportunistic FD (OFD) self-backhauled scheme. To this end, an instantaneous channel gain-based FD/HD switching rule is derived from a condition under which FD cannot instantaneously satisfy the target SINR. We confirm the substantial capacity gain of the proposed user-wise instantaneous OFD over a cell-wise static duplex switching scheme, as well as the fixed duplex (HD or FD) schemes. When compared to the static duplex switching scheme, the proposed OFD is most beneficial at the boundary of HD-preferred and FD-preferred regions. Based on this, a system-level guideline is proposed for selecting the most practical scheme among OFD, FD, and HD by trading off capacity gain and switching overhead. Extensive simulation results are provided to confirm the correctness of the derivations and the related investigations.

TIME-VARYING EPIDEMIC TRANSMISSION IN HETEROGENEOUS NETWORKS AND APPLICATIONS TO MEASLES

In this paper, we analyze some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modeled as a heterogeneous network. We establish some stability results related to the behavior of the time-weighted average Basic Reproduction Number (BRN). Later, a Susceptible–Exposed–Infectious–Recovered (SEIR) model which describes the measles disease is proposed and we show that its dynamics is determined by a threshold value, below which the disease dies out. Moreover, compared with models without the Exposed compartment, we can find weaker stability results. A control strategy with an imperfect vaccine is applied, to determine how it could effect the size of the peak. Due to the periodic behavior of the switching rule, we compare the results with the BRN of the model. Some simulations are given, using a scale-free network, to illustrate the threshold conditions found.

On fault detection of discrete-time switched systems via designing time-varying residual generators

This paper investigates the problem of fault detection (FD) for discrete-time switched systems. Under a dwell time constraint, a switching rule that depends on the measured output is constructed for the system. Time-varying residual generators are designed such that the switched system is asymptotically stable and also with the detection performance under this switching rule. The advantages of the proposed technique are threefold: 1) It has the advantages of both slow switching and fast switching. 2) It can extend the classic design of time-invariant residual generator. 3) It can guarantee the switched system still has the desired fault detection performance even if all subsystems are without it. This feature reduces the performance requirements for each subsystem. A numerical example illustrates the effectiveness of the proposed method.

Stability Analysis and Control for Switched System With Bounded Actuators

This paper addresses the control problem of the switched system with bounded actuators and average dwell-time. We present the switching rules for the designed controllers based on two kinds of parametric algebraic Riccati equation. The exponential stability of the switched system under the average-dwell time is ensured by the designed controllers and the switching rules. The dynamic performance of the control system is enhanced greatly by the proposed method. The simulation results illustrate the effectiveness and the usefulness of the obtained theoretical results.

Stabilization of Linear Systems With Input Saturation and Large Delay

This paper investigates a stabilization problem for linear systems subject to saturation and time-varying delays in the control input, where the delay takes both large and small values in an alternating manner. Based on the delay values, the considered system is described by a switched system including a stabilizable subsystem and an unstabilizable subsystem. By using Lyapunov-Krasovskii functional method, a time-dependent switching rule orchestrating the proposed controllers is established to guarantee the regional stabilization of the closed-loop system. To obtain a domain of attraction as large as possible, an optimization problem is formulated in the form of linear matrix inequalities. Numerical examples and simulations are provided to demonstrate the effectiveness of the proposed method.

Distributed Asynchronous Consensus Control for Nonlinear Multiagent Systems Under Switching Topologies

This article addresses the distributed asynchronous consensus problem for nonlinear multiagent systems with switching topologies. Different from the existing results, we consider the detection delay of topology modes and some topologies having no directed spanning tree with leader as the root. In these conditions, the distributed asynchronous switched observer is first developed for each follower to accurately estimate the state information of the leader. Then, an output feedback distributed controller is designed for each follower by means of the switched observer. According to the Lyapunov stability theory, it is proved strictly that the controller can guarantee all agents achieving a consensus if the topologies are switched by the switching signal fulfilling a general rule. Moreover, the switching rule compared with the one satisfying average dwell-time condition can render the number of topology switches growing faster on any time interval. Finally, the numerical simulation is presented to verify the effectiveness of proposed theoretical results.

Novel Data and Neural Network-Based Nonlinear Adaptive Switching Control Method.

We propose an adaptive nonlinear control method for a discrete-time dynamical system. First, the nonlinear term is decomposed into a previous sampling instant term and an unknown increment term, which are determined using an intelligent estimation algorithm based on adaptive fuzzy neural networks. The problem of obtaining accurate input data due to the unknown current control signal in unmodeled dynamics using conventional estimation algorithms is addressed, and the conservativeness is reduced. Furthermore, historical data of the controlled plant are leveraged, and the data in the nonlinear term containing repeated estimation information are disregarded. Then, we apply the proposed decomposition method for the nonlinear term to design nonlinear switching controllers. One linear and two nonlinear adaptive controllers are designed, all with compensation of the nonlinear term at the previous sampling instant and increment estimation. These three adaptive controllers coordinately operate the plant by switching rules to guarantee the stability of the controlled plant and to improve the system performance. The stability and convergence of the system are analyzed and verified. Finally, simulation examples are used to verify the effectiveness of the proposed method and compare it with existing methods to confirm its superior performance.

Distinct performance profiles on the Brixton test in frontotemporal dementia

The Brixton Spatial Anticipation Test is a well-established test of executive function that evaluates the capacity to abstract, follow, and switch rules. There has been remarkably little systematic analysis of Brixton test performance in the prototypical neurodegenerative disorder of the frontal lobes: behavioural variant frontotemporal dementia (bvFTD) or evaluation of the test's ability to distinguish frontal from temporal lobe degenerative disease. We carried out a quantitative and qualitative analysis of Brixton performance in 76 patients with bvFTD and 34 with semantic dementia (SD) associated with temporal lobe degeneration. The groups were matched for demographic variables and illness duration. The bvFTD group performed significantly more poorly (U=348, p<.0001, r=.58), 53% of patients scoring in the poor-impaired range compared with 6% of SD patients. Whereas bvFTD patients showed problems in rule acquisition and switching, SD patients did not, despite their impaired conceptual knowledge. Error analysis revealed more frequent perseverative errors in bvFTD, particularly responses unconnected to the stimulus, as well as random responses. Stimulus-bound errors were rare. Within the bvFTD group, there was variation in performance profile, which could not be explained by demographic, neurological, or genetic factors. The findings demonstrate sensitivity and specificity of the Brixton test in identifying frontal lobe degenerative disease and highlight the clinical value of qualitative analysis of test performance. From a theoretical perspective, the findings provide evidence that semantic knowledge and the capacity to acquire rules are dissociable. Moreover, they exemplify the separable functional contributions to executive performance.

Asynchronously switching control for a class of switched neutral systems: a novel discontinuous Lyapunov function approach

In this study, a sampling control problem is investigated for a class of switched linear neutral systems under asynchronous switching. By developing a novel edge-dependent discontinuous Lyapunov function (EDDLF) approach, new exponential stability conditions are established for the considered switched system with sampled-data partitioned feedback controllers. In addition, the switching rule characterised by admissible edge-dependent average dwell time (AED-ADT) is first explored for sampling asynchronous switching studies of switched systems, and tighter bounds of AED-ADT are obtained by the EDDLF strategy. By properly assigning the sampling period and the number of segments, the proposed controller gains and smaller AED-ADT are followed, which can guarantee the exponential stability of the closed-loop switched system. Finally, some simulation results show the advantages of the developed control strategy.