State-dependent Switching Law Research Articles

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.

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.

A Dual Triggering Scheme to Adaptive Fuzzy Resilient Control of Switched Nonlinear Systems Against Mixed Attacks.

A dual event-triggered adaptive fuzzy resilient control scheme for a class of switched nonlinear systems with vanishing control gains under mixed attacks is proposed in this article. The scheme proposed achieves dual triggering in the channels of sensor-to-controller and controller-to-actuator by designing two new switching dynamic event-triggering mechanisms (ETMs). An adjustable positive lower bound of interevent times for each ETM is found to preclude Zeno behavior. Meanwhile, mixed attacks, that is, deception attacks on sampled state and controller data and dual random denial-of-service attacks on sampled switching signal data, are handled by constructing event-triggered adaptive fuzzy resilient controllers of subsystems. Compared with the existing works for switched systems with only single triggering, more complex asynchronous switching caused by dual triggering and mixed attacks and subsystem switching is addressed. Further, the obstacle caused by vanishing control gains at some points is eliminated by proposing an event-triggered state-dependent switching law and introducing vanishing control gains into a switching dynamic ETM. Finally, a mass-spring-damper system and a switched RLC circuit system are applied to verify the obtained result.

Adaptive Dynamic Event-Triggered Tracking Control for Uncertain Switched Nonlinear Systems Under State-Dependent Switching.

This article introduces an adaptive dynamic event-triggered technique for addressing the output tracking control problem of uncertain switched nonlinear systems with prescribed performance. First, a switching dynamic event-triggered mechanism (SDETM) is established to alleviate network burden and conserve computational resources. A notable aspect is the inclusion of asynchronous switching between the switching subsystems and controllers. Second, a state-dependent switching law ensuring a dwell-time constraint is designed, which avoids the frequent switching phenomenon within any finite time interval. Third, an SDETM and an adaptive dynamic event-triggered controller are developed to confine the output tracking error within predefined decaying boundaries, while ensuring that all the signals of the closed-loop switched system remain within bounded regions. Finally, the validity and applicability of the developed control scheme are demonstrated through a one-link manipulator example.

Global Event-Triggered Funnel Control of Switched Nonlinear Systems via Switching Multiple Lyapunov Functions.

In this article, the global event-triggered (ET) funnel tracking control problem is studied for a class of switched nonlinear systems with structural uncertainties, where the solvability of the control problem for each subsystem is not needed. A switching multiple Lyapunov functions (MLFs) method is established, where MLFs are designed to handle switched inverse dynamics, and a switching barrier Lyapunov function is constructed to address switched sampled errors that may compromise system stability. This is achieved alongside a new switching dynamic event-triggering mechanism (DETM). By combining this method with backstepping, a dwell-time state-dependent switching law and an ET funnel controller of each subsystem are constructed, effectively eliminating the issue of the "explosion of complexity" encountered in traditional backstepping without using dynamic surface control or command filters. Additionally, the designed switching DETM ensures that the tracking error always evolves within a performance funnel in any consecutive triggering interval, excluding Zeno behavior, and guaranteeing positive constant lower bounds for two consecutive triggering intervals and any switching interval, respectively. Finally, an example is provided to show the validity of the theoretical results.

Membership-function-dependent [formula omitted] bumpless transfer control for switched interval type-2 fuzzy systems with time-delay

This paper addresses the H∞ bumpless transfer control for switched nonlinear delayed systems with exogenous perturbations via the interval type-2 fuzzy model. We firstly establish a novel characterization of bumpless transfer performance, which provides a framework to the bumpless transfer control of switched nonlinear systems. By using the multiple Lyapunov-Krasovskii functionals and the state-dependent switching strategy, sufficient conditions for asymptotically stability with H∞ bumpless transfer performance are obtained. More incisively, different from the existing results where the H∞ bumpless transfer control design conditions do not involve the information of membership functions, we adopt the piecewise-linear-membership-function technique to remove this limitation. Correspondingly, novel membership-function-dependent H∞ bumpless transfer criteria are derived, under which the state-dependent switching law and H∞ bumpless transfer controllers are jointly designed. Finally, a tunnel diode circuit model is exploited to verify the applicability and validity of the developed method.

Multi-variable anti-disturbance controller with state-dependent switching law for adaptive cycle engine

Compared with the conventional turbofan engine, the adaptive cycle engine (ACE) has more extensive flight envelope and the more types and number of adjustable components. While the performance of each mission profile is improved adaptively, the controller design of profile switching process will face strong flight condition disturbance and internal uncertainty. The traditional control system's single loop controller and discrete switching method of control parameters are to some extent difficult to meet the adaptive and robustness requirements of ACE. Thus, this paper proposed a multi-variable decoupling anti-disturbance controller for ACE based on the results of flight envelope partitioning with similar distances, embedded a state-dependent switching law. By analyzing the impact of inlet disturbances, internal actuator actuation, and random degradation of component performance on different switching laws, the adjust time and overshoot of the controller with state-dependent switching law proposed in this paper are reduced by an average of about 11.91 % and about 9.98 %, and the average thrust linearity and robustness has increased by about 0.096 % and 20.02 %. Finally, the reliability and feasibility of the control system were verified based on a hydraulic driven semi-physical experimental platform, providing reference for more complex and dynamic engine operation control in the future.

Fault estimation and tolerant bumpless transfer control for switched systems

A novel fault estimation and tolerant bumpless transfer control strategy is proposed for switched systems. In this control scheme, a switched estimator, a switched estimator-based tolerant bumpless transfer controller and a switching logic are jointly designed. The estimator relaxes the assumption on the usual observer matching condition in the fault estimation issue of switched linear systems. The controller can tolerate the fault with small input bumps at switching time. The switching law is an improvement of the traditional state-dependent switching law with dwell time still maintained, permitting the increase of the Lyapunov function for subsystems within the ensured dwell time interval. Through the presented control scheme, a criterion is developed to drive the solvability of the fault estimation and tolerant bumpless transfer control issue for the SSs. Also, with this criterion, this control issue of subsystems can be unsolvable. An example of regulating the current for a chua’s circuit system is provided for purpose of verifying the theoretical result.

Output Regulation Bumpless Transfer Control for Discrete-Time Switched Linear Systems

This paper mainly focuses on the output regulation (OR) bumpless transfer (BT) control problem for discrete-time switched linear systems (DSLSs). A procedure for solving the OR BT control problem is given by means of the multiple Lyapunov functions technique. Firstly, the definition of the performance of BT for DSLS is introduced. Next, the state-dependent switching law and a group of BT feedback controllers for solving the OR BT problem are designed. Then, a sufficient condition and its deformation form are obtained without the solvability requirement of OR BT control problem for every subsystem. Finally, the Chua’s circuit example is presented and the results of the simulation verify the effectiveness of the proposed control scheme.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Neural-Network-Based Adaptive Constrained Control for Switched Systems Under State-Dependent Switching Law.

This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.

Fixed-time periodic stabilization of discontinuous reaction–diffusion Cohen–Grossberg neural networks

This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction–diffusion Cohen–Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction–diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction–diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.

Control for Hybrid Bumpless Transfer Performance of Discrete-Time Switched Systems With Event-Triggering

This paper addresses the dynamic event-triggered l2-l∞ bumpless transfer control for discrete-time switched systems without stable subsystems. A unified framework of bumpless transfer performance for discrete-time switched systems called hybrid bumpless transfer performance is established to rule out sudden large hybrid bumps induced by both triggering and switching. By constructing the multiple Lyapunov functions, sufficient conditions for the considered switched systems to be asymptotically stable with both l2-l∞ performance and hybrid bumpless transfer performance are obtained. Then, the state-dependent switching law and the dynamic event-triggered hybrid bumpless transfer controllers are jointly designed. Finally, the PWM-driven boost converter system is provided to verify the validity and applicability of our method.

Event-triggered finite-time stabilization of nonlinear switched affine systems under mode-dependent and state-dependent switchings

This paper investigates the event-triggered finite-time stabilization (FTS) problem of nonlinear switched affine systems (NSASs) under mode-dependent and state-dependent switching signals, respectively. Firstly, an event-triggered control (ETC) strategy for NSASs with mode-dependent average dwell time constraint is proposed. Note that the presence of affine terms gives rise to difficulties in the exclusion of Zeno behavior for the widely-adopted triggering mechanism consisting of current state and error information. Therefore, a novel triggering mechanism including affine term threshold is proposed to exclude Zeno behavior. Secondly, an event-triggered impulsive control strategy for NSASs under autonomous state-dependent switching is studied. Some Lyapunov-based criteria and a state-dependent switching law for FTS are presented. Moreover, the established event-based control strategies are applied to FTS of boost converter to illustrate the effectiveness of the proposed results.

Output tracking control for state-dependent switched systems with input delay

This paper investigates the H∞ output tracking control problem for state-dependent switched systems with delays, where the existence of input delay is fully considered. Based on hysteresis switching strategy, a state-dependent switching law is designed through dividing the whole state space. In contrast to general time-dependent switching, the switching instants need not be predetermined and all subsystems can be unstable under state-dependent switching. Meanwhile, we design a delayed state-feedback controller that takes into account the effect of input delay. In the framework of Lyapunov–Krasovskii (L-K) functional method, some sufficient conditions for ensuring the H∞ output tracking performance of the switched system with delays are obtained by employing state-dependent switching and delayed state-feedback control. Moreover, the information of input delay and state delay are both included in linear matrix inequalities (LMIs). In addition, the obtained results are further extended to the system with parameter uncertainties by establishing the corresponding state-dependent switching law and some sufficient conditions. The effectiveness of the proposed results is demonstrated by two examples and their simulations.

Quadratic Stability of Switched a ne DAEs Via State-Dependent Switching Law

In this paper, we deal with quadratic stabilization for a particular class of impulse-free switched differential affine algebraic systems (switched affine DAEs) which consisted of a finite set of affine subsystems with the same algebraic constraint, where both subsystem matrices and affine vectors in the vector fields are switched independently and no single subsystem has desired quadratic stability. We show that if a convex combination of subsystem matrices such that the result LTI algebraic system is assymptotically stable, and another convex combination of affine vectors is zero, then we can design a state-dependent switching law such that the entire switched affine DAEs system is quadratically stable at the origin. But when the convex combination of affine vectors is not zero, we discuss the quadratic stabilization to a convergence set defined by the convex combination of subsystem matrices and the convex combination of affine vectors. &nbsp

Fault Ride-through Hybrid Controller for MMC-HVDC Transmission System via Switching Control Units Based on Bang-bang Funnel Controller

This paper proposes a fault ride-through hybrid controller (FRTHC) for modular multi-level converter based high-voltage direct current (MMC-HVDC) transmission systems. The FRTHC comprises four loops of cascading switching control units (SCUs). Each SCU switches between a bang-bang funnel controller (BBFC) and proportional-integral (PI) control loop according to a state-dependent switching law. The BBFC can utilize the full control capability of each control loop using three-value control signals with the maximum available magnitude. A state-dependent switching law is designed for each SCU to guarantee its structural stability. Simulation studies are conducted to verify the superior fault ride-through capability of the MMC-HVDC transmission system controlled by FRTHC, in comparison to that controlled by a vector controller (VC) and a VC with DC voltage droop control (VDRC).

Formula omitted]-dissipativity for switched non-linear delay systems

In this paper, we investigate (Q,S,R)-dissipativity for a class of switched non-linear systems with time-varying delay based on a state dependent switching law. Firstly, sufficient conditions for (Q,S,R)-dissipativity are developed by using Hurwitz convex combination approach, these conditions are provided in terms of linear matrix inequalities (LMIs). Secondly, passivity as a special form of (Q,S,R)-dissipativity is preserved for the feedback interconnected switched systems with time-varying delay by the merging switching signal technique. Finally, an example is provided to illustrate the effectiveness of the main results.

Adaptive Fuzzy Decentralized Dynamic Surface Control for Switched Large-Scale Nonlinear Systems With Full-State Constraints.

In this study, an adaptive fuzzy decentralized dynamic surface control (DSC) problem is investigated for switched large-scale nonlinear systems with deferred asymmetric and time-varying full-state constraints. Due to the existence of additional general nonlinearities, complicated output interconnections, and full-state constraints, it is difficult to address the above control problem using existing methods. Fuzzy-logic systems are, therefore, utilized to approximate the unknown nonlinear functions, and the DSC technique is adopted to overcome the "curse of dimensionality" problem. A novel fuzzy adaptive decentralized controller design is presented using the proposed convex combination technique. Furthermore, it is proven that under the proposed controller and state-dependent switching law, all states of the closed-loop system are bounded and deferred asymmetric, and the time-varying full-state constraints are strictly obeyed. The simulation results are presented to demonstrate the effectiveness of the proposed method.