State-dependent Switching Research Articles

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.

Safety-Critical Model Reference Adaptive Control of Switched Nonlinear Systems With Unsafe Subsystems: A State-Dependent Switching Approach.

In this article, a novel safety-critical model reference adaptive control approach is established to solve the safety control problem of switched uncertain nonlinear systems, where the safety of subsystems is unnecessary. The considered switched reference model consists of submodels possessing safe system behaviors that are governed by switching signals to achieve satisfactory performances. A state-dependent switching control technique based on the time-varying safe sets is proposed by utilizing the multiple Lyapunov functions method, which guarantees the state of the subsystem is within the corresponding safe set when the subsystem is activated. To deal with uncertainties, a switched adaptive controller with different update laws is constructed by resorting to the projection operator, which reduces the conservatism caused by the common update law adopted in all subsystems. Moreover, a sufficient condition is obtained by structuring a switched time-varying safety function, which ensures the safety of switched systems and the boundedness of error systems in the presence of uncertainties. As a special case, the safety control problem under arbitrary switching is considered and a corollary is deduced. Finally, a numerical example and a wing rock dynamics model are provided to verify the effectiveness of the developed approach.

Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes

AbstractA comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to pathwise-control the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions of switching processes in the spirit of Skorokhod’s representation theorem varying according to the problem being dealt with. In particular, this method can cope with switching processes in an infinite state space and not necessarily of birth–death type. As an application, some known results on the ergodicity and stability of state-dependent regime-switching processes can be improved.

Recent developments of Boolean networks with switching and constraints

A switched Boolean network (SBN) is an important model for describing hybrid phenomena in gene regulatory networks, and it has received increasing attention since the development of the semi-tensor product of matrices. This paper aims to present a comprehensive survey on SBNs. First, the fundamental issues for SBNs with arbitrary switching signals are reviewed, including stability, stabilisation, controllability, observability, optimal control, and synchronisation. Next, a brief review of the stability analysis of SBNs with constrained switching, consisting of time-dependent switching, state-dependent switching, and logical switching, is given. In addition, some basic results on the SBNs under non-ideal conditions are also introduced comprehensively.

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.

Robust Adaptive Dynamic Event-Triggered Control of Switched Nonlinear Systems

This paper investigates the robust adaptive event-triggered control (ETC) problem for switched nonlinear systems. A novel robust adaptive controller for nonlinear systems under dwell-time switching is first constructed based on a common virtual control Lyapunov function method using backstepping. Then, a dynamic ETC (DETC) strategy is integrated into the switching controller to constitute an overall solution to the problem under investigation while the challenges caused by interaction of switching and triggering instants are well addressed. In particular, global asymptotic stability and exclusion of Zeno behavior are guaranteed for the resulting closed-loop system. Furthermore, the solution is extended to a larger class of switched nonlinear systems whose subsystems are not assumed to be asymptotically stable. In this case, a state-dependent switching strategy with guaranteed dwell-time must be constructed such that the proposed switching DETC can be applied. Finally, three examples are presented to demonstrate the effectiveness of the proposed design strategies.

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.

Synchronization of switched complex dynamical networks with impulses: state-dependent switching approach

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Multistability of switched complex-valued neural networks with state-dependent switching rules

The paper focuses on the multistability problems of the switched complex-valued neural networks with state-dependent switching rules. Based on the differential inclusions theory and fixed point theorem, several sufficient conditions are derived to ascertain that there exist 25n equilibria, 9n of which are locally ex for n-neuron switched complex-valued neural networks. The number of stable equilibria of an n-neuron switched complex-valued neural network increases significantly from 4n to 9n compared with the conventional complex-valued neural networks. Finally, four numerical examples are presented to substantiate the theoretical results.

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.

Dissipativity for Discrete-Time Switched Positive Delay Systems: A Dwell-Time-Dependent Linear Copositive Storage Functional Method

This article addresses the problems of dissipativity analysis and feedback dissipativity of discrete-time switched positive systems with time-varying delay. On the basis of the positivity property of the investigated system, the definition of linear <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(q,r)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -dissipativity, utilizing the linear copositive storage functionals with linear supply rates, is first introduced. The switching among subsystems is orchestrated by a state-dependent switching policy that obeys prespecified dwell-time constraints. Second, in order to reduce the conservatism brought by the identical summation term functional for all positive subsystems, we propose a dwell-time-dependent linear copositive storage functionals involving summation terms which are diverse appearing in the functional. Then, less conservative criteria are developed to guarantee the system is strict <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(q,r)$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -dissipativity by resorting to the switching policy or the joint implementation of the switching policy and time-varying controllers for subsystems. Finally, the validity of the proposed techniques is illustrated through two examples, and the relationship among the minimum dwell time, performance index, and time-varying delay is also revealed.

Control of a Double-Pendulum Overhead Crane System Based on Hierarchical Sliding Mode Control Techniques

The double-pendulum overhead crane system belongs to a class of underactuated mechanical systems, which is challenging to control due to its strong nonlinearities. This study deals with the nonlinear controller design for a double-pendulum overhead crane based on hierarchical sliding mode control with state-dependent switching gain. The equivalent and switching controls are obtained with the aid of first-level and second-level sliding surfaces. The asymptotic stability of sliding surfaces is proved theoretically and also shown graphically. Numerical simulations show that the proposed controller performs better than conventional hierarchical sliding mode control. The proposed controller effectively suppresses the load and hook swing and precisely controls the trolley’s displacement. It has strong robustness to the payload displacement and the change of the crane parameters.

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.

The fastest stabilization of second-order switched systems with all modes unstable via an optimal state-dependent switching rule revisited

In this paper, an optimal state-dependent switching rule design method is proposed for the fastest asymptotic stabilization of second-order switched systems, wherein all eigenvalues of each subsystem are positive real parts. First, the definition of an optimal invertible transformation is proposed based on the physical meaning of a vibrational system with one degree-of-freedom. Then, the formulas of both the optimal invertible transformations and the optimal switching lines are calculated. In this way, the designed optimal state-dependent switching rule can minimize the energy increment of unstable subsystem operation and maximize the energy loss of system switching simultaneously, achieving the fastest asymptotic stability. Moreover, the critical stability condition for a general switched system is investigated, demonstrating that this state-dependent switching rule is optimal. Finally, three examples are provided to verify the effectiveness and superiority of the results.

State-dependent Switching Stabilization of Fourth-order Switched Systems With Fully Unstable Subsystems

State-dependent Switching Stabilization of Fourth-order Switched Systems With Fully Unstable Subsystems

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

Reachable set estimation for switched linear systems with state-dependent switching and bumpless transfer based event-triggered control

This article focuses on the reachable set estimation and the state-feedback controller design for switched linear systems with a state-dependent switching and event-triggered control. First, the event-triggered bumpless transfer performance is given. The reachable set of the switched system is estimated under the proposed bumpless transfer based event-triggered mechanism by using the multiple Lyapunov functions method. A co-design of the event-triggered mechanism, a switching law and the controller gain is provided. Second, Zeno behavior is avoided by showing the existence of a positive lower bound on the event triggered interexecution intervals. Third, we design a state-feedback controller which contains the system states in a preset ellipsoid. Finally, numerical examples are given to illustrate the effectiveness of the theoretical claims.