State-dependent Switching Law Research Articles

Almost output regulation model reference adaptive control for switched systems: combined adaptive strategy

ABSTRACTThis paper proposes the almost output regulation model reference adaptive control problem for switched systems with parametric uncertainties and multiple types of disturbances. By the almost output regulation model reference adaptive control strategy, the parametric uncertainties are suppressed and the multiple types of disturbances are rejected, simultaneously. In order to improve the transient performance of switched systems, the combined model reference adaptive control strategy is applied. A key point is to set up the almost output regulation model reference adaptive control strategy to achieve the tracking and the disturbance rejection performance. First, we design a switched identification model to estimate the plant uncertain parameters, by which more accurate plant parameters will be obtained. Secondly, based on the switched identification model, controllers with combined adaptive laws and a state-dependent switching law are designed to solve the almost output regulation model reference adaptive control problem for switched systems. Finally, a sufficient condition is given, which guarantees that the problem of the almost output regulation model reference adaptive control for switched systems is solvable in spite of the problem of almost output regulation model reference adaptive control for each subsystem is not solvable.

Command-Filter-Based Adaptive Fuzzy Finite-Time Control for Switched Nonlinear Systems Using State-Dependent Switching Method

The adaptive fuzzy finite-time tracking control problem of a class of switched nonlinear systems is investigated in this study. Fuzzy logic systems are introduced to handle the unknown nonlinear terms in the considered system. To overcome the drawback in the recursive design method, a finite-time command filter is employed. By constructing a new state-dependent switching law and adaptive fuzzy control signal, the existing restrictions on subsystems of switched systems are relaxed, all subsystems of the considered system are allowed to be unstabilizable. To avoid the Zeno behavior, a new hysteresis switching law is derived. It is proven that all states of the closed-loop system are bounded in finite time under the proposed fuzzy finite-time control scheme. Additionally, the proposed control method is extended to a class of more general switched large-scale nonlinear systems. Finally, two examples are provided to verify the developed method's effectiveness.

Robust Semipassivity and Practical Stability for Uncertain Switched Nonlinear Systems

This paper addresses several issues including robust semipassivity and practical stability analysis for a switched nonlinear system with structural uncertainties. First, robust semipassivity is firstly defined to describe the overall semipassivity property of switched nonlinear systems without requiring the conventional semipassivity property of each active subsystem. Then, the robust semipassive system is shown to be practically stable. Second, a state-dependent switching law is designed to render the switched system robust semipassive. This switching law is a generalization of KYP lemma. Third, robust semipassification for a switched nonlinear system is achieved by the design of a state-dependent switching law and a set of feedback controllers. Finally, a composite state-dependent switching law is designed to render the feedback interconnection of switched nonlinear systems robust semipassive. The effectiveness of the obtained resultsis verified by two numerical examples.

Geometrical Quasi-Passivity and Practical Stability Property for Switched Discrete-Time Nonlinear Systems

This paper investigates geometrical quasi-passivity, feedback quasi-passification and related properties for switched discrete-time nonlinear systems using multiple storage functions and multiple supply rates. First, a concept of geometrical quasi-passivity for a switched discrete-time nonlinear system is firstly proposed to describe the overall quasi-passivity property of switched discrete-time nonlinear systems in the absence of the conventional geometrical quasi-passivity property of each active subsystem. Then, a geometrically quasi-passive switched nonlinear system is shown to be practically stable. Compared with passive switched system, quasi-passive switched system whose subsystems contain energy source can produce energy itself. Second, a state-dependent switching law is designed to achieve geometrical quasi-passivity. Finally, the feedback geometrical quasi-passification problem is solved by the design of a state-dependent switching law and a set of feedback controllers. A numerical example is presented to the effectiveness of the obtained results.

Global adaptive stabilization of stochastic high-order switched nonlinear non-lower triangular systems

This paper aims to deal with the global adaptive stabilization problem for a class of uncertain stochastic high-order switched nonlinear systems. The most distinctive feature of the studied system is that all drift terms of each subsystem are non-lower triangular nonlinear functions. To achieve the control objective, the retrogressed form of the studied system is first considered and a common state-feedback controller of all subsystems is first systematically constructed in the framework of the common Lyapunov function (CLF) method combined with the adding a power integrator technique, which assures the global stability in probability of the corresponding closed-loop retrogressed system under arbitrary switching. Then a sufficient condition is deliberately proposed by designing a state-dependent switching law in combination with the common state-feedback controller to ensure that the system states can be regulated to the origin almost surely and the globally stability in probability of the whole closed-loop system. Finally, two simulation examples are given to illustrate the effectiveness of the presented control schemes.

Stabilization of Switched Linear Systems Subject to Actuator Saturation via Invariant Semiellipsoids

This article presents new stabilization conditions for the state feedback control of switched linear systems subject to actuator saturation. Based on the semiellipsoidal approach and the multiple Lyapunov functions method, state feedback controllers and a state-dependent switching law are designed. The presented stabilization conditions are less conservative than those obtained by the ellipsoidal method and simpler than those established by the polyhedral method. Moreover, the union of all positively invariant semiellipsoids is constructed to approximate the region of attraction. Each semiellipsoidal set is the intersection of a positively invariant ellipsoidal set and a constraint set. Constructive solutions of the presented conditions are obtained based on two different techniques: the sum-of-squares technique and the nonlinear matrix inequality technique. Two illustrative examples are given to demonstrate the effectiveness of the main results.

Quadratic stabilisation of switched affine systems

We deal with quadratic stabilisation for switched systems which are composed of a finite set of affine subsystems, 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 is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law and an output-dependent switching law such that the entire switched system is quadratically stable at the origin. If the convex combination of affine vectors is not zero, we discuss the quadratic stabilisation to a convergence set defined by the convex combination of subsystem matrices and that of affine vectors. We extend the discussion to switched uncertain affine systems with norm bounded uncertainties, and establish a quadratically stabilising state-dependent switching law based on an norm condition for a combination of subsystems. Several numerical examples show effectiveness of the results.

Quadratic stabilization of switched uncertain linear systems: a convex combination approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuous-time linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an output-dependent switching law by constructing a robust Luenberger observer for each subsystem.

Switched-system-based four-scroll chaotic attractor generation and its application in color image encryption

In this paper, a four-scroll chaotic attractor is generated based on a switched system, and moreover, it is applied to color image encryption. First, the canonical Chen system and a modified chaotic system are used as two subsystems to construct the switched system. Meanwhile, a state-dependent switching law with a threshold is designed to regulate the switching between the two subsystems. Then, a four-scroll chaotic attractor is generated by tuning the threshold value. Last, the chaotic sequence extracted from the switched chaotic system is applied to image encryption. The experimental results show that the encryption performance of this switched chaotic system is better than that of a single Chen system.

Design of State-Dependent Switching Laws for Stability of Switched Stochastic Neural Networks With Time-Delays.

We study the stability properties of switched stochastic neural networks (SSNNs) with time-varying delays whose subsystem is not necessarily stable. We introduce state-dependent switching (SDS) as a tool for stability analysis. Some SDS laws for asymptotic stability and p th moment exponentially stable are designed by employing Lyapunov-Krasovskii (L-K) functional and Lyapunov-Razumikhin (L-R) method, respectively. It is shown that the stability of SSNNs with time-varying delays composed of unstable subsystems can be achieved by using SDS law. The control gains in the designed SDS laws can be derived by solving the LMIs in derived stability criteria. Two numerical examples are provided to demonstrate the effectiveness of the proposed SDS laws.

Incremental passivity-based H∞ output tracking control for switched nonlinear systems

This paper is concerned with the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances using incremental passivity, even if the problem of H∞ output tracking control for none of subsystems is solvable. First, an incremental passivity concept of switched nonlinear systems without external disturbances is proposed. This incremental passivity property requires each active subsystem is incrementally passive. Then, sufficient conditions to be incrementally passive are given. Second, by resorting to the established incremental passivity theory, a state-dependent switching law and a set of feedback controllers are designed to solve the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances. This avoids solving Hamilton-Jacobi (HJ) inequality. Third, a composite state-dependent switching law and the state feedback controllers are designed to solve the H∞ output tracking problem for a class of cascaded switched nonlinear systems with external disturbances. The designed composite switching law allows the driven switched system and the driving switched system switch asynchronously. Finally, two examples are provided to verify the effectiveness of the proposed method.

Vector incremental L2-gain and incremental stability for switched nonlinear systems

This paper studies vector incremental L2-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L2-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L2-gain, but it has its own incremental L2-gain and the related storage function, when it is active. The transformation of “energy” from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L2-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L2-gain, even if each subsystem does not have incremental L2-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L2-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method.

Composite anti-disturbance model reference adaptive control for switched systems

This paper investigates the problem of the composite anti-disturbance model reference adaptive control for switched systems with parametric uncertainties and multiple types of disturbances. It is worth emphasizing that the measurability of the system state and the disturbance generated by an exosystem is unnecessary. A key point is to design a composite anti-disturbance model reference adaptive control strategy to achieve the state tracking and the anti-disturbance performance. First, a switched adaptive state-disturbance observer is designed to estimate the system state and the disturbance generated by the exosystem simultaneously. Secondly, based on the switched adaptive state-disturbance observer, a composite switched adaptive controller and a state-dependent switching law are designed to solve the composite anti-disturbance model reference adaptive control problem for switched systems. Thirdly, a sufficient condition ensuring the solvability of the composite anti-disturbance model reference adaptive control problem for switched systems is given, even if the problem is unsolvable for individual subsystems. Finally, an example of the electrohydraulic system is used to verify the availability of the acquired approach.

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.

Integral ISS for Switched Nonlinear Time-Varying Systems Using Indefinite Multiple Lyapunov Functions

This paper is concerned with studying Lyapunov characterization of integral input-to-state stability (iISS) for switched nonlinear time-varying systems. Sufficient conditions are given to verify iISS for switched nonlinear time-varying systems under a time-varying state-dependent switching law designed, which allow all subsystems to be not integral input-to-state stable (iISS) and the time derivative of Lyapunov functions of individual subsystems to be indefinite. An indefinite multiple Lyapunov functions (iMLFs) method for analyzing the dynamic behavior of switched nonlinear time-varying systems is provided. Also, an iMLFs-based small-gain theorem for switched interconnected nonlinear time-varying systems is presented, where each lower dimensional subsystem is allowed to be not iISS, which extends the small-gain technique from its original nonswitched nonlinear time-invariant version to a switched nonlinear time-varying version. Finally, an illustrative example is used to demonstrate the feasibility of the theoretical results.

Disturbance Attenuation and Rejection for Nonlinear Uncertain Switched Systems Subject to Input Saturation

This paper studies the problem of disturbance attenuation and rejection for switched systems with nonlinear uncertainty and input saturation via composite anti-disturbance control technique, in which the exosystem-generated disturbance and H 2 -norm-bounded disturbance are considered. For switched systems, the switching law and input saturation increase the difficulty for the design of the disturbance observer and the composite control scheme. A switching disturbance observer is designed to obtain the estimation of the matched disturbance, and a novel switching composite controller is further constructed based on the estimated value. By proposing a state-dependent switching law and utilizing the multiple Lyapunov function technology, the criteria are presented to ensure the local asymptotic stability with an H ∞ performance level for the closed-loop system. Furthermore, two optimal algorithms of the design of the controller are put forward to maximize the estimation of the domain of attraction of the closed-loop and the upper bound on the H 2 -norm of the disturbance, respectively. The effectiveness of the proposed technique is illustrated via the numerical examples.

Adaptive Fuzzy Tracking Control for a Class of Switched Uncertain Nonlinear Systems: An Adaptive State-Dependent Switching Law Method

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. The unknown nonlinear functions are approximated by using fuzzy logic systems, and the adaptive backstepping technique is applied to a convex combination of the subsystems. To ensure the continuousness of the Lyapunov function at switching instants, common Lyapunov function (CLF) technique is adopted and the proposed CLF permits switched parameter adaptive laws. Besides, two classes of adaptive laws are proposed, one for designing control laws and one for designing switching law. Then, the common control laws are obtained with the help of the convex combination. Based on the switched adaptive laws, common control laws, a new adaptive state-dependent switching law is proposed. It is shown that the designed state-feedback controllers and switching law can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin. Moreover, a modified switching law is proposed to avoid Zeno behavior or switching too quickly. Finally, two examples are provided to show the effectiveness of the proposed approaches.

Quadratic Performance Analysis of Switched Affine Time–Varying Systems

Abstract We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

Incremental H∞ performance for a class of stochastic switched nonlinear systems

In this paper, we investigate the incremental H∞ performance problem for a class of stochastic switched nonlinear systems by using a state-dependent switching law and the maximum and minimum dwell time approach. By resorting to the state-dependent switching law, some sufficient conditions are provided to cope with the incremental H∞ performance problem, which can be applied even if all subsystems are unstable. Then, based on the maximum and minimum dwell time scheme, the incremental H∞ performance problem to be solvable is derived for two cases: one is all subsystems are incrementally globally asymptotically stable in the mean(IGASiM), another is both IGASiM subsystems and unstable subsystems coexist. When all subsystems are IGASiM, the stochastic switched nonlinear system is IGASiM and possesses a incremental L2-gain under given conditions. When both IGASiM subsystems and unstable subsystems coexist, if the activation time ratio between IGASiM subsystems and unstable ones is not less than a specified constant, the sufficient conditions for the incremental H∞ performance of the stochastic switched nonlinear system are given. Two numerical examples are given to illustrate the validity of methods proposed.

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACTIn this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.