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1.
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form, which are treated in analogy with robust constraints, by using the probabilistic reachable set. The first one is the time-varying tube-based stochastic model predictive control algorithm, which is designed by employing the time-varying probabilistic reachable sets as tubes. The second one is the constant tube-based stochastic model predictive control algorithm, which is developed by enforcing a constant tightened constraint in the entire prediction horizon. In addition, the soft constraints are proposed to associate with the state initialization in the algorithms to enhance the feasibility. The algorithm feasibility and closed-loop stability results are provided. The efficacy of the approaches is demonstrated by means of numerical simulations.  相似文献   

2.
This work is concerned with the problem of reachable set synthesis for a class of singular systems with time-varying delay via the adaptive event-triggered scheme. Compared with the static event-triggered mechanism, the adaptive event-triggered mechanism can save the communication resources more effectively. By virtue of Lyapunov stability theory, sufficient conditions are given to guarantee the stability of the closed-loop system and that the reachable set of the resulting system is bounded by the obtained ellipsoid. In addition, by using linear matrix inequality technique and free-weighting matrix method, the weighting matrix of event-triggered condition and proportional-derivative (P-D) feedback controller gains are obtained. The effectiveness and superiority of the developed control approach are substantiated by a numerical example and two practical examples.  相似文献   

3.
This paper is concerned with the problems of set-based finite-time stability (SFTS) and set-based finite-time boundedness (SFTB) for both certain and uncertain linear time-varying systems. The concepts of SFTS and SFTB are defined. Different from existing results, sufficient conditions for SFTS and SFTB are directly derived from the basic definitions of finite-time stability (FTS) and finite-time boundedness (FTB) by using the convex hull technique rather than utilizing the weighted quadratic functions. Thus, more practical constraints on the system states can be dealt with. Furthermore, intervals, zonotopes and polytopes are employed to describe the typical compact convex sets. For linear uncertain systems, the uncertain time-varying state sets are assumed to be represented by interval matrices and matrix zonotopes, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the main results.  相似文献   

4.
This paper is concerned with the robust stability of uncertain neutral-type Lur?e system with time-varying delays and sector bounded nonlinearities. By constructing a modified Lyapunov–Krasovskii functional (LKF), some new robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) without using the general free-weighting matrix method. The criteria are less conservative and more efficiently calculative than some previous ones. Four numerical examples are presented to show the effectiveness and merits of the proposed approach.  相似文献   

5.
This paper is concerned with robust stability analysis of second-order linear time-varying (SLTV) systems with time-varying uncertainties (perturbations). With the specific Lyapunov functions, a simple and neat algebraic criterion for testing uniformly asymptotic stability of SLTV systems are derived. Without transformation to a system of first-order equations, the new conditions are imposed directly on the time-varying coefficient matrices of the system. The main feature of the proposed algebraic criterion is that the uncertain coefficient matrices are time-varying and not necessarily symmetric. Finally, the proposed stability conditions are used to design the extending space structures system of the spacecraft. Simulation results are provided to illustrate the convenience and effectiveness of the proposed method.  相似文献   

6.
In this paper, a robust adaptive control scheme is proposed for the leader following control of a class of fractional-order multi-agent systems (FMAS). The asymptotic stability is shown by a linear matrix inequality (LMI) approach. The nonlinear dynamics of the agents are assumed to be unknown. Moreover, the communication topology among the agents is assumed to be unknown and time-varying. A deep general type-2 fuzzy system (DGT2FS) using restricted Boltzmann machine (RMB) and contrastive divergence (CD) learning algorithm is proposed to estimate uncertainties. The simulation studies presented indicate that the proposed control method results in good performance under time-varying topology, unknown dynamics and external disturbances. The effectiveness of the proposed DGT2FS is verified also on modeling problems with high dimensional real-world data sets.  相似文献   

7.
In this study, the stabilizability irrespective of the bounds of uncertain parameters and time delays is investigated for linear uncertain delay systems. For uncertain systems without delays, a linear time-varying or time-invariant uncertain system has been shown to be stabilizable independent of the bounds of uncertain variations if and only if the system has a particular geometric configuration called an antisymmetric stepwise configuration (ASC) or a generalized antisymmetric stepwise configuration (GASC), respectively. In this study, fundamental approaches to investigating the stabilizability of delay systems with specific uncertainty structures such as ASCs or GASCs are presented. For a class of 3-dimensional systems, it is shown here that if a linear time-varying or time-invariant uncertain delay system has an ASC or a GASC, respectively, then the system can be stabilized, however large the given bounds of delays and uncertain parameters might be.  相似文献   

8.
In this paper, we study the consensus tracking control problem of a class of strict-feedback multi-agent systems (MASs) with uncertain nonlinear dynamics, input saturation, output and partial state constraints (PSCs) which are assumed to be time-varying. An adaptive distributed control scheme is proposed for consensus achievement via output feedback and event-triggered strategy in directed networks containing a spanning tree. To handle saturated control inputs, a linear form of the control input is adopted by transforming the saturation function. The radial basis function neural network (RBFNN) is applied to approximate the uncertain nonlinear dynamics. Since the system outputs are the only available data, a high-gain adaptive observer based on RBFNN is constructed to estimate the unmeasurable states. To ensure that the constraints of system outputs and partial states are never violated, a barrier Lyapunov function (BLF) with time-varying boundary function is constructed. Event-triggered control (ETC) strategy is applied to save communication resources. By using backstepping design method, the proposed distributed controller can guarantee the boundedness of all system signals, consensus tracking with a bounded error and avoidance of Zeno behavior. Finally, the correctness of the theoretical results is verified by computer simulation.  相似文献   

9.
In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.  相似文献   

10.
This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.  相似文献   

11.
In this paper, we consider the problem of finding an ellipsoidal bound of reachable sets for neutral systems with bounded peak disturbances. Up to now, the result related to the ellipsoidal bound of reachable sets was rarely proposed for linear neutral systems. Based on the modified augmented Lyapunov-Krasovskii type functional, we obtain some delay-dependent results expressed in the form of matrix inequalities containing only one non-convex scalar. Furthermore, a modified integral inequality is used to remove the limitation on the variation rate of the delay. Numerical examples are given to indicate significant improvements over some existing results.  相似文献   

12.
This work deals with the problem of absolute stability analysis for a class of uncertain Lur’e systems with time-varying delays. Novel delay-partitioning approaches are presented, which are dividing the variation interval of the delay into three subintervals. Some new augment Lyapunov–Krasovskii functionals (LKFs) are defined on each of the obtained subintervals which can efficiently make use of the information of the delay and relate to the reciprocally convex combination technique and the Wirtinger-based integral inequality method. Several improved delay-dependent criteria are derived in terms of the linear matrix inequalities (LMIs). The merit of the proposed criteria lies in their less conservativeness and lower numerical complexity than relative literature. Two numerical examples are included to illustrate the effectiveness and the improvement of the proposed method.  相似文献   

13.
The robust stochastic convergence in mean square is investigated for a class of uncertain Cohen–Grossberg neural networks with both Markovian jump parameters and mode-dependent time-varying delays. By employing the Lyapunov method and a generalized Halanay-type inequality, a delay-dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a pre-specified convergence rate. After some parameters being fixed in advance, the proposed conditions are all in terms of linear matrix inequalities, which can be solved numerically by employing the LMI toolbox in Matlab. Finally, an illustrated example is given to show the effectiveness and usefulness of the obtained results.  相似文献   

14.
The problem of the reachable set (RS) control of sliding mode control (SMC) for a class of singular systems with or without time-varying delay under zero initial conditions is studied. The purpose is to get an RS boundary containing all states of the system by designing an SMC. Firstly, singular systems with or without time-varying delay are decomposed into slow and fast subsystems by using the decomposition approach. Then, the augmented Lyapunov functional is built utilizing the decomposed state vector. The SMC is designed based on the exponential reaching criterion, resulting in the corresponding closed-loop control system (CLCS) construction. As a consequence, an RS criterion is constructed by employing the inequality scaling approach and the free-weighting matrix in conjunction with the linear matrix inequality (LMI). Finally, the validity and primacy of the results are provided by two numerical and practical examples.  相似文献   

15.
This paper focuses on the problem of robust H∞ filter design for uncertain systems with time-varying state and distributed delays. System uncertainties are considered as norm-bounded time-varying parametric uncertainties. The delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A new delay-derivative-dependent approach of filter design for the systems is proposed. A novel Lyapunov-Krasovskii functional (LKF) is employed, and a tighter upper bound of its derivative is obtained by employing an inequality and using free-weighting matrices technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is established in terms of linear matrix inequality (LMI). Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed method.  相似文献   

16.
This paper addresses the reachable sets bounding problem for time-delay positive singular systems subject to bounded disturbances. The time delays in the considered systems are assumed to be time-varying. Both invariant and time-varying singular systems are investigated in this paper. Existence conditions of componentwise ultimate bounds of the state vector of considered systems are derived and given in terms of the spectral abscissa of the system matrices, which are easy to be checked. The obtained results are demonstrated by two numerical examples.  相似文献   

17.
This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model.  相似文献   

18.
This paper studies the stability analysis of linear systems with time-varying delay, which is supposed to be the trigonometric form. By utilizing the characteristics between time-varying delay and its derivative, a novel interval approximation method is proposed, which provides the new allowable delay sets. Then making use of Wirtinger inequality, reciprocally convex inequality and the looped Lyapunov–Krasovskii functionals, the stability criteria with less conservatism are obtained. Finally, two examples are used to show the effectiveness and efficiency of the stability criteria.  相似文献   

19.
In this paper, we first deal with the robust stability of uncertain linear stochastic differential delay systems. The parameter uncertainties are time-varying and unknown but are norm-bounded via two types of uncertainties, and the delays are time invariant. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems. These results are given in terms of linear matrix inequalities. Two examples are presented to illustrate the effectiveness.  相似文献   

20.
This note focuses on the robust stabilization of discrete-time fuzzy uncertain systems with time-varying delays under a delayed nonparallel distributed compensation scheme. The key idea is twofold: first, the linear matrix inequalities (LMI) proposed here are shown to generalize some previous similar results available in recent literature, and second, the design of control parameters is decoupled from the proposed fuzzy-basis dependent Lyapunov–Krasovskii functional (FBDLKF) by means of Finsler?s lemma. Finally, a numerical example is provided to illustrate the effectiveness of this method.  相似文献   

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