Decentralized adaptive synchronization with bounded identification errors for discrete-time nonlinear multi-agent systems with unknown parameters and unknown high-frequency gains

This paper addresses the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-agent systems, in which each agent is described by a nonlinearly parameterized uncertain model in discrete time and can interact with its neighbors via the history information from its neighbors. One of the agents is a leader, who knows the desired reference trajectory, while other agents cannot receive the desired reference signal or are unaware of existence of the leader. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-type parameter estimation algorithm is proposed. Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, it is shown that the multi-agent system eventually achieves synchronization in the presence of strong couplings. Finally, a simulation example is given to support the results of the proposed scheme.     

Dissipative observers for discrete-time nonlinear systems

This paper addresses the problem of designing a state observer for a class of nonlinear discrete-time systems using the dissipativity theory. We show that the dissipative observation methodology, originally proposed by one of the authors for continuous-time nonlinear systems, can be extended to the discrete-time case. For constructing a convergent observer, the methodology is applied to the nonlinear estimation error dynamics, which is decomposed into a discrete-time Linear Time-Invariant (LTI) subsystem in the forward loop, connected to a time-varying static nonlinearity in the feedback loop. In order to assure asymptotic stability of the closed-loop, complementary dissipativity conditions are imposed on each of the subsystems: (i) the static nonlinearity is required to be dissipative with respect to a quadratic supply rate, and (ii) the observer gains are designed such that the LTI system is dissipative with respect to a complementary supply rate. As in the continuous time framework, the proposed method includes as special cases, unifies and generalizes some observer design methods proposed previously in the literature. A great advantage of the Dissipative Observer Design Method proposed here is that it leads to Matrix Inequalities for the design of the observer gains, and these can be usually converted into Linear Matrix Inequalities (LMI’s). The results are illustrated using Chua’s Chaotic system.     

Adaptive tracking control for nonlinear heterogeneous multi-agent systems with unknown dynamics

This paper is concerned with the tracking control problem for nonlinear heterogeneous multi-agent systems with a static leader, where the leader’s state is only available to a small portion of follower agents. The considered multi-agent system is composed of first- and second-order follower agents with unknown nonlinearities and unknown disturbances, and the communication graph of follower agents is fixed and directed. A robust adaptive neural network controller is designed for each follower agent. By applying the Lyapunov theory with the singular value analysis method, it is shown that all follower agents will synchronize to the leader agent with bounded residual errors. A numerical example is presented to demonstrate the effectiveness of the theoretical findings.     

Observer design for a class of nonlinear fractional-order systems with unknown input

A full order fractional-order observer is designed for a class of Lipschitz continuous-time nonlinear fractional-order systems with unknown input. Sufficient conditions of existence for the designed observer and stability of state estimation error system are developed by reconstructing state and using general quadratic Lyapunov function. By applying fractional-order extension of Lyapunov direct method, the stability of the fractional-order state estimation error system is analyzed. Due to the conditions involving a nonlinear matrix inequality, a new sufficient condition with linear matrix inequality (LMI) is reformulated, which makes the full order fractional-order observer implemented easily by using Matlab LMI toolbox. Examples are taken to show the effectiveness of the proposed approach by numerical simulations.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Moving horizon estimation for multirate systems with time-varying time-delays

This paper presents a moving horizon estimation approach for the multirate sampled-data system with unknown time-delay sequence. To estimate the unknown variables of interest, two main challenging issues need to be addressed: (a) synthesizing the multirate input and output data for state estimation, (b) simultaneously estimating the continuous state and discrete time-delay sequence. In this work a moving horizon estimation based approach is developed to tackle these issues. The proposed approach can simultaneously estimate both the continuous states and discrete time-delay sequence for dynamic systems. The effects of different noise level on the estimation of continuous states and discrete time-delay sequence are analyzed. The effectiveness of this method is illustrated through a simulation study.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

Terminal iterative learning control for discrete-time nonlinear systems based on neural networks

The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms.     

Adaptive finite-time control for stochastic nonlinear systems subject to unknown covariance noise

This paper is devoted to the adaptive finite-time control for a class of stochastic nonlinear systems driven by the noise of covariance. The traditional growth conditions assumed on the drift and diffusion terms are removed through a technical lemma, and the negative effect generated by unknown covariance noise is compensated by combining adaptive control technique with backstepping recursive design. Then, without imposing any growth assumptions, a smooth adaptive state-feedback controller is skillfully designed and analyzed with the help of the adding a power integrator method and stochastic backstepping technique. Distinctive from the global stability in probability or asymptotic stability in probability obtained in related work, the proposed design algorithm can guarantee the solution of the closed-loop system to be finite-time stable in probability. Finally, a stochastic simple pendulum system is skillfully constructed to demonstrate the effectiveness of the proposed control scheme.     

Fuzzy adaptive control of nonlinear MIMO systems with unknown dead zone outputs

This paper addresses a novel fuzzy adaptive control method for a class of uncertain nonlinear multi-input multi-output (MIMO) systems with unknown dead-zone outputs and immeasurable states. The immeasurable states under consideration are estimated by designing a fuzzy state observer. Based on the properties of the Nussbaum-type function, the difficulty of fuzzy adaptive control caused by the unknown dead zone outputs of MIMO nonlinear uncertain systems is overcome. The presented design algorithm not only guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, but also ensures that the outputs of the MIMO system converge to a small neighborhood of the desired outputs. The main contributions of this research lie in that the developed MIMO systems are more general, and an efficient design method of output-feedback controller is investigated for the studied MIMO systems, which is more applicable in practical environment. Simulation results illustrate the effectiveness of the proposed scheme.     

Decentralized low-complexity tracking of uncertain interconnected high-order nonlinear systems with unknown high powers

A global decentralized low-complexity tracker design methodology is proposed for uncertain interconnected high-order nonlinear systems with unknown high powers. It is assumed that interconnected nonlinearities are bounded by completely unknown nonlinearities, rather than, a linear combination of high-ordered state variables. Compared with the existing decentralized results for interconnected nonlinear systems with known high powers, the decentralized robust controller, which achieves the pre-designable transient and steady-state tracking performance for each subsystem, is designed by employing nonlinear error surfaces with time-varying performance functions, regardless of unknown nonlinear interactions and high powers related to virtual and actual control variables. The proposed decentralized continuous robust low-complexity tracker is realized without the use of any adaptive or function approximation techniques for estimating unknown parameters and nonlinearities. The stability and preassigned tracking performance of the resulting decentralized low-complexity control system are thoroughly analyzed in the Lyapunov sense. Finally, simulation results on coupled underactuated mechanical systems are provided to show the effectiveness of the proposed theoretical result.     

Stability analysis of linear continuous-time delay-difference systems with multiple time-delays

This paper is concerned with the stability analysis of linear continuous-time delay-difference systems with multiple delays. Firstly, a new method for testing the L₂-exponential stability of the considered system is proposed, which is easier to use than the one in the existing literature. In view of the conservatism and the complexity of the obtained stability conditions in the existing literature, a complete Lyapunov–Krasovskii functional (LKF) is constructed by analyzing the relationship among the multiple delays. Sufficient conditions for both L₂-exponential stability and exponential stability are then derived based on the constructed LKFs, which are delay-independent. Exponential convergence rate for the considered system is also investigated by a new method, which is shown to be equivalent to the existing approach by using weighted LKFs. Robust stability under parameter uncertainties is also investigated. Numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed method.     

Reachable set estimation for discrete-time bilinear systems with time-varying delays

The problem of reachable set estimation is studied for discrete-time bilinear system in this paper. Time-varying delays and bounded input disturbances are both considered in bilinear system. The aim is to find reachable set that converges from all the states of system with initial conditions. By constructing Lyapunov–Krasovskii functional, sufficient delay-dependent less conservative stable conditions of reachable set estimation are obtained for bilinear delay system via the reciprocally convex combination and delay partition approaches. The derived theorem can guarantee that all the states of system with initial conditions from some domain are bounded in an ellipsoid and all the states from other domain are converged exponentially within a ball. One simulation example is presented to illustrate the correctness of the derived result in this paper.     

Output reachable set estimation for discrete-time switched systems with persistent dwell-time

This paper is concerned with the output reachable set estimation for discrete-time switched systems. The switching signal is considered as persistent dwell-time (PDT), which is more general and flexible compared with the common dwell-time and average dwell-time switching. The estimation of output reachable set is determined by a collection of bounding ellipsoids based on a family of quasi-time-dependent (QTD) Lyapunov functions. Furthermore, a set of non-fragile QTD controllers is designed. Finally, two examples are employed to illustrate the potentials of proposed methods.     

Controller design for discrete-time hybrid linear parameter-varying systems with semi-Markov mode switching

The paper is concerned with the stability and stabilization problems for a family of hybrid linear parameter-varying systems with stochastic mode switching. The switching phenomenon is modeled by a semi-Markov stochastic process which is more generalized than a Markov stochastic process. With the construction of a Lyapunov function that depends on both the parameter variation and operating mode, numerical testable stability and stabilization criteria are established in the sense of σ-error mean square stability with the aid of some mathematical techniques that can eliminate the terms containing products of matrices. To test the effectiveness of the designed stabilizing controller, we apply the developed theoretical results to a numerical example.     

Distributed MPC-based adaptive control for linear systems with unknown parameters

This paper is concerned with the adaptive control problem for a class of linear discrete-time systems with unknown parameters based on the distributed model predictive control (MPC) method. Instead of using the system state, the state estimate is employed to model the distributed state estimation system. In this way, the system state does not have to be measurable. Furthermore, in order to improve the system performance, both the output error and its estimation are considered. Moreover, a novel Lyapunov functional, comprised of a series of distributed traces of estimation errors and their transposes, has been presented. Then, sufficient conditions are obtained to guarantee the exponential ultimate boundedness of the system as well as the asymptotic stability of the error system by solving a nonlinear programming (NP) problem subject to input constraints. Finally, the simulation examples is given to illustrate the effectiveness and the validity of the proposed technique.     

Discrete Razumikhin-type stability theorems for stochastic discrete-time delay systems

By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.