Abstracts:The sampled-data event-triggered control problem of switched linear systems in which both the sampled information of the system states and the switching signal are available to the controller at the event-triggered transmission instants is studied here. The coexistence of the event-triggered transmission and the switching behaviour makes the switching signal of the controller and the switching signal of the system asynchronous. By constructing a new multiple Lyapunov–Krasovskii functional and using the asynchronous switching method, the exponential stability conditions characterised by mode-dependent average dwell time of the switching signal are proposed. Then, the corresponding solvability conditions for the event-triggered state feedback controller are formulated. Finally, a numerical example is given to illustrate the validity of the proposed results.

Abstracts:The tracking consensus problem for stochastic Markovian multi-agent systems (MASs) with mismatched uncertainty is investigated in this study. A restrictive assumption for stochastic systems in existing results is removed in this study. Under the directed interacted topology, the sliding mode control method is utilised to achieve leader-following consensus for general linear MASs in the sense of mean square. Integral sliding mode surfaces are employed to tackle the mismatched uncertainties. Then, with the transition rates of Markov process being completely known or partly unknown, two kinds of distributed sliding mode protocols are given, respectively. Based on the sliding mode control theory, algebraic graph theory and stochastic differential equation theory, mean square stability of sliding mode dynamics are ensured by LMIs and reachability of sliding mode surfaces almost surely from the initial time are obtained. Finally, simulations are given to illustrate the effectiveness of the results.

Abstracts:This study discusses the parameter estimation of the Hammerstein output-error moving average system using the dual-rate sampled data. The polynomial transformation technique is used to obtain the identification model of the discussed dual-rate sampled systems. The stochastic gradient optimisation method is an effective optimisation method. Compared with the Newton optimisation, it only needs to calculate the first derivative during the optimisation and the amount of calculation is relatively small. It is a good choice to use the stochastic gradient algorithm for the identification of Hammerstein dual-rate model after using the polynomial transformation technique. In order to improve the convergence speed, a maximum likelihood forgetting factor stochastic gradient identification algorithm is proposed by combining the maximum likelihood principle and the gradient search method. The convergence of the algorithm is analysed by using the stochastic process theory. Furthermore, in order to improve the estimation accuracy of the identification algorithm, a maximum likelihood multi-innovation forgetting factor stochastic gradient algorithm is proposed by using the multi-innovation identification theory. The effectiveness of the proposed algorithms is illustrated by a numerical simulation example and a water tank system.

Abstracts:When designing interval observers for switched systems, for simplicity, it is always assumed that the switching signal of interval observers is synchronised with one of subsystems. However, in fact, they are asynchronous in most cases. In this study, the interval observer design problem for discrete-time switched systems with asynchronous switching law is investigated. At first, a robust observer is designed based on the H_∞ observer theory. Then, in order to reduce the conservatism of design conditions and improve the performance of the interval observer, the zonotope method is applied to estimate the bounds of system state. Finally, two examples are provided to highlight the efficiency of the proposed method.

Abstracts:This study proposes a robust tracking controller for an underactuated quadrotor model based on the flatness theory and active disturbance rejection control (ADRC). Exploiting the differential flatness characteristic, it is demonstrated that a non-linear quadrotor system can be changed into a linear canonical form, where it is easier to create a state feedback controller that ensures accurate trajectory tracking. In order to improve the tracking performance of the quadrotor, other factors are considered in the conception of the state feedback controller consisting in the estimation of the un-measurable state variables in a canonical (Brunovsky) form and in the elimination of external perturbations and modelling uncertainties affecting the quadrotor system. To deal with this problem, first, an extended state observer (ESO) is designed to estimate a system state and an extended state known as lumped uncertainties. The latter represents the total effects of uncertain parameters, the neglected part of non-linearity and the external disturbances. Second, based on the ESO result, an additional term is integrated into the feedback controller to eliminate the lumped disturbance effects and to ensure the stability of the closed loop. Simulation results are introduced to prove the benefits of associating the ADRC approach with flatness control.

Abstracts:For valve-controlled hydraulic servo system, the suppression of mechanical dynamics uncertainties and the analysis of internal pressure dynamics stability (i.e. the pressure into the two chambers of the actuator) are still the widespread concern issues. This study presents an easy-to-implement observer-based output feedback control scheme for hydraulic valve-controlled single-rod actuator system with addressing mismatched mechanical dynamic uncertainties and proving internal pressure dynamics stability analysis. The singular value perturbation approach is used to simplify the system model, and then a practical output feedback controller augmented with extended-state observer is developed through back-stepping design approach. The main contribution of this study is two-fold. First, a practical reduced-order model-based back-stepping controller is developed. Second, the stability issue of internal pressure dynamics is analysed. Besides giving theoretical analysis, extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method. The present method can guarantee prescribed tracking transient performance in the presence of uncertain disturbances. Also, the stability of internal dynamics is proved.

Abstracts:This study addresses the finite-time non-fragile sampled-data control for a Takagi-Sugeno (T-S) fuzzy system with passivity and passification approaches. Firstly, a new finite-time boundedness (FTB) condition is acquired for the considered system by using a Lyapunov-Krasovskii functional and inequality approaches. Secondly, finite-time passivity (FTP) conditions are achieved to ensure that the T-S fuzzy system is not only FTB but also finding passivity performance index. Moreover, under the FTP conditions, the non-fragile sampled-data controller is designed for linear matrix inequalities to achieve the stability conditions of the considered system. Finally, the corresponding simulation results for the application examples related to a permanent magnet synchronous motor system, truck trailer system, and Lorenz system are applied to verify the performance of the proposed design method.

Abstracts:This study investigates the admissibility analysis and stabilisation problems for singular interval type-2 Takagi-Sugeno fuzzy systems with time delay. A generalised integral inequality method is used to obtain the delay-dependent condition. The criteria for admissibility analysis and controller synthesis are given in terms of linear matrix inequalities. In order to reduce the conservatism of the system, some free weighting matrices and advanced integral inequalities are introduced. Finally, two illustrative examples are exhibited to demonstrate the effectiveness of the proposed method.

Abstracts:This study is concerned with the event-triggered finite-time control of periodic systems via a piecewise method. The continuous-time periodic system is formulated by finite-number linear time-invariant subsystems, of which the system parameters are determined by the piecewise approximation method. In consideration of the mitigation of network communication in networked control loops, some event-triggering mechanisms are designed in terms of the networks between the sensor (or controller) and the controller (or actuator). Three different event-triggered control schemes are designed for the networked periodic system. The finite-time stability of the resulting closed-loop system is analysed by using a Lyapunov function approach with a well-defined matrix-valued function. The controller gains depending on the piecewise parameters are thus designed with several matrix inequalities that can be solved by off-line procedures. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design scheme.