Adaptive event‐triggered control for nonlinear discrete‐time systems

This paper focuses on the analysis and the design of event‐triggering scheme for discrete‐time systems. Both static event‐triggering scheme (SETS) and adaptive event‐triggering scheme (AETS) are presented for discrete‐time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event‐triggering condition. The sufficient conditions of asymptotic stability of the closed‐loop event‐triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event‐triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.     

Recursive state estimation for discrete‐time nonlinear systems with event‐triggered data transmission,norm‐bounded uncertainties and multiple missing measurements

In this paper, we consider the recursive state estimation problem for a class of discrete‐time nonlinear systems with event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements. The phenomenon of event‐triggered communication mechanism occurs only when the specified event‐triggering condition is violated, which leads to a reduction in the number of excessive signal transmissions in a network. A sequence of independent Bernoulli random variables is employed to model the multiple measurements missing in the transmission. The norm‐bounded uncertainties that could be considered as external disturbances which lie in a bounded set. The purpose of the addressed filtering problem is to obtain an optimal robust recursive filter in the minimum‐variance sense such that with the simultaneous presence of event‐triggered data transmission, norm‐bounded uncertainties, and multiple missing measurements; the filtering error is minimized at each sampling time. By solving two Riccati‐like difference equations, the filter gain is calculated recursively. Based on the stochastic analysis theory, it is proved that the estimation error is bounded under certain conditions. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Design and implementation of a block‐backstepping based tracking control for nonholonomic wheeled mobile robot

This paper presents formulation of a novel block‐backstepping based control algorithm to overcome the challenges posed by the tracking and the stabilization problem for a differential drive wheeled mobile robot (WMR). At first, a two‐dimensional output vector for the WMR has been defined in such a manner that it would decouple the two control inputs and, thereby, allow the designer to formulate the control laws for the two inputs one at a time. Actually, the decoupling has been carried out in a way to convert the system into block‐strict feedback form. Thereafter, block‐backstepping control algorithm has been utilized to derive the expressions of the control inputs for the WMR system. The proposed block‐backstepping technique has further been enriched by incorporating an integral action for enhancing the steady state performance of the overall system. Global asymptotic stability of the overall system has been analyzed using Lyapunov stability criteria. Finally, the proposed control algorithm has been implemented on a laboratory scale differential drive WMR to verify the effectiveness of the proposed control law in real‐time environment. Indeed, the proposed design approach is novel in the sense that it has judiciously exploited the nonholonomic constraint of the WMR to result in a reduced order block‐backstepping controller for the WMR, and thereby, it has eventually yielded a compact expression of the control law that is amenable to real‐time implementation. Copyright © 2015 John Wiley & Sons, Ltd.     

A Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems

This paper studies a Lyapunov‐based small‐gain approach on design of triggering conditions in event‐triggered control systems. The event‐triggered control closed‐loop system is formulated as a hybrid system model. Firstly, by viewing the event‐triggered control closed‐loop system as a feedback connection of two smaller hybrid subsystems, the Lyapunov‐based small‐gain theorems for hybrid systems are applied to design triggering conditions. Then, a new class of triggering condition, the safe, adjustable‐type triggering condition, is proposed to tune the parameters of triggering conditions by practical regulations. This is conducive to break the restriction of the conservation of theoretical results and improve the practicability of event‐triggered control strategy. Finally, a numerical example is given to illustrate the efficiency and the feasibility of the proposed results. Copyright © 2015 John Wiley & Sons, Ltd.     

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

This paper studies the problems of stabilization of discrete‐time linear systems with a single input delay. By developing the methodology of pseudo‐predictor feedback, which uses the (artificial) closed‐loop system dynamics to predict the future state, memoryless state feedback control laws are constructed to solve the problem. Necessary and sufficient conditions are obtained to guarantee the stability of the closed‐loop system in terms of the stability of a class‐difference equations. It is also shown that the proposed controller achieves semi‐global stabilization of the system if its actuator is subject to either magnitude saturation or energy constraints under the condition that the open‐loop system is only polynomially unstable. Numerical examples have been worked out to illustrate the effectiveness of the proposed approaches. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐global and global containment control of multi‐agent systems with second‐order dynamics and input saturation

This paper considers both semi‐global and global containment control for a second‐order multi‐agent system that is composed by a network of identical harmonic oscillators or double integrators with multiple leaders and input saturation. A distributed low gain feedback algorithm is proposed to solve the semi‐global containment control problem for the network whose topology is directed and initial condition is taken from any a priori given bounded set. In particular, by using a parametric Lyapunov equation approach, M‐matrix properties and algebraic graph theory, an upper bound of the low gain parameter is estimated such that the low gain feedback matrix can be analytically determined without involving numerical computation. Furthermore, under the assumption that the induced subgraph formed by the followers is strongly connected and detail balanced, two linear feedback protocols are designed for coupled harmonic oscillators and coupled double integrators, respectively, to asymptotically achieve the global containment control of the network with any initial condition. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Controller design and analysis for singularly perturbed switched systems with actuator saturation

This paper investigates the problems of controller design and stability analysis for singularly perturbed switched systems subject to actuator saturation. A set of well‐defined sufficient conditions for the existence of state feedback controllers is proposed, under which the closed‐loop system is locally asymptotically stable for arbitrary switching law as long as the singular perturbation parameter is sufficiently small. With the obtained controller, the estimation problem of stability bound and basin of attraction of the closed‐loop system is reduced to solving a convex optimization problem. A numerical example and a hydraulic servo position system are used to illustrate the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

The presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez–Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez‐Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez–Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non‐Gaussian distributions, is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive actuator failure compensation for multivariable feedback linearizable systems

A feedback linearization‐based adaptive control scheme is developed for multivariable nonlinear systems with redundant actuators subject to uncertain failures. Such an adaptive controller contains a direct adaptive actuator failure compensator to compensate the uncertain actuator failure, a nonlinear feedback to linearize the nonlinear dynamics, and a linear feedback to stabilize the linearized system. The key new design feature is the estimation of both the failure patterns and the failure values, for direct adaptive actuator failure compensation, newly developed for multivariable feedback linearizable nonlinear systems. With direct control signal adaptation, the adaptive failure compensation design ensures closed‐loop stability and asymptotic output tracking in the presence of actuator failure uncertainties. Simulation results from an application to attitude control of a near‐space vehicle dynamic model are presented to verify the desired system performance with adaptive actuator failure compensation. Copyright © 2015 John Wiley & Sons, Ltd.     

The design and test of dual/triple‐mode bandpass filter based on temporal coupled‐mode theory

In this article, the design and test of both a K‐band dual‐mode bandpass filter (BPF) pair and a K‐band triple‐mode BPF are presented based on N‐mode temporal coupled‐mode theory (CMT). The expressions of transmission and reflection responses are analytically derived. All the parameters in the expressions have clear physical meanings and are easily optimized to reach the required filter performance. Aided by eigenmode simulations, concrete structures of the three integrated BPFs are designed and optimized to approach the calculated physical parameters. After the fabrications and measurements of the three BPFs, extended upper/lower stopband with high stopband rejections are achieved, and by increasing the number of resonant modes, improved frequency selectivity and better passband flatness are obtained. The analytical analysis well predicts the simulation and measurement results, which provides an efficient way for BPF designs. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:609–622, 2016.