查看更多>>摘要：Abstract In this article, we propose fixed‐order set‐valued (in the form of ?2$$ {\ell}_2 $$‐norm hyperballs) observers for several classes of quadratically constrained nonlinear dynamical systems with unknown input signals that simultaneously/jointly find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of linear matrix inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for (?,γ$$ \mathcal{M},\gamma $$)‐quadratically constrained ((?,γ$$ \mathcal{M},\gamma $$)‐QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) (??,γ)‐QC* and (III) linear parameter‐varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal ?∞$$ {\mathscr{H}}_{\infty } $$ observer among those that satisfy the quadratic stability conditions and show that the design results in uniformly bounded‐input bounded‐state (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed‐form upper bound sequences for the estimate radii and sufficient conditions for their convergence to steady state. Finally, the effectiveness of the proposed set‐valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.
查看更多>>摘要：Abstract This article mainly discusses the problem for adaptive event‐triggered H∞$$ \infty $$ state estimation of semi‐Markovian jump neural networks (s‐MJNNs) subject to random sensor nonlinearity. To reduce the communication load, adaptive event‐triggered scheme (AETS) is introduced to decide whether to transmit sampled data or not. Also, considering the possible sensor nonlinearity, a new estimation error model is established under the framework of AETS. An appropriate Lyapunov–Krasovskii functional (LKF) containing the proposed adaptive event trigger condition is constructed, and sufficient conditions are obtained to guarantee the asymptotic stability of the estimation error system. Then, through a set of feasible linear matrix inequalities (LMIs), the co‐design method of estimator and AETS is proposed. Finally, the feasibility of this paper is proved by three numerical examples.
查看更多>>摘要：Abstract This article investigates the stability problem of a class of switched nonlinear systems by using the codesign of the switching law, the output feedback controller and the static output feedback based dynamic event‐triggered control (ETC). Each subsystem of such switched systems is allowed to be uncontrollable. The codesign method can not only guarantee asymptotic stability of the origin but also exclude Zeno behavior even if none of subsystems of the closed‐loop systems is stable and the switching can lead to the triggers instantaneously. A sufficient condition of using the above codesign method to ensure asymptotic stability without Zeno behavior is given. In addition, sufficient conditions of using the codesign of the output feedback controller and the static output feedback based dynamic ETC under arbitrary switching signals with dwell time for guaranteeing asymptotic stability and the positive lower bound of the interexecution times are developed even if the switching can result in the triggers instantaneously and some closed‐loop subsystems are still unstable. Further, sufficient conditions of using the codesign method to guarantee asymptotic stability without Zeno behavior under arbitrary switching signals with average dwell time are also developed. Finally, a numerical example is given to illustrate the effectiveness of the results.
查看更多>>摘要：Abstract In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous‐time system by a discrete linear complementarity system (LCS) through the use of the Schatzman–Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity‐based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so‐called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design.
查看更多>>摘要：Abstract This article investigates the fixed‐time adaptive anti‐disturbance and fault‐tolerant control problem for a class of nonlinear multi‐agent systems with non‐affine nonlinear faults. A simplified backstepping approach is presented that only requires designing one Lyapunov function for high‐order multi‐agent systems, which reduces the computational burden. By designing a new compound observer, an anti‐disturbance and fault‐tolerant control strategy is developed to estimate and compensate the compound nonlinear terms composed of external disturbances and nonlinear faults. In addition, an auxiliary control variable is designed to solve the problem of “explosion of complexity” and ensure the system stability in a fixed time. Based on the Lyapunov stability method, it is proved that the nonlinear multi‐agent systems are semi‐global practical fixed‐time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results.
查看更多>>摘要：Abstract This article focuses on the adaptive output feedback fault‐tolerant control (FTC) problem for nonlinear stochastic systems with output constraint. Different from the existing FTC results, the actuator replacement time is considered, which may cause the tracking error to violate the constraint boundaries. First, because only inaccurate output information is available, a dynamic gain‐based reduced‐order K‐filter is designed to reconstruct unmeasurable state variables. Second, by means of a shifting function, a funnel‐like constraint function is proposed to constrain the tracking error into the pre‐given asymmetric constraint boundaries within a predefined time. Third, monitoring function is proposed to detect actuator failures. Once the tracking error violates the monitoring function, it is determined that the actuator failure has occurred, and then the backup actuator driven by the recovery controller will replace the failed actuator. With the help of Lyapunov stability theory, it is strictly proved that all closed‐loop system signals are bounded in probability. Finally, the simulation result is presented to verify the validity of the proposed algorithm.
查看更多>>摘要：Abstract This article is concerned with the sufficient and necessary conditions for the global uniform exponential stability (GUES) of a class of uncertain nonautonomous switched nonlinear systems (UNSNS), that is, systems with time‐varying uncertain information. To start with, based on a piecewise continuous scalar function and a piecewise differentiable uncertainty‐dependent Lyapunov function along the trajectories, we propose alternative sufficient and necessary conditions for the GUES of UNSNS. Afterwards, for removing the dependence on uncertain information of the required Lyapunov functions, we combine an uncertainty‐independent Lyapunov function with its right upper Dini derivative and the above piecewise continuous scalar function to further obtain other alternative sufficient and necessary conditions for the GUES of UNSNS. Note that our conditions release the requirement on negative definiteness of the time‐derivatives and Dini derivatives of Lyapunov functions respectively, which is illustrated by Example 1. Further, for the rational UNSNS, we propose a linear semidefinite programming based computable approach to mechanically verify our current theoretical results. In the end, the effectiveness of our theoretical results and mechanical approach are illustrated by two examples.
查看更多>>摘要：Abstract In this article, a new decentralized adaptive neural output feedback control scheme based on first‐order command filter is proposed for stochastic nonstrict‐feedback interconnected systems with prescribed performance, input quantization, actuator failures and unmodeled dynamics. The unknown smooth functions are eliminated by using the radial basis function neural networks. The immeasurable states in the system are estimated using the decentralized K‐filters, unmodeled dynamics is processed using dynamic signal, and the hyperbolic tangent function is applied to the construction of the prescribed performance function. The hysteretic quantizer and actuator failure are denoted in the form of linearization, and a smoothing function is introduced to compensate for the effects of quantization and bounded stuck faults. Based on the dynamic surface control (DSC) method and using the properties of Gaussian function to deal with stochastic nonstrict‐feedback interconnected systems, the first‐order command filter is used to replace the first‐order filter in the traditional DSC to eliminate the influence of filtering error on the systems, and an error compensation signal is introduced at the recursive each step of the design to construct a new error dynamic surface, which simplifies the derivation process and the design of the controller. Finally, the Lyapunov method is used to prove that all the signals in the whole controlled system are semiglobally uniformly ultimately bounded in probability and the tracking error is within the time‐varying constraint. The effectiveness of the proposed decentralized adaptive control method is verified by a numerical simulation and an example simulation.
查看更多>>摘要：Abstract This article investigates the mean‐square strong stability and stabilization of a discrete‐time stochastic system corrupted by multiplicative noises. First, the definition of the mean‐square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS‐strong stability are derived. Moreover, the relationship between MS‐strong stability and MS‐stability is given. Second, some necessary and sufficient conditions of the MS‐strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.
NSTL
Wiley