Adaptive Fault‐Tolerant Attitude Tracking Control of Rigid Spacecraft on Lie Group with Fixed‐Time Convergence

This paper investigates the fixed‐time attitude tracking problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The logarithm map is first utilized to transform the tracking problem on SO(3) into the stabilization one on its associated Lie algebra ( ). A novel nonsingular fixed‐time‐based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault‐tolerant control law is constructed, in which an online adaptive law is incorporated to estimate the upper boundary of the lumped uncertainties. The combined control scheme enforces the system state to reach a neighborhood of the sliding surface in the sense of the fixed‐time concept. The key feature of the resulting control scheme is that it can accommodate actuator failures under limited control torque without the knowledge of fault information. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed fixed‐time controllers.     

Dynamic event-triggered dissipative control of nonlinear networked control systems with deception attacks

For nonlinear networked control systems with deception attacks, the problem of dynamic event-triggered dissipative control is researched in this article. First, on the basis of nonlinear networked control systems model, a dynamic event triggered scheme is proposed to save impact of network bandwidth. Second, considering the impact of time delay, a networked time-delay system model under deception attacks is established. Third, by constructing a new and less conservative Lyapunov function, using linear matrix inequality and unilateral Lipschitz condition, we derive some new sufficient conditions to guarantee the asymptotically stability of nonlinear networked control systems and strictly $({\mathrm{\mathbb{Q}}}_1,{\mathrm{𝕊}}_1,{\mathrm{ℝ}}_1)$-dissipative performance. Besides, a cooperative design strategy of dynamic event triggered scheme parameters and controller gain is put forward. Finally, a simulation example is given to prove feasibility and rationality of the proposed strategy.     

Network‐based robust event‐triggered control for continuous‐time uncertain semi‐Markov jump systems

This article investigates the event‐triggered (ET) states feedback robust control problem for a class of continuous‐time networked semi‐Markov jump systems (S‐MJSs). An ET scheme, which depends on semi‐Markov process, is presented to design a suitable controller and save communication resources. To cope with the network transmission delay phenomenon, a time‐delay S‐MJSs model under the ET scheme is introduced to describe this phenomenon. Then, it is assumed that the communication links between event detector and zero‐order holder are imperfect, where the signal quantization and the actuator fault occur simultaneously. The sufficient conditions are derived by means of linear matrix inequalities approach, which guarantees the stochastic stability of the constructed time‐delay S‐MJSs in an optimized performance level. Based on these criteria, the parameters of controller under the ET scheme are readily calculated. Some simulation results with respect to F‐404 aircraft engine system for two kinds of ET parameters are given to validate the proposed method.     

Set stabilization of boolean networks via sampled‐data control

The paper investigates the sampled‐data state feedback control (SDSFC) for set stabilization of Boolean control networks (BCNs). Set stabilization means that a system converges to a subset of the state space under certain controllers. Assume that the given subset is , where and sampling period is τ. We consider two conditions q ≤ τ;q > τ and for any given subset , calculate the corresponding largest control invariant subset (LCIS). Moreover, a design procedure to calculate all possible SDSFCs for set stabilization of BCNs is obtained. Ultimately, we provide an example to demonstrate the efficiency of the results.     

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile performance, non‐fragile performance, non‐fragile passive performance, non‐fragile mixed and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system.     

Robust Adaptive Dynamic Surface Control for a Class of MIMO Nonlinear Systems with Unknown Non‐Symmetric Dead‐Zone

This paper is devoted to adaptive output tracking for a class of multi‐input multi‐output nonlinear systems with unknown non‐symmetric dead‐zone. With the aid of a matrix factorization and a similarity transformation, a robust adaptive dynamic surface control scheme is proposed and the difficulty caused by the control gain matrix and the dead‐zone is circumvented. By introducing a surface error modification and an initialization technique, we show that the performance of the tracking errors can be guaranteed. Moreover, the proposed scheme contains only one updated parameter at each design step, which significantly reduces the computational burden. It is proven that all signals of the closed‐loop system are semi‐globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme.     

Low Frequency Sensitivity Function Constraints for Nonlinear ‐stable Networked Control

The paper derives a robust networked controller design method for systems with saturation where the delay is large and uncertain, as in one‐directional data flow‐control. A classical linear H_∞ criterion is first formulated in terms of the sensitivity and complementary sensitivity functions. A new asymptotic constraint is then derived, which specifies the minimum amount of low frequency gain that is needed in the sensitivity function to conclude on non‐linear closed loop ‐stability using the Popov criterion. This result guides the selection of the design criterion, thereby adjusting the linear controller design for better handling of delay and saturation. The controller design method then uses gridding to pre‐compute a subset of the stability region. Based on the pre‐computed region, a robust ‐stable controller can be selected. Alternatively, an adaptive controller could recompute ‐stable controllers on‐line using the pre‐computed region. Simulations show that the controller meets the specified stability and performance requirements.     

Non‐Fragile Observer‐Based Control for Uncertain Neutral‐Type Systems via Sliding Mode Technique

This paper is concerned with the problem of observer‐based control for a class of uncertain neutral‐type systems subjected to external disturbance by utilizing sliding mode technique. A novel sliding mode control (SMC) strategy is proposed based on the state estimate and the output. A new sufficient condition of robust asymptotic stability with disturbance attenuation level for the overall systems composed of the original system and error system in the sliding mode is derived in terms of a linear matrix inequality (LMI). Then, a new adaptive controller is designed to guarantee the reachability of the predefined sliding surface in finite‐time. Finally, numerical examples are provided to verify the effectiveness of the proposed method.     

Dynamic Output‐Feedback Control for T‐S Fuzzy Systems with Input Time‐Varying Delay

This paper considers the problem of the control for T‐S fuzzy systems with input time‐varying delay via dynamic output feedback. Firstly, by applying the reciprocally convex approach, new delay‐dependent sufficient condition for performance analysis is obtained. Then, a less conservative condition for the existence of the controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in the considered system, the time‐delay term is included in the measured output. This results in the difficulty in designing the controllers being increased and the obtained results being applied to a wider class of fuzzy systems than the most existing ones. The main contribution of this work lies in the application of the reciprocally convex inequality and the time‐delay term included in the measured output. Finally, the advantages and effectiveness of the present results are shown by several numerical examples.     

Observer-based event-triggered H-infinity sliding control of Markovian jump system suffer from actuator attacks

This article investigates the issue of observer-based $H_{\infty }$ sliding mode control for Markovian jump systems suffer from actuator attacks through an adaptive technique. During the communication channel from the plant output to estimator, a dynamic event-triggered generator is employed in enhancing communication efficiency. Taking consideration of malicious attacks on the plant actuator, an adaptive compensator is put forward for security purposes. By designing a state observer, the desired sliding mode dynamics can be derived based on an integral-type sliding surface. Further, maintaining the sliding motion with uncertain mode information is ensured in finite time by proposing a feasible sliding mode control law. In addition, both stochastic stability and $H_{\infty }$ performance conditions are established for closed-loop systems in terms of linear matrix inequalities. Finally, a numerical example is offered to illustrate the validity of the constructed strategy.     

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

In this paper, the sliding mode control (SMC) problem for continuous‐time Markovian jump systems (MJSs) is considered, in which the transition rate matrix (TRM) is partially unknown and uncertain. Firstly, the sliding mode surface S(t) = 0 is designed, which is mode‐dependent. Therefore, is used instead of in the SMC algorithm. Via adopting a linear matrix inequality (LMI) approach, sufficient conditions are proposed to ensure that the reduced order system is exponentially stable in mean square. Furthermore, the reduced order system is completely insensitive to the external disturbance. Secondly, SMC law is designed correspondingly which dominated by a Markov process. It could drive the state trajectories onto the specified sliding mode surface in finite time quickly and maintain them on the surface in subsequently time. Thirdly, a new term in will be introduced in the designed SMC and should be handled by a new approach. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

Robust recursive linear quadratic regulator for wheeled mobile robots based on optical motion capture cameras

In this paper, we deal with nonholonomic wheeled mobile robots (WMR) modeled as uncertain nonlinear systems. Sources of uncertainties can be due to erroneous estimation of mass, inertia, and center of gravity and due to payload time‐varying. They also can be considered as external disturbances generated from unstructured environments. We are proposing the use of a robust linear quadratic regulator (RLQR) to deal with tracking problems of WMR. In order to guarantee the effectiveness of this control approach, the robot posture is measured through a high‐precision motion capture system. This RLQR encompasses in a unified framework all state and output uncertain parameters of the system and does not depend on any auxiliary parameter to be tuned. It is useful to be used in online applications. Experimental results are presented with a comparative study among the R‐LQR, the nonlinear control via game theory, and the standard proportional‐derivative controller plus computed torque (PD+CT).     

Dynamic event‐triggered control for linear time‐invariant systems with ‐gain performance

In this paper, a novel dynamic event‐triggered control scheme is presented for linear time‐invariant systems. Under this control scheme, criteria that guarantee the asymptotic stability and the ‐stability are derived, by which the triggered parameters and the feedback gain can be codesigned. The stability criteria are derived by using Lyapunov‐based analysis tools, and a new Lyapunov‐Krasovskii functional is constructed to further reduce conservatism. Moreover, the projection technique and the mathematical induction are introduced in the stability analysis. Compared with the existing results for static strategies, the proposed dynamic strategy is more flexible and generates fewer events. Finally, simulation examples are provided to demonstrate the effectiveness of this new scheme.     

Improved Adaptive Controller Synthesis of Piecewise‐Affine Systems

This paper considers the adaptive control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive control of PWS can be reduced to the control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.     

Approximate Controllabilty of Semilinear Dynamic Equations on Time Scale

In this paper we study the approximate controllability of semilinear systems on time scale. In order to do so, we first give a complete characterization for the controllability of linear systems on time scale in terms of surjective linear operators in Hilbert spaces. Then we will prove that, under certain conditions on the nonlinear term, if the corresponding linear system is exactly controllable on , for any , then semilinear system on time scale is approximately controllable on .     

Reliable Decentralized Supervisors for Discrete‐Event Systems Under Communication Delays: Existence and Verification

A reliable decentralized supervisory control framework for discrete‐event systems is proposed to deal with possible actuation failures and communication delays. We mainly focus on the existence of such a controller that the control performance can be guaranteed even in face of local supervisor failures and communication delays. Especially, the existence of k‐reliable decentralized supervisors under communication delays is characterized by the notion of k‐reliable together with . In addition, the verification for k‐reliable decentralized supervisors is investigated by developing a constructive methodology to test the k‐reliable . It is shown that for a given number of distributed components, the existence of such k‐reliable decentralized supervisors can be checked with a polynomial complexity in the size of the state space.     

Stabilization of Stochastic Coupled Systems With Time Delay Via Feedback Control Based on Discrete‐Time State Observations

In this paper, the stabilization of stochastic coupled systems (SCSs) with time delay via feedback control based on discrete‐time state observations is investigated. We use the discrete‐time state feedback control to stabilize stochastic coupled systems with time delay. Moreover, by employing Lyapunov method and graph theory, the upper bound of the duration between two consecutive state observations is obtained and some criteria are established to guarantee the stabilization in sense of ‐stability and mean‐square asymptotic stability of SCSs with time delay via feedback control based on discrete‐time state observations. In addition, to verify the theoretical results, stochastic coupled oscillators with time delay are performed. At last, a numerical example is given to illustrate the applicability and effectiveness of our analytical results.     

Robust Partially Mode Delay‐Dependent ℋ∞ Output Feedback Control of Discrete‐Time Networked Control Systems

In this paper, a methodology for designing an output feedback controller for discrete‐time networked control systems has been considered. More precisely, network‐induced delays between the sensor and the controller is modelled by a Markov chain with transition probabilities which are not assumed to be fully known. The systems parameter uncertainties are assumed to be norm‐bounded and possibly time‐varying. To the best of the authors knowledge, the problem of designing a partially mode delay‐dependent output feedback controller for NCSs with partially known transition probability matrix has not been investigated in the literature. Based on the Lyapunov‐Krasovskii functional approach, sufficient conditions for the existence of a robust partially mode delay‐dependent output feedback controller are given in terms of bilinear matrix inequalities which can be solved using a cone complementarity linearization algorithm. The proposed design methodology differs from the existing design methodologies in that dynamic output feedback controllers are parameterized by both modes and transition probabilities, as opposed to the existing design approaches which parameterize controllers by modes only. The results obtained reduce to the existing results on fully known transition matrices when transition probabilities are fully known. It is shown that the proposed methodology can be applied to real world systems. The proposed design methodology is verified by using a DC servo motor system where the plant and the controller are connected via a cellular network with partially known transition probability matrix.     

Hybrid-triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

This paper is concerned with the issue of hybrid-triggered scheme $H_{\infty }$ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid-triggered scheme includes time-triggered scheme and event-triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean-square asymptotically stable (MSAS) and $H_{\infty }$ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width-modulation-driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.