Control Gain Matrix Research Articles

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Synchronization of nonlinear neural networks with hybrid couplings and uncertain time-varying perturbations: A novel distributed-delay impulsive comparison principle

This paper investigates the synchronization of nonlinear drive-response neural networks subject to uncertain time-varying perturbations, non-delayed coupling, and distributed delay coupling. To address the influence of distributed and discrete delays on the system, we establish a novel impulsive comparison principle, extending the Halanay inequality. By leveraging Lyapunov stability theory, we derive sufficient conditions for the exponential synchronization of the neural networks using a delayed impulsive controller with historical status information. This approach relaxes the conventional constraint that impulsive delays must be smaller than impulsive intervals, thereby generalizing existing synchronization results for distributed delay networks. Numerical simulations for chaotic neural networks validate the theoretical results and demonstrate the sensitivity of the control gain matrix.

A novel control approach for discrete-time 2D Roesser systems under input saturation and intrinsic nonlinearity: A region of stability investigation

This paper presents the control system design for the nonlinear discrete-time Roesser systems under saturated control input. A deficiency in the existing literature has been addressed in this study for the control of two-dimensional (2D) systems. A generalized boundary condition analysis is presented in the form of tractable invariant sets for the derivation of region of stability to design a suitable state feedback control. A mechanism for the evaluation of controller parameters is presented by considering the generalized structure of 2D Lyapunov function. The work has been extended when external disturbances are present in the 2D systems, and a robust design condition by accounting the perturbations as well as the input saturation has been established. In comparison to the existing works, a control system design for 2D Roesser systems under input saturation and intrinsic nonlinearity by application of a generalized Lyapunov function has been revealed. Furthermore, a tractable 2D region of stability for the local control of the 2D systems is achieved, rather than the conventional global controllers. Furthermore, a method has also been studied for obtainment of the controller gain matrix through convex optimization regarding the complete structure of the 2D Lyapunov function. Simulation results are provided for the stabilization of an unstable nonlinear 2D system under input saturation.

An Adaptive Learning Control for MIMO Nonlinear System with Nonuniform Trial Lengths and Invertible Control Gain Matrix

In the traditional iterative learning control (ILC) method, the operational time interval is conventionally fixed to facilitate a seamless learning process along the iteration axis. However, this condition may frequently be contravened in real-time applications owing to unknown uncertainties and unpredictable factors. In essence, replicating a control system at a consistent time interval proves challenging in practical scenarios. This paper proposes an adaptive iterative learning control (AILC) method for the multi-input–multi-output (MIMO) nonlinear system with nonuniform trial lengths and an invertible control gain matrix. Compared to the existing AILC research that features nonuniform trial lengths, the control gain matrix of the system in this paper is assumed to be invertible. Hence, the general requirement in the conventional AILC method that the control gain matrix of the system is positive-definite (or negative-definite) or even known is relaxed. Moreover, the tracking reference allows it to be iteration-varying. Finally, to prove the convergence of the system, the composite energy function is introduced and to verify the validity of the AILC method, a robot movement imitation with an uncalibrated camera system is used. The simulation results show that the actual output can track the desired reference trajectory well, and the tracking error converges to zero after 30 iterations.

Asynchronous output feedback quantized sliding mode dissipative control for Markovian jump time-delay systems with generally bounded transition rates

This article figures out the asynchronous output feedback sliding mode dissipative control issue for Markovian jump delay systems (MJDSs) with uncertain parameters and external disturbances. Different from the massive methods of constructing sliding mode surfaces (SMS), a new dynamic output feedback (DOF) integral SMS is developed, where the SMS is composed of a virtual controller with quantized output and the controller is asynchronous with the system mode. Meanwhile, the reachability of the SMS is guaranteed. In addition, the transition rates (TRs) considered in this paper are generally bounded, which means that the designed method applies to the more general case of TRs, such as fully known and partially unknown TRs. The sufficient criteria of stochastic stability and strict dissipation for the MJDSs are deduced. The design scheme of the controller gain matrix is proposed by the linear matrix inequality (LMI) technique. Finally, two examples are shown to demonstrate the effectiveness and feasibility of the designed technique.

Adaptive event-triggered based path following output feedback control for networked autonomous vehicles

This paper studies the adaptive event-triggered (AET)-based path following controller design problem for a networked autonomous vehicle, where the limited networked bandwidth, system nonlinearities and uncertainties are considered. The polytopic model is proposed to construct a linear parameter varying (LPV) system for the nonlinear vehicle system. Taking into account the effects of event trigger on the path following performance, an improved AET mechanism is designed to achieve a balance between efficient communication and accurate path following requirements. Sufficient conditions are developed to guarantee that the closed-loop system is exponentially stable with an H∞ performance index being satisfied. In addition, a co-design method with less conservatism is derived to obtain the event-triggered weight matrix and output feedback controller gain matrix simultaneously. Finally, simulation results verify the effectiveness of the proposed control strategy.

Exponential Synchronization of Markovian Jump Neural Networks Based on Asynchronous Delayed-Feedback Controller With Uncertain Hidden Information.

Due to the complex network environment, the feedback information cannot be timely received by the controller. This article proposes a method on the exponential synchronization for the Markovian jump neural networks, which is achieved by designing a new asynchronous delayed-feedback controller, with its feedback delay taken into account. The quantized relationship between the exponential synchronization and the feedback delay is derived from a new designed Lyapunov functional, to acquire delay boundaries. With the help of a hidden-Markov process, the designed controller shows asynchrony, which allows controller modes to run free. In particular, the detection probability is assumed to be bounded known, marking a breakthrough over existing results. Moreover, the proposed method proves to be applicable in both synchronous and asynchronous cases. By using the proposed method, the computation freedom of the controller gain matrix can be substantially augmented. Further, comparative numerical studies are implemented to validate the effectiveness and superiority of the proposed method.

Adaptive iterative learning control for high‐order nonlinear systems with different types of uncertainties

AbstractThe present work aims at investigating the adaptive iterative learning control (AILC) design for uncertain high‐order fully actuated nonlinear systems. In order to show the design principles, three types of nonlinear systems are considered, including systems with just parametric uncertainty, systems with both parametric and input distribution uncertainties as well as systems with both parametric uncertainty and an unknown control gain matrix. For different systems, the corresponding AILC schemes are proposed with different techniques in dealing with various system uncertainties, for which the convergence analysis are conducted rigorously based on the composite energy function. The effectiveness of the proposed AILC strategies is verified through numerical simulations.

Stabilization of Discrete-Time Hidden Semi-Markov Jump Linear Systems With Partly Unknown Emission Probability Matrix

This paper studies the stabilization problem for a class of discrete-time hidden semi-Markov jump linear systems with partly unknown emission probability matrix. By virtue of the improved semi-Markov kernel approach and emission probability approach, the less conservative sufficient stability conditions are proposed on the basis of emission probability matrix with partly unknown elements. With the aid of an improved eliminating matrix product technique, the nonlinear matrix terms with respect to system coefficient matrix and controller gain matrix in the above conditions are decoupled into the linear matrix forms, and the numerically testable existence conditions of the observed mode dependent controller for the corresponding closed-loop systems are obtained. An example is given to illustrate the effectiveness of our results.

Finite-time stability for impulsive stochastic nonlinear system with uncertain parameter

This paper considered the finite-time mean square stability for impulsive stochastic nonlinear system(ISNS) with uncertain parameter. By selecting the modal dependent Lyapunov functional, using average impulsive interval approach and combining Linear Matrix Inequality (LMI) method, the correlation stability criterion of ISNS was obtained. A gain matrix of the feedback controller is obtained on the basis of this sufficient condition. Finally, the LMI toolbox in Matlab was used for data simulation, and the relevant state trajectory demonstrates the availability of the proposed theory.

Adaptive containment control of heterogeneous high‐order fully actuated multi‐agent systems

AbstractIn this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes.

Disturbance rejection-based non-fragile hybrid-triggered control design for repeated scalar nonlinear systems

This article features the composite disturbance estimation and non-fragile hybrid-triggered control problems for continuous-time repeated scalar nonlinear systems prone to external disturbances. Priorly, the proportional integral observer comprising of both proportional and integral loops is incorporated to obtain better state estimations. Further, the external disturbance weakening the system performance is carefully estimated by deploying an improved equivalent-input-disturbance technique. Then, the availed disturbance estimate is blended into the control algorithm to exterminate the influence of the disturbance acting upon the proffered system. Next, a hybrid-triggered control comprised of a transition among event and time triggered paradigms are considered to reduce the network transmittance and also to simultaneously enhances the system outcomes. On top of that, the perturbations in controller gain matrix are taken into concern in order to make the controller more resilient towards redundant changes. Following that, utilising the Lyapunov theory, we obtain the mean-square asymptotic stability requirements for the developed system with the use of linear matrix inequalities and configure the gain matrices. Successively, the credibility of the synthesised control system is portrayed by exhibiting two numerical examples.

Removing Chaos while preserving equilibria by means of 2-contraction

Conditions for designing a feedback control law to remove the dense set of Unstable Periodic Orbits and chaotic attractors while preserving equilibria are formulated in terms of 2-contractivity of the closed loop system, by means of the second additive compound of the system's Jacobian. Matrix inequalities to allow computing the control gain matrix are discussed. An example of application of the method to the Thomas’ system is presented.

Fault Mode Analysis and Convex Optimization-Based Fault-Tolerant Control for New Type Dissimilar Redundant Actuation System of Near Space Vehicle

A new type dissimilar redundant actuation system (NT-DRAS), which is composed of an electro-hydrostatic actuator (EHA) and an electro-mechanical actuator (EMA), is applied in high value unmanned aerial vehicles such as the future near space vehicles to improve their reliability and performance index simultaneously. Further improvement in the flight safety is achieved with the fault-tolerant control (FTC) technique which deals with system faults. This paper proposes a novel convex optimization-based fault-tolerant control (CO-FTC) strategy for the NT-DRAS subject to gradual faults which are included in the state space representation of the system. A convex analysis-based treatment for system uncertainty caused by gradual faults is applied to determine the control gain matrix. The existence condition of the control gain matrix is optimized in the linear matrix inequality (LMI) form. Finally, the determined subsystems based on the novel technique is used to solve the modeled robust FTC problem. Case studies of NT-DRAS subject to different gradual faults have been accomplished to illustrate the FTC necessity for NT-DRAS. Furthermore, the effectiveness of the proposed CO-FTC strategy is validated by comparative analysis of the simulation results.

Adaptive backstepping control for multiple Euler–Lagrangian systems with independent dynamic communication

This paper presents a novel backstepping formation control strategy for multiple Euler–Lagrange (EL) systems. To enhance parallel communication capability, the communication channels for systems’ position vectors and filters’ states are independent. Subsequently, the corresponding dynamic event-triggered mechanisms are designed specifically for them to reduce the frequency of interactive communication networks, and a distributed filter is devised to eliminate the non-differentiability problem of event-triggered signals, respectively. Furthermore, we introduce a new barrier Lyapunov function (BLF) to indirectly restrict the velocity vector. The key novelty of this BLF is that the controller gain matrix caused by the designed BLF can be approximated as an identity matrix, when the distance between the velocity component and the designed boundary is substantial. To prevent the designed dynamic event-triggered mechanisms from being triggered infinitely for a period of time, Zeno behavior is excluded. By leveraging Lyapunov stability theory and Barbalat lemma, we demonstrate that all signals of the closed-loop system are bounded and the formation error asymptotically converges to the origin. Finally, simulation results are provided to demonstrate the efficacy of the proposed control schemes.

Semiglobal stability of PID for uncertain nonaffine systems

Proportional–integral–derivative (PID) controller is the most widely used form of feedback control by far. However, a satisfactory theory is still lacking to explain the rationale of the widespread PID control, and the gap between theory and practice of PID needs to be filled by control scientists. It is worth noting that a recent work (Zhao and Guo, 2022) proved that the classical PID controller has the ability to globally stabilize a basic class of uncertain nonaffine nonlinear systems, while the system nonlinear function is required to have a linear growth rate with respect to the state variables. In this paper, we will consider the more general case where the system nonlinear function may have super-linear growth rates, and show that the classical PID control can always be designed to stabilize such systems in the semiglobal sense, provided that the smallest eigenvalue of the control gain matrix has a positive lower bound. Moreover, a three dimensional parameter set for the stabilizing PID parameters will be constructed. Furthermore, under some additional knowledge about the system uncertain functions, we will propose a simpler PD controller with desired compensation, and show that the proposed controllers can still be designed to achieve semiglobal stability and desired tracking targets.

A sampled-data stabilisation analysis on memristive BAM neural networks for memductance function

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results.

Formula omitted]-[formula omitted]-dissipative control of T-S fuzzy systems via aperiodic sampling control with communication delay

This article concerns the strict (Q,S,R)-γ dissipativity of Takagi–Sugeno fuzzy systems (TSFSs) via aperiodic sampled-data control with communication delay. The motivations of this paper are that the transmission channels have communication delay and the original dissipative analysis method may be conservative. In order to consider the impact of communication delays, first of all, a sampled-data controller (SDC) with a constant communication delay is conceived to analyze the dissipativity of TSFSs. Next, the overall closed-loop system model is established stemming from the designed controller. In order to attain less conservative results, a new looped-functional which can take advantage of the available information of the sampling instants is formed. Then, strict (Q,S,R)-γ dissipativity can be guaranteed by a criterion obtained by using the looped-functional and the modified free-matrix-based inequality (FMBI) technique. By working out the obtained linear matrix inequalities (LMIs), the controller gain matrix that meets the requirement can be determined. Finally, the truck trailer and the mass–spring systems are showcased as simulation examples to provide evidence of the effectivity and superiority of the devised approach. In the presence of 0.1 s communication delay in the truck trailer system controller, the maximum γ can reach 0.9751 when sampling interval h takes 0.15 s, which makes the system can achieve strict (Q,S,R)-γ dissipativity.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

A Novel relaxation of the static output feedback problem for a class of plants

The static output feedback control problem is important, as it is concerned with the case when one cannot measure all state variables. It seeks to obtain a stabilising control under these conditions and is, often, difficult to solve. For a certain class of linear dynamical systems, we provide a novel approach to obtain a stabilising control gain matrix. The class of plants considered is of those, for which we can measure at least half of all state variables and where those measurements affect at least half of all state variables. Moreover, when we write the (linearly transformed) system matrix in block form, we require that either the two lower block matrices are nonsingular, or, if the inputs affect the measured state variables directly, at least the lower left one is nonsingular. We then show that we can determine the stabilising control gain matrix from the solution of a linear matrix inequality. Finally, we apply the approach to different benchmark problems, where it performs well, and confirm its good performance through additional numerical experiments.