Control Gain Matrix Research Articles

Robust path following control for autonomous vehicle considering actuator fault

The development of drive-by-wire chassis technology increases the flexibility of vehicle dynamic control. However, more actuators have higher potential failure risk and lead model mismatch, which brings a severe challenge for the control precision and system robustness. Regarding to the potential failure risk of the steering actuator, this research presents a feedback gain scheduling H∞ controller for autonomous vehicle path tracking. Firstly, the linear parameter-varying (LPV) model is established considering the speed variation and potential actuator fault. Then the state feedback control algorithm is proposed to maintain the tracking performance and system robustness. The control gain matrix is optimized via linear matrix inequation (LMI). Finally, the closed loop system is proved to be asymptotic stable by Lyapunov function and the simulation results demonstrate that the proposed controller has satisfactory tracking performance under unpredictable actuator fault degree, which provides good robustness and better reliability for autonomous vehicle in complex conditions.

PDE‐based event‐triggered containment control of multi‐agent systems with input delay under spatial boundary communication

AbstractThis article studies the containment control problem for multi‐agent systems with input delay under spatial boundary communication by employing an event‐based approach. Firstly, the collective dynamics of multi‐agent systems are described as parabolic partial differential equations (PDEs). Applying the integral transformation method developed in PDEs, the delayed parabolic PDEs are transformed into a series of new coupled PDE‐PDE systems. Then, by taking the spatial boundary communication scheme into account and using the local boundary information, two boundary containment control protocols together with a dynamic event‐triggered scheme (DETS) are designed, such that the states of all followers converge to a convex hull formed by multiple leader agents with and without input delay. The optimal protocols are given by minimizing the 2‐norm of the designed control gain matrix, and the exclusion of the Zeno behavior is analyzed. Finally, a numerical simulation example is provided to support the main results.

Resilient finite-time distributed event-triggered consensus of multi-agent systems with multiple cyber-attacks

This study addresses the resilient finite-time distributed event-triggered (ET) consensus control of multi-agent systems (MASs) with multiple cyber-attacks, such as replay, deception, and denial-of-service (DoS) attacks. For the first attempt, a model is proposed for multiple cyber-attacks on MASs under DoS, deception, and replay attacks, that occur stochastically in a unified framework. Furthermore, an appropriate distributed ET consensus control mechanism is proposed to handle the unwanted traffic in the network communication channel. This scheme determines whether or not the signal can be transmitted to each agent in MASs. Sufficient conditions for the consensus of MASs are derived using Lyapunov stability theory and linear matrix inequalities (LMIs), which ensure the exponentially mean-square finite-time stability. On the basis of the obtained conditions, the explicit expressions of the consensus control gain matrix and trigger parameter matrices are given. Eventually, simulation results are provided to verify the proposed theoretical results.

A Systematic Control Design Method with Active Damping Control in Voltage Source Converters

This paper proposes a systematic control design method for active damping control of grid-connected voltage source converters (VSCs). The proposed control method considers the conventional cascaded control loops and improves them by including additional states feedback-based active damping. In such a way, all control gains are lumped into one control gain matrix based on the proposed formulation. The lumping of all control gains into one matrix leads to a linear optimization problem, so different techniques can be used to calculate control gains. This work calculates them by using a simple but effective optimal control theorem as a noteworthy feature. The proposed control method can overcome the challenges of designing multiple control loops, evaluating wide time scale dynamics, and tuning required control parameters. Moreover, direct relationships between the proposed tuning parameters and system well-known stability and performance indicators such as maximum damping factor, minimum damping ratio, and the control efforts are identified, providing good physical insight. Finally, the proposed control structure and optimal gain calculations ensure power converter robustness against uncertainties in the grid’s short-circuit ratio (SCR) and different operating-point conditions. When the grid’s SCR changes from 10 (strong grid condition) to 1 (ultra-weak grid condition), the system under the proposed control method maintains good stability margins and simultaneously provides a fast dynamic response by facilitating the implementation of a high-bandwidth phase-locked loop (PLL). The performance of the proposed control strategy was investigated analytically and practically by conducting eigenvalue analysis, simulations, and experiments.

Cooperative Adaptive Model-Free Control With Model-Free Estimation and Online Gain Tuning.

In this article, a distributed adaptive model-free control algorithm is proposed for consensus and formation-tracking problems in a network of agents with completely unknown nonlinear dynamic systems. The specification of the communication graph in the network is incorporated in the adaptive laws for estimation of the unknown linear and nonlinear terms, and in the online updating of the elements in the main controller gain matrix. The decentralized control signal at each agent in the network requires information about the states of the leader agent, as well as the desired formation variables of the agents in a local coordinate frame. These two sets of variables are provided at each agent by utilizing two recently proposed distributed observers. It is shown that only a spanning-tree rooted at the leader agent is enough for the convergence and stability of the proposed cooperative control and observer algorithms. Two simulation studies are provided to evaluate the performance of the proposed algorithm in comparison with two state-of-the-art distributed model-free control algorithms. With lower control effort as well as fewer offline gain tuning, the same level of consensus errors is achieved. Finally, the application of the proposed solution is studied in the formation-tracking control of a team of autonomous aerial mobile robots via simulation results.

Full State Feedback H-Infinity Controller Design for Nonlinear Systems

Real world systems are inherently nonlinear in nature. Over the last few decades, nonlinear systems are regarded as the most significant issue in control theory. In this work, a nonlinear full state feedback H-infinity controller is proposed for nonlinear systems. The black hole optimization method (BHO) is used as an effective optimization technique to find the optimal parameters for the proposed controller based on the proposed cost function. The suggested controller gain matrix is computed by solving the H-infinity algebraic Riccati equation. As case studies, two types of nonlinear systems are demonstrated to demonstrate the utility of the proposed controller. Finally, simulation findings show that the suggested nonlinear controller improves the stability and performance of nonlinear systems by compensating them and compelling their states to track the reference input asymptotically with a workable and feasible control action.

Robust Finite-time H∞ Control for Discrete-time Nonlinear Uncertain Singular Systems with Time-delay

This paper deals with the problems of finite-time H∞ control for a class of discrete-time nonlinear singular systems subject to uncertainties and external disturbance. Firstly, the finite-time stability problem is discussed for discrete-time nonlinear uncertain singular systems with time-delay. The sufficient conditions of finite-time stability of discrete-time nonlinear singular systems are established. Then, by using the Lyapunov functional method, a criterion is established to ensure that the closed-loop system with external disturbance is finite-time bounded. We design the controller gain matrix. Finally, we provide a numerical example to illustrate the effectiveness of the proposed results.

Formation Control of Multi-Agent Systems With Constrained Mismatched Compasses

Due to inaccurate sensing results, the direction of the agent may be mismatched with each other, and constrained by a certain boundary condition, such that the directions of all the agents can not be aligned, e.g., the measurement biases or the drifts of sensors in inertial navigation. In this paper, such direction information, modeled as constrained mismatched compasses in the measurement or communication processes, has been considered for a kind of displacement-based formation control. To understand the introduced concept underlying how affects the system performance, several convex polytopes have been constructed to approximate rotation behaviors under the action of constrained mismatched compasses. The main aim of these polytopes is to recombine a larger convex region for containing the rotation behaviors, and is to further design a control gain matrix in view of the contracting mapping principle. The obtained results illustrate that all the agents can converge to the desired formation shape exponentially fast no matter whether the direction of each agent can be aligned with each other. Simulation is provided to verify the obtained results.

Exponential H∞ stabilization of uncertain neural networks with time-varying delay and external disturbance via periodically intermittent control

This paper is concerned with the exponential [Formula: see text] stabilization for a class of uncertain neural networks with interval time-varying delay and external disturbance via periodically intermittent control. By constructing a novel Lyapunov–Krasovskii functional (LKF) and applying some inequality techniques, delay-dependent sufficient conditions are derived to guarantee the exponential [Formula: see text] stabilization of the considered closed-loop system. These conditions are given in the form of linear matrix inequalities (LMIs). The intermittent state-feedback controller can reduce the effect of external disturbance to a prescribed attenuation level [Formula: see text]. Furthermore, the desired controller gain matrix can be obtained by solving the obtained LMIs. Finally, numerical simulations are given to show the effectiveness and the benefits of the proposed method.

Sliding mode control for multi‐agent systems under stochastic communication protocol

AbstractThis article investigates the consensus problem for the multi‐agent system (MAS) via a sliding mode control method. The stochastic communication protocol (SCP) obeying Markovian chain is adopted to schedule the information transmission among agents, by which only one state component of each agent is stochastically selected and transmitted to other agents at each transmission instant. Through the use of the merging technique, a joint Markovian chain is introduced to model the multi‐agent consensus error system. And then, a distributed sliding mode controller is designed to achieve the stochastic consensus of the MAS. Meanwhile, the desired controller gain matrix is obtained via solving a minimization problem. Finally, a numerical example has been provided to illustrate the proposed results.

Networked control systems with probabilistic time-varying delay based on event-triggered non-fragile [formula omitted] control

The non-fragile H∞ problem for networked control systems with probabilistic time-varying delay, stochastic nonlinear, controller gain fluctuation and adaptive event-triggered mechanism is studied. The random interval delay, nonlinear fluctuation and gain fluctuation of the controller all obey a certain uncorrelated Bernoulli distribution white noise sequence. An improved time continuous delay system model for networked control systems is constructed by using input delay method. A two-sided closed-loop Lyapunov–Krasovskii functional is constructed considering the sawtooth structure of artificial time delay, and the asymptotically stable conditions of closed-loop system with little conservatism are obtained. A non-fragile H∞ control strategy based on adaptive event-triggered is proposed and the co-design method for gain matrix of the non-fragile controller and event-triggered matrix is obtained. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Non-fragile H ∞ control for event-triggered networked control systems with probabilistic time-varying delay

This paper studies the non-fragile output-feedback control problem for event-triggered networked control system with probabilistic time-varying delay and controller gain uncertainties. With known conditional probability distribution, the time-varying delay is modelled as a Bernoulli distributed white sequences. An improved two-side closed-loop functional is constructed by using the sawtooth structure characteristic of artificial time delay. By applying the Lyapunov–Krasovskii stability theory, the lower conservative stability criterions for time-delay system are derived. Aiming at the external disturbance and the parameter uncertainty of controller gain, a non-fragile output-feedback control strategy based on event-triggered mechanism is proposed. Moreover, a co-design scheme of controller gain and event-triggered matrix is obtained based on linear matrix inequality technique. Finally, three simulation examples are utilised to verify the effectiveness of the presented method.

Optimal Design of a Proportional-Derivative State Feedback Controller Based on Meta-Heuristic Optimization for a Quarter Car Suspension System

This paper presents a Proportional-Derivative State Feedback (PDSF) controller approach to design an active suspension system for quarter car. The objective of the PDSF controller is to eliminate the effects of road disturbances to achieve ride comfort of the driver and passengers. Finding the optimal feedback gain matrix of the PDSF controller is formulated as an optimization problem. Then, two meta-heuristic optimizations named Bees Algorithm (BA) and Grey Wolf Optimization (GWO) are employed to optimize the feedback gain matrix of the PDSF controller based on the Integral Time of Absolute Error (ITAE) index. The results show the superiority of the BA-based PDSF controller in terms of reducing the ITAE index in comparison with the results obtained from GWO based PDSF.

On the Stabilization of a Network of a Class of SISO Coupled Hybrid Linear Subsystems via Static Linear Output Feedback

This paper deals with the closed-loop stabilization of a network which consists of a set of coupled hybrid single-input single-output (SISO) subsystems. Each hybrid subsystem involves a continuous-time subsystem together with a digital (or, eventually, discrete-time) one being subject to eventual mutual couplings of dynamics and also to discrete delayed dynamics. The stabilizing controller is static and based on linear output feedback. The controller synthesis method is of algebraic type and based on the use of a linear algebraic system, whose unknown is a vector equivalent form of the controller gain matrix, which is obtained from a previous algebraic problem version which is based on the ad hoc use of the matrix Kronecker product of matrices. As a first step of the stabilization, an extended discrete-time system is built by discretizing the continuous parts of the hybrid system and to unify them together with its digital/discrete-time ones. The stabilization study via static linear output feedback contains several parts as follows: (a) stabilizing controller existence and controller synthesis for a predefined targeted closed-loop dynamics, (b) stabilizing controller existence and its synthesis under necessary and sufficient conditions based on the statement of an ad hoc algebraic matrix equation for this problem, (c) achievement of the stabilization objective under either partial or total decentralized control so that the whole controller has only a partial or null information about couplings between the various subsystems and (d) achievement of the objective under small coupling dynamics between subsystems.

Sliding mode control of uncertain FMII 2D systems under directional event‐triggered schemes

AbstractThis article is concerned with the event‐triggered sliding mode control problem for two‐dimensional (2D) systems depicted by the second Fornasini–Marchesini (FMII) model. By considering the structural characteristics of FMII 2D systems, three event‐triggering schemes in one or two directions are analyzed and the corresponding partial ordering on pairs of triggering instants are given. In particular, the two‐directional event‐triggering scheme reflects the essential difference between FMII model and Roesser model. Accordingly, a two‐directional event‐triggered mechanism from sensors to controller is developed and the event‐triggered sliding mode controller is designed. Since the FMII 2D model is affected by two adjacent control signals, the updation of the control signals at two points and is detailedly discussed. Both the reachability of the sliding surface and the uniform ultimate boundedness of the resultant closed‐loop system are achieved. Meanwhile, the desired controller gain matrix and sliding matrix are determined by solving stability conditions. Finally, the proposed control scheme is further demonstrated via the heat exchanger process.

Robust control for uncertain variable fractional order differential systems considering time‐varying delays and nonlinear perturbations

AbstractThe robust control for uncertain variable fractional order time‐varying delayed differential systems with nonlinear perturbations are concerned in this article. Firstly, by introducing a novel form of the control law which is inspired by the sliding mode design, a new state feedback controller is built. Besides, a specific and comprehensive Lyapunov–Krasovskii function is adopted to deduce the sufficient conditions for the stability and robust stabilization of the system by using some linear matrix inequalities. In addition, the controller gain matrix can also be derived from the point of stability. Finally, two comparison examples are presented to demonstrate the effectiveness of the proposed control technique. The simulation results show that this method can make the state variables converge to the steady ones more quickly and stably.

A dual-channel switching mechanism for uncertain NCSs against DoS attacks

Abstract In this paper, the stabilization mechanism, dual-channel switching mechanism, is investigated for a class of discrete-time networked control systems with parameter uncertainties and cyber attacks. A novel dual-channel switching mechanism is proposed against the denial-of-service attacks and achieve system asymptotic stability. The event-triggered scheme is considered to control unnecessary data communications. Based on this, a memory-based event-triggered scheme is put forward to overcome the drawback of event-triggered scheme so that the system dynamic performance is greatly improved and the network resources are saved also. Using the Lyapunov theory and linear matrix inequality, two sufficient conditions of memoryless and memory-based closed-loop systems are, respectively, derived to guarantee the desired stability. Furthermore, the controller gain(s) and event-triggered matrix are co-designed. Finally, the effectiveness of the proposed method is verified by the pendulum system and the satellite control system.

Event-Triggered Control for Networked Systems Under Denial of Service Attacks and Applications

In this paper, the resilient controller design and synthesis issues of networked control systems under denial-of-service (DoS) attacks are investigated via an adaptive event-triggered strategy. In a networked control system, DoS attacks have serious impacts on the security of communication, possibly causing degraded stability performance of the system. To remove threats from DoS attacks, an adaptive event-triggered communication mechanism is proposed, which also provides benefits in reducing the consumption of communication resources and relieving the pressure on network bandwidth. Since the system state information is usually not fully known, an observer-based controller is developed to stabilize the system and maintain a desired performance index despite the occurrence of stochastic attacks. Furthermore, a joint design method is proposed to obtain the controller gain, observer gain and event-triggered weight matrix. Finally, practical examples based on a four-tank system, an Internet-based three-tank system and an Internet-based test rig system are presented to illustrate the effectiveness of the proposed techniques to respond and eliminate the impact of DoS attacks.

Extended dissipativity analysis for T-S fuzzy systems based on reliable memory control and aperiodic sampled-data method

This paper studies the extended dissipativity (ED) issue for T-S fuzzy systems (TSFSs) via reliable memory control scheme and aperiodic sampled-data (ASD) method. First, considering the random variation of sampling interval and the time delays (TDs) of sampling signal transmission in the communication network, a reliable aperiodic memory sampled-data control (RAMSDC) strategy is proposed. Then, the developed delay-dependent Lyapunov-Krasovskii functional (LKF) with some two-sided looped-functional (TSLF) terms is constructed to fully utilize sampled state information. The introduced free matrices in the TSLF need not to be positive definite, which reduces the conservativeness of the obtained results. Next, a sufficient condition is given to ensure the ED, and the controller gain matrix is obtained by means of linear matrix inequality (LMI) technique. At last, the effectiveness of theoretical results in practical application is verified by the use of a truck-trailer model.

Integration of inventory control into the port‐Hamiltonian framework for dissipative stabilization of chemical reactors

AbstractThis work integrates passivity‐based inventory control with the port‐Hamiltonian framework to design stabilizing feedback laws for lumped parameter chemically reacting systems. A static state feedback law with admissible controls is developed using an inventory‐related storage function as a closed loop Hamiltonian function. The control gain matrix is derived from the interconnection and damping matrices of the resulting Hamiltonian representation. Consequently, the proposed controller globally and exponentially stabilizes the system at a desired set‐point (including the open loop unstable equilibrium point) without restrictions on the reaction kinetics. Numerical simulations illustrate the application of the theory to a nonisothermal, continuous stirred tank reactor with the steady‐state multiplicity. The proposed approach is compared with the thermodynamic availability‐based control approach in terms of amplitude and variation rate to show its performance and effectiveness.