Linear Matrix Inequality Theory Research Articles

LMI-based state observer design for supercavitating vehicles with time delay

Due to the existence of the planing force, the control of the supercavitating vehicle is difficult, and the vertical velocity which has a great influence on the planing force cannot be directly measured. Therefore, considering the time-delay effect of the planing force and the external disturbance, the state observer and controller based on linear matrix inequality (LMI) have been designed. By decomposing the planing force into two parts of time delay and non-time delay, and a longitudinal plane Linear Parameter Varying (LPV) time-delay model for supercavitating vehicles is derived. In addition, the controller and state observer for the supercavitating vehicle system with time-delay characteristics and external disturbances are simultaneously designed. The gains of the controller and observer are obtained by combining the theory of linear matrix inequalities and convex polytopes, ensuring the convergence of estimation error. At the same time, taking into account the possibility of exceeding the physical limits of the actuator when the input value is too large, the compensator has been added. Finally, the simulation results demonstrate that the designed controller exhibits good stability and tracking performance.

Generalized uniform optimization for robust adaptive Buck converter with uncertain perturbations

This paper presents an event-triggered impulse (ETI) control mechanism with generalized uniform optimization, endowing robust adaptive for various uncertain Buck converter perturbations. An impulse compensates for the state fluctuation error, and the event triggering mechanism (ETM) is introduced into the control process of the stochastic model of the Buck converter. The mean square stability theory of linear matrix inequality (LMI) stochastic systems is provided, wherein the cost function incorporates uncertain perturbation-induced state feedback impulses and adaptive system tuning. Unlike traditional event-triggered control with manually determined triggering times, ETI is activated only when events conform to the optimal design, significantly enhancing error-tracking accuracy and adaptive capability. Moreover, the parameters of the optimal controller remain independent of the statistical characteristics of uncertain noise, ensuring globally optimal operational control and model generality. Namely, the proposed method demonstrates versatility by extending its application to DC motor control, addressing various perturbations Buck converters encounter. Finally, the designed controller can closely track the required angular velocity trajectory across sudden changes in system uncertain perturbation.

Path-following control of 4WIS/4WID autonomous vehicles considering vehicle stability based on phase plane

In order to ensure the following accuracy and improve the operational stability of four-wheel independent driving and four-wheel independent steering autonomous vehicles, this paper proposes a path-following control strategy based on the β−[Formula: see text] phase plane. First, based on the kinematic relationship between the vehicle and the reference path, the linear matrix inequality theory is used to design the H∞ controller to obtain the wheel steering angle. Then, the vehicle steering system is subjected to nonlinear analysis according to phase plane theory, and a partition region controller is designed. In the unstable region, the instability degree of the vehicle is predicted by quadratic polynomial extrapolation and the particle swarm optimization PID controller is designed to determine the required yaw moment to restore the vehicle to the stable region. In the stable region, a fuzzy sliding mode controller is adopted to determine the required yaw moment so that the actual state variable of the vehicle follows the ideal state variable. Finally, the optimal tire force distributor is designed such that the required forces are allocated to all four wheels. The simulation results show that the proposed method can obtain excellent path-following performance and stability performance under different driving conditions.

Integral sliding mode control for uncertain impulsive stochastic systems

This paper studies the integral sliding mode control (ISMC) for uncertain impulsive stochastic systems. An ISMC law is proposed by designing a new integral sliding surface. Then, by constructing a piecewise time-dependent Lyapunov function, the uniformly almost surely exponentially stability conditions of the closed-loop system are established. Furthermore, an optimal design algorithm of solving control gains is formulated based on the established stable conditions and linear matrix inequalities (LMIs) theory. Finally, a simulation example and the simulation comparisons with the existing control methods are provided to demonstrate the effectiveness of the proposed ISMC scheme.

H∞ control for cyber physical systems under DoS attacks via tracking-removed autoencoder

In this paper, we consider cyber physical systems security control problems under DoS attacks via the tracking-removed autoencoder. The DoS attack model is described by the switch signal, which occurs in the controller-actuator transmission channel. Then, the linear matrix inequality theory is used to solve the average dwell time of the attack mode that the system can tolerate. Moreover, when the attack dwell time exceeds the tolerance range, a tracking-removed autoencoder is chosen to train to get the control signal. And it can be proved that the closed-loop system with the controller based on the tracking-removed autoencoder is asymptotically stable with H ∞ performance index. Finally, the correctness and advancement of the theory are proved by an example.

Event-triggered boundary consensus control for multi-agent systems of fractional reaction–diffusion PDEs

The distributed consensus is considered for multi-agent systems (MASs), which characterized by fractional reaction–diffusion partial differential equations (RDPDEs) in this paper. Based on Lyapunov technique and linear matrix inequalities (LMIs) theory, the consensus can be realized via two novel event-triggered boundary control schemes. Firstly, a novel convergence principle subject to finite time is presented for the continuously differentiable function. Secondly, the cooling fin on surface of high-speed aerospace vehicle is remodeled by fractional RDPDEs system, and the well-posedness of presented system is discussed applying the monotone iterative approach. Thirdly, according to the presented static event-triggered boundary control strategy, the consensus criterion in finite time is addressed in the form of LMIs, in addition, the settling time is calculated accurately. Applying the dynamic event-triggered control protocol, the Mittag-Leffler (M-L) consensus condition is achieved. Moreover, the Zeno behaviors are ruled out for proposed event-triggered mechanisms. Finally, the high-speed aerospace vehicle model is presented to verify the effectiveness of the control performance.

Robust fuzzy predictive switching control for nonlinear multi-phase batch processes with synchronous vs asynchronous cases

Multi-phase batch processes (MPBP) have the characteristics of nonlinearity and various cases of switching, where the switching between two adjacent phases can be divided into synchronous vs asynchronous cases. The present study introduces a robust fuzzy predictive method for switching control to ensure that an MPBP can still operate stably in the above two cases. First, considering the multi-phase characteristics of MPBP, multiple stable sub-models are established under the synchronous case. On this basis, unstable sub-models are established between adjacent phases under the asynchronous case. Second, in order to deal with the inherent nonlinearity of MPBP, each sub-model is locally linearized and a mixed Takagi-Sugeno (T-S) model is established. Third, using a mapping relationship between controller and local subsystem including direct mapping and fully associative mapping, a global output control law is designed. By combining the Lyapunov stability theory, linear matrix inequality (LMI) theory, mode-dependent average dwell time method, etc., corresponding LMI conditions are derived by the mapping relationship of different cases, making each phase asymptotically stable and each batch exponentially stable. Then, the distribution compensation gains of the corresponding controllers, the shortest operating time of the stable subsystem and the longest operating time of the unstable subsystem can be obtained by solving corresponding LMI conditions in a synchronous or an asynchronous case. Finally, if the MPBP is in an asynchronous case, according to the longest operating time of the unstable subsystem, a time compensation method based on the obtained operating time is proposed to avoid the occurrence of an unstable subsystem. The simulation results demonstrate that the proposed method has greater advantages than the reference methods.

H∞ robust control for underwater supercavitating vehicle with time delay

According to Logvinovich cavity dependent expansion principle, a cavity developed by cavitator has memory effect, which arises cavity deformation at aft part of a supercavitating vehicle and leads time delay of travel state. This delay affects the dynamic behavior through changing hydrodynamic and moment on the control surface, and even induces instability. This paper focuses on the time delay effect of the underwater supercavitating vehicle, and a simplified dynamic model of underwater supercavitating vehicle with delay was established. First, a planing force was simplified in straight level state, then a simplified model of supercavitating vehicle with delay in longitude plane was obtained. Taking depth, pitch angle, vertical speed and pitch rate as state variant, H ∞ state feedback controller was designed by linear matrix inequality (LMI) and Lyapunov stable theory was exploited to prove the asymptotic stability of the system. Simulation results show that, the controlled system is effectiveness for both simplified model and non-simplified model and it can track reference command signal.

Semi-active fuzzy cooperative control of vehicle suspension with a magnetorheological damper

This study attempts to improve the vibration isolation performance of a vehicle suspension system with a magnetorheological damper (MRD) under complex driving conditions. Structure parameter uncertainty, disturbance of the driving process, and response time delay of MRD are all addressed. Firstly, experiments of MRD were carried out in a damping force testing machine to identify the parameters of the MRD adjustable Sigmoid model by the Levenberg-Marquardt optimization algorithm. Then, the parameter identification is verified by comparing experimental and simulation data. Secondly, the state space equations of the suspension system are derived by Newton’s second law. The transfer function from the bounded disturbance input to the control output is obtained based on H∞ control theory. To make the Infinite norm of the system transfer function less than a certain value, three control strategies are proposed: variable structure control (VSC), disturbance rejection control (DRC), and delay tolerance control (DTC). Thirdly, considering these issues together to weaken the effect of disturbances on vehicle driving conditions, a fuzzy cooperative control (FCC) strategy is proposed based on the linear matrix inequality (LMI) theory. Simulation results demonstrate that FCC semi-active vehicle suspension systems conduct effective vibration isolation performance while responding to multiple external disturbances.

A Fractional-Order Density-Dependent Mathematical Model to Find the Better Strain of Wolbachia

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.

Data-sampled mean-square consensus of hybrid multi-agent systems with time-varying delay and multiplicative noises

This paper addresses the issue of dynamic mean-square consensus for second-order hybrid multi-agent systems. Time-varying delays and multiplicative noises are considered. New distributed control protocols are designed based on data-sampled information of neighbor agents. Equivalently using the error system based on Laplacian matrix, the method could make a dynamic consensus both under the fixed and switching topologies. By adopting stochastic system theory, Lyapunov stability method and linear matrix inequality theory, several sufficient conditions for the dynamic mean-square consensus are obtained. The upper bound of time delay and the discrete-time sampling period of hybrid multi-agent systems under a stochastic noises environment are inferred. Several simulations are presented to demonstrate the effectiveness of the proposed methods.

Robust path following control of 4WID autonomous vehicle with driving condition adaptive mechanism

This paper proposes a novel integrated path following control scheme for a 4-Wheel Independent Drive (4WID) autonomous vehicle that can adaptively change its mechanism according to the driving conditions. The proposed integrated system handles the lateral steering controller, longitudinal speed, and yaw moment controls considering tire force capacity of each corner. For the lateral controller, the cornering stiffness uncertainties and the transient performance are considered and combined into an H∞ robust controller based on linear matrix inequality (LMI) theory. A super-twisting sliding mode controller (STSMC) based longitudinal controller is designed to deal with disturbances and suppress chattering. When encountering extreme conditions, the active yaw moment controller with hierarchical structure is adaptively activated to prevent large deviation from the reference path and maintain the stability of vehicle. For the tire force allocation, an optimization algorithm is proposed, which has flexible equality constraints to coordinate the longitudinal and lateral motions according to the driving conditions. Simulations based on Carsim-Simulink co-simulation platform show that the proposed method is effective and has excellent performance in both normal and extreme driving conditions.

A novel H∞ observer for sensor fault diagnosis of vehicle electronic stability control system with disturbance and input delay

This paper mainly focuses on the sensor fault diagnosis method based on H∞ observer in vehicle electronic stability control (ESC) system with disturbance and input delay. Firstly, the four-wheel steering vehicle model is established. Secondly, the system state and sensor fault are reconstructed into new system variables by a special matrix transformation method, based on which a new H∞ observer is developed to estimate system state and sensor fault signals. Then, based on Lyapunov method and linear matrix inequality (LMI) theory, the conditions for asymptotic stability and H∞ performance of the estimation error system are proved. Finally, Carsim and Matlab/Simulink co-simulation are used to show the effectiveness of the method.

Distributed Adaptive Control for Nonlinear Heterogeneous Multi-agent Systems with Different Dimensions and Time Delay

A distributed neural network adaptive feedback control system is designed for a class of nonlinear multi-agent systems with time delay and nonidentical dimensions. In contrast to previous works on nonlinear heterogeneous multi-agent with the same dimension, particular features are proposed for each agent with different dimensions, and similar parameters are defined, which will be combined parameters of the controller. Second, a novel distributed control based on similarity parameters is proposed using linear matrix inequality (LMI) and Lyapunov stability theory, establishing that all signals in a closed loop system are eventually ultimately bounded. The consistency tracking error steadily decreases to a field with a small number of zeros. Finally, simulated examples with different time delays are utilized to test the effectiveness of the proposed control technique.

Finite-time energy-to-peak control for Markov jump systems with pure time delays

This study investigates finite-time energy-to-peak control for pure-time-delay Markov jump systems. The main objective is to obtain some theorems such that the corresponding pure-time-delay Markov jump systems are finite time energy-to-peak stable or stabilizable. First, based on mathematical transformation, the pure-time-delay Markov jump systems are described in a model description that includes the current system state and several distributed time-delay items. Second, according to linear matrix inequality (LMI) theory, a positive energy functional is constructed, which includes a triple integral item. Then, after some mathematical operations, some sufficient conditions are obtained for Markov jump systems to be finite-time energy-to-peak stable or stabilizable. The obtained results are expressed in LMIs, which can be conveniently solved by computers. Finally, examples are given to show the usefulness of the obtained theorems.

A New Power Flow Model With a Single Nonconvex Quadratic Constraint: The LMI Approach

In this paper, we propose a new mathematical model for power flow problem based on the linear and nonlinear matrix inequality theory. We start with rectangular model of power flow (PF) problem and then reformulate it as a Bilinear Matrix Inequality (BMI) model. A <b>Theorem</b> is proved which is able to convert this BMI model to a Linear Matrix Inequality (LMI) model along with One Nonconvex Quadratic Constraint (ONQC). Our proposed LMI-ONQC model for PF problem has only one single nonconvex quadratic constraint irrespective of the network size, while in the rectangular and BMI models the number of nonconvex constraints grows as the network size grows. This interesting property leads to reduced complexity level in our LMI-ONQC model which in turn makes it easier to solve for finding a PF solution. The non-conservativeness, iterative LMI solvability, well-defined and easy-to-understand geometry and pathwise connectivity of feasibility region are other important properties of proposed LMI-ONQC model which are discussed in this paper. An illustrative two-bus example is carefully studied to show different properties of our LMI-ONQC model. We have also tested our LMI-ONQC model on 30 different power-system cases including four ill-conditioned systems and compared it with a group of existing approaches. The numerical results show the promising performance of our LMI-ONQC model and its solution algorithm to find a PF solution.

H‐infinity fault‐tolerant control for Markov jump system with actuator time delay

This study investigates H-infinity fault-tolerant control for Markov jump systems with actuator time delay. The main objective is to obtain some theorems such that the corresponding Markov jump systems with actuator time delay to be H-infinity stable and with some fault-tolerant performances. First, based on an integral transformation, the Markov jump systems with actuator time delay are described in a system description with a distributed time-delay item. Second, based on utilizing the linear matrix inequality theory, a positive energy functional, which includes a double integral item, is constructed. Then, after some mathematical operations, a sufficient condition is obtained for the Markov jump systems with actuator time delay to be H-infinity stable. If the condition is solvable, fault-tolerant controller can be gotten to guarantee the controlled system to be H-infinity stable no matter there are some actuator faults existing in the system or not. Finally, examples are given to show the usefulness of the obtained theorem.

Cluster Synchronization in Variable-Order Fractional Community Network via Intermittent Control

In this paper, the cluster synchronization of a variable-order fractional community network with nonidentical dynamics is investigated. For achieving the cluster synchronization, intermittent controllers are designed, and the sufficient conditions with respect to system parameters, intermittent control instants and control gains are derived based on stability theory of fractional-order system and linear matrix inequalities (LMIs). To avoid verifying the LMIs, a corresponding simple corollary is provided. Finally, a numerical example is performed to verify the derived result.

Generator and grid side converter control for wind energy conversion system

&lt;p&gt;This paper focuses on the modeling and control of a wind energy conversion chain using a permanent magnet synchronous machine. This system behaves a turbine, a generator, DC/DC and DC/AC power converters. These are connected on both sides to the DC bus, where the inverter is followed by a filter which is connected to the grid. In this paper, we have been used two types of controllers. For the stator side converter, we consider the Takagi-Sugeno approach where the parameters of controller have been computed by the theory of linear matrix inequalities. The stability synthesis has been checked using the Lyapunov theory. According to the grid side converter, the proportional integral controller is exploited to keep a constant voltage on the DC bus and control both types of powers. The simulation results demonstrate the robustness of the approach used.&lt;/p&gt;

Spectrahedral representation of polar orbitopes

Let K be a compact Lie group and V a finite-dimensional representation of K. The orbitope of a vector xin V is the convex hull {mathscr {O}}_x of the orbit Kx in V. We show that if V is polar then {mathscr {O}}_x is a spectrahedron, and we produce an explicit linear matrix inequality representation. We also consider the coorbitope {mathscr {O}}_x^o, which is the convex set polar to {mathscr {O}}_x. We prove that {mathscr {O}}_x^o is the convex hull of finitely many K-orbits, and we identify the cases in which {mathscr {O}}_x^o is itself an orbitope. In these cases one has {mathscr {O}}_x^o=ccdot {mathscr {O}}_x with c>0. Moreover we show that if x has “rational coefficients” then {mathscr {O}}_x^o is again a spectrahedron. This provides many new families of doubly spectrahedral orbitopes. All polar orbitopes that are derived from classical semisimple Lie algebras can be described in terms of conditions on singular values and Ky Fan matrix norms.