Cone Complementary Linearization Research Articles

[formula omitted] security control for 2-D switched time delay systems under arbitrary delay time-variation rate and stochastic cyber attacks

This study focuses on H∞ security control for 2-D switched time delay systems subject to stochastic cyber attacks by the Roesser model, where the delay time-variation rate can be arbitrary. First, the time-delay system is modeled as the feedback interconnection of the delay-less system. To guarantee the security of the system under stochastic cyber attacks, a state-dependent switching signal and an anti-deception attack controller are constructed. Stability conditions of 2-D delay-less feedback interconnection systems are given for the first time. Then, for the considered system, some criteria based on bilinear matrix inequalities (BMIs) are established via the Lyapunov function technology such that the mean-square asymptotic stability with H∞ performance is guaranteed under arbitrary delay time-variation rate. Moreover, a cone-complement linearization (CCL) method is proposed to compute the optimized controller gains for BMIs. The effectiveness of the proposed method is validated via two numerical simulations.

Resilient robust model predictive load frequency control for smart grids with air conditioning loads

AbstractThis paper investigates the robust model predictive load frequency control problem for smart grids with wind power under cyber attacks. To accommodate intermittent power generation, the demand response of the system is considered by involving the air conditioning loads in the frequency regulation. In addition, the system uncertainties produced by the air conditioning load users and wind turbines when replacing traditional generator sets are considered. By using the cone complementary linearization algorithm and the linear matrix inequality technique, a resilience robust model predictive control strategy with mixed performance indexes is proposed. Furthermore, a rigorous derivation of the recursive feasibility of robust model predictive control is given. Finally, the simulation results of the two‐area load frequency control scheme show that the proposed model predictive control strategy is capable of realizing the load frequency control of the multi‐area smart grid and is robust to the parameter uncertainties and frequency regulation of the system. The results also show that the proposed model predictive control strategy has some resistance to cyber attacks and external disturbances.

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.

Multirate Sampled-Data Control for Quadrotor UAV With Network-Induced Delay: An IQC-Based Cone Complement Linearization Algorithm

Multirate Sampled-Data Control for Quadrotor UAV With Network-Induced Delay: An IQC-Based Cone Complement Linearization Algorithm

Output Feedback Control of Fuzzy Systems via Reduced-Order Approximation Technique

This article focuses on the problem of designing the reduced-order dynamic output feedback (DOF) controller for discrete-time T–S fuzzy plants. Differing from the existing methodologies, the reduced-order approximation technique is applied to simplify the pregiven high-order DOF controller. The key point is to construct a reduced-order closed-loop model to approximate the original high-order closed-loop system. First, a new error auxiliary system between the high-order closed-loop system and the reduced-order closed-loop model is obtained. The sufficient conditions to guarantee that the corresponding error system is asymptotically stable with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{H}_{\infty}$</tex-math> </inline-formula> performance index are developed. Then, the parameters of the desired reduced-order controller are derived by utilizing the projection lemma and the cone complementary linearization algorithm. Finally, the advantages of the proposed technique are illustrated by a series of simulation analysis.

Cloud Control of Connected Vehicle Under Both Communication-Induced Sensing and Control Delay: A Prediction Method

In this paper, we focus on the problem of cloud control of the connected vehicle with time-varying communication-induced sensing delay and control delay. First, the connected vehicle cloud control system containing communication-induced delay is modeled as the discrete linear output feedback system with bounded input and output delay. Second, corresponding to the linear output feedback system, the “predictor-observer” structured controller is introduced and redesigned to compensate for the delay in both output and input channels actively, without measurement of actual input delay as its original version. The stability of the close-looped prediction-based control system under a certain delay boundary is analyzed, and the sufficient stability condition is proposed. Third, with the help of Cone Complementary Linearization (CCL), an iterative algorithm is proposed to design stabilized controller and observer gains. Finally, the proposed method is verified through vehicle lateral and longitudinal control simulations, and the effectiveness and the performance of the proposed delay compensation strategy are innovatively evaluated under real vehicle control scenarios.

Reduced-Order Static -Gain Control of Rotorcraft with Guaranteed Rotor–Fuselage Stability

A reduced-order control design method for rotorcraft is proposed in this work. Explicit constraints on the closed-loop fuselage–rotor stability are considered in the fuselage dynamics-based control design, aiming for the -gain performance for the fuselage dynamics under pole placement constraints and the guaranteed fuselage–rotor stability. Sufficient conditions for the control design problem are presented, formulated as a feasibility problem based on bilinear matrix inequalities. Such an NP-hard problem is approximated using convex relaxation techniques and the cone complementary linearization method, leading to an iterative control design algorithm. An altitude–velocity vector tracking concept is also proposed in this work, integrated with the proposed control design method to design rotorcraft trajectory controllers. Performance of the resultant rotorcraft trajectory controllers is examined via numerical simulations against representative maneuvers from the ADS-33E specification.

Finite-Time Contractive Control of Spacecraft Rendezvous System

In this paper we investigate the problem of a finite-time contractive control method for a spacecraft rendezvous control system. The dynamic model of relative motion is formulated by the C-W equations. To improve the convergent performance of the spacecraft rendezvous control system, a finite-time contractive control law is introduced. Lyapunov’s direct method is employed to obtain the existence condition of the desired controllers. The controller parameter can be obtained with the help of the cone complementary linearization algorithm. A numerical example verifies the effectiveness of the obtained theoretical results.

A Looped Functional Method to Design State Feedback Controllers for Lurie Networked Control Systems

Dear Editor, This letter deals with the stabilization of Lurie networked control systems with network-induced delays (NID). By constructing a two-sided looped Lyapunov functional, a sufficient condition is derived to ensure the absolute stability of the resultant closed-loop system under a state feedback controller. Then, based on this condition, a cone complementary linearisation (CCL) iterative algorithm is presented to design state feedback controller. It is shown via a numerical example that the proposed method can deliver less conservative results as well as fewer iterations if compared with existing ones.

A vehicle cloud control system considering communication quantization and stochastic delay

AbstractA novel kind of networked feedback controller is designed for the vehicle cloud control system in the presence of both sensor‐controller/controller‐actuator delay and communication quantization. Firstly, the vehicle cloud control system with delayed and quantized communication is modeled using the lateral/longitudinal vehicle dynamic and Markovian jump linear system (MJLS) theory. Then, some efficient stabilization conditions in matrix inequalities forms are derived for the considered cloud‐controlled vehicles. Furthermore, a cone complementary linearization method is utilized to solve the nonlinear matrix inequalities involved in the stabilization conditions. Simulation tests on connected vehicle lateral and longitudinal control are conducted to verify the effectiveness of the analytical results. Compared with the commonly used constant‐parameter controllers, the proposed method is practical to design vehicle cloud controllers under stochastic delay and communication quantization scenarios, with known delay distribution. Lastly, the stability of the vehicle cloud control system is guaranteed under the infection of unreliable communication factors with the proposed control method.

Distributed control for spatially interconnected time-varying delay systems under input saturation

This paper presents the distributed control design for a class of spatially interconnected continuous-time time-varying delay (SICTD) systems under input saturation. A distributed controller and distributed anti-windup compensator (AWC) are proposed based on the distributed structure of the SICTD system. Then, a sufficient condition is derived to guarantee the asymptotic stability and H∞ performance of the closed-loop system under the saturation constraints. We have also provided an algorithm for obtaining the AWC parameters by employing the elimination lemma and the cone complementary linearization approach. The proposed anti-windup compensation methodology can also be employed to compensate for the actuator saturation of the spatially interconnected delay-free systems. Finally, two practical examples are presented to verify the effectiveness of the proposed AWC design method.

Security-Based Resilient Robust Model Predictive Control for Polytopic Uncertain Systems Subject to Deception Attacks and RR Protocol

This article is concerned with the security-based resilient robust model predictive control (RMPC) problem for a class of discrete-time polytopic uncertain systems with deception attacks and the round-robin (RR) protocol. The well-known RR protocol is adopted with the hope to reduce the communication burden, where the control signal is transmitted only at the given transmission instant. By means of the concept of bounded energy and the independent Bernoulli-distributed (BD) white sequences, a representative attack model is given. A definition of mean-square (MS) security in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -sense is employed to reasonably explain the dynamics process of the controlled systems. We aim at designing a set of resilient RMPC controllers so as to make the closed-loop system state under consideration of deception attacks and the RR protocol enter and stay in a certain bounded region. Furthermore, with the aid of stochastic analysis methods and inequality analysis techniques, sufficient conditions are obtained to satisfy the desirable security requirements. To tackle the nonconvex obstacles resulting from attacks and the RR protocol, the cone complementary linearization (CCL) method is exploited to cast them into a convex optimization problem (OP) for its solvability. Then, an online OP regarding a certain upper bound of the concerned objective is provided for the solvability and resilient RMPC-based controller gains are obtained. Finally, two examples, including a high-purity distillation one and a numerical one, are used to demonstrate the effectiveness and the validity of the proposed techniques.

Event-triggered based security consensus control for multi-agent systems with DoS attacks

This work devotes to the security consensus problems for time-varying multi-agent systems (MASs) based on event-triggered control method with denial-of-service (DoS) attacks and parameter uncertainties. During information transmission, DoS attacks exist in both control and measurement channels, regarded as a dwell-time switching scheme, and hence the augmented system can be transformed into a class of discrete-time switched system subject to dwell-time property which contains an unstable and a stable subsystem. To increase the utilization of communication resources, the control input signal can be updated by adopting a novel event-driven mechanism with state-dependent threshold over a given finite horizon. By utilizing multiple Lyapunov functions analysis strategy, two sufficient conditions are obtained to achieve the desired H∞ consensus performance. The cone complementary linearization algorithm is employed to cope with the nonlinear terms, and the desired controller gain matrices are calculated via resolving the corresponding linear matrix inequalities. Finally, the effectiveness of this proposed method is verified by providing a simulation example and the multi-automobile system.

H ∞ state-feedback control for saturated 2-D Roesser systems: the event-triggered case

This work discusses the state-feedback control issue for a class of state saturated two-dimensional (2-D) Roesser systems under the event-triggered mechanism. Here, the state saturation is considered to cater the practical situation. First, an event-triggered strategy is exploited to make use of resources rationally in the communication network with finite capacity. Based on the Lyapunov method, the sufficient criterion is presented to achieve the desired performance of the corresponding closed-loop saturated 2-D system and the existence of event-triggered state-feedback (ET-SF) controller is ensured. Particularly, a positive scalar is introduced to cope with the state saturation term. With the aid of sufficient criterion and cone complementary linearisation (CCL) algorithm, the design problem of ET-SF controller can further be transformed into seeking the feasible solution to linear matrix inequalities. Eventually, a simulation example is implemented to reveal the usefulness of the presented control scheme.

Finite-Time Contractively Bounded Control of Positive Linear Systems under H∞ Performance and Its Application to Pest Management

This paper investigates the finite-time contractively bounded control issue for positive linear systems under H∞ performance. The notion of H∞ finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H∞ finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions.

반복적인 선형행렬부등식을 이용한 연속시간 T-S 퍼지 시스템에 대한 정적 출력궤환 제어

This investigation deals with the design method of a static output feedback controller for continuous-time T-S fuzzy systems via iterative linear matrix inequalities. First, a matrix inequality that guarantees the stability of the nonlinear system is introduced. Based on this, an algorithm for finding the stabilization control gains, using the cone complementary linearization method, for continuous-time T-S fuzzy systems is presented. The validity of the proposed algorithm is verified through a simple example.

A novel delay-range-dependent observer-based control approach for one-sided Lipschitz systems under measurement delays

This paper presents the observer-based control methodology for the one-sided Lipschitz (OSL) nonlinear systems over measurement delays. A controller design method, based on the estimated states, has been provided by applying the Lyapunov-Krasovskii functional for the delayed dynamics and by inserting the OSL constraint and quadratic inner-boundedness condition. The stability of the resultant delayed dynamics is achieved through the delay-range-dependent approach, and derivative of Lyapunov functional is exploited through the Wirtinger's integral inequality approach to reduce the conservatism of the conventional Jensen's inequality scheme. Further, a necessary and sufficient solution for the main design method has been provided by employing a tedious decoupling technique to render the observer and controller gains, simultaneously, by using the recursive optimization tools. Furthermore, the solution of matrix inequality-oriented results is handled via the cone complementary linearization technique to validate the controller and observer gains through convex optimization. The effectiveness of the resultant observer-oriented control formulation for the OSL nonlinear systems under measurement delays is validated via numerical simulation examples.

H∞ Filtering of Repeated Scalar Nonlinear Systems: Event-Triggered Communication Case

In this paper, the event-triggered filter design problem is investigated for a class of discrete-time repeated scalar nonlinear systems. An admissible filter is introduced and sufficient conditions to ensure the asymptotical stability of the controlled system with a given performance are established. The solution of the corresponding event-triggered filter problem is settled by the projection lemma, and the cone complementary linearization technique is introduced to derive the filter parameters. An example is provided to demonstrate the effectiveness and potential of the proposed new design method.

Sliding-Mode Control of T-S Fuzzy Systems Under Weighted Try-Once-Discard Protocol.

This article investigates the sliding-mode control (SMC) problem for a class of T-S fuzzy systems with communication constraints. The weighted try-once-discard (WTOD) protocol is utilized to arrange the transmission order of actuator nodes, under which only one node is permitted to obtain access to the communication network at any time. A key issue is how to integrate the WTOD protocol into the design of the SMC system. To this end, an update rule is proposed for the actuators to obtain the actual actuator signals. And then, a membership-function-dependent (MFD) sliding surface and a token-dependent sliding-mode controller are designed. By taking the information of membership functions into stability and reachability analysis, MFD sufficient conditions are derived such that both the asymptotic stability of the closed-loop fuzzy systems and the reachability of the specified sliding surface can be guaranteed. Moreover, the cone complementary linearization (CCL) algorithm is employed to convert nonlinear inequalities into a minimization problem with linear constraints. Finally, a numerical example is utilized to illustrate the proposed SMC design approach.

H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information

In this paper, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stabilization problem is studied for discrete-time semi-Markov jump singularly perturbed systems (SMJSPSs) with repeated scalar nonlinearities. As the exact statistical information of the sojourn time or the mode transition is difficult to obtain, the case with only partial semi-Markov kernel information available is considered. Furthermore, introducing an external disturbance or nonlinearity into the analysis of discrete-time semi-Markov jump systems (DTSMJSs) meets critical obstacles, since the relation between the system state vectors at two nonadjacent instants is difficult to determine. To address this issue, the variation trend of the Lyapunov function for a semi-Markov jump sequence is analyzed in detail. Subsequently, criteria of mean-square exponential stability (MSES) for DTSMJSs are established for the first time based on the Lyapunov stability theory. By virtue of the criteria obtained and the cone complementary linearization algorithm, a controller ensuring MSES and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for discrete-time nonlinear SMJSPSs is constructed. Finally, the effectiveness and applicability of the proposed method are validated by simulation examples including an inverted pendulum model.