Cone Complementary Linearization Research Articles

GeneralizedH2control of the linear system with semi‐Markov jumps

AbstractThis article studies a class of asynchronous generalizedH2control problems for continuous‐time discrete‐state semi‐Markov jump linear systems. By constructing a Lyapunov function based on the semi‐Markov process, introducing a weak infinitesimal operator and applying the smoothness of the expectation, sufficient conditions are obtained to ensure stochastic stability and generalizedH2performance of the system. Simultaneously, equivalent conditions are given by introducing slack variables and an asynchronous controller is designed. Moreover, we derive the sufficient conditions for the case where the transition rate is partially unknown. Finally, we use the cone complement linearization iterative algorithm to simulate two examples to prove the effectiveness of the design scheme.

Event‐triggered dynamic output feedback control for networked nonlinear systems

SummaryIn this article, the problem of event‐triggered dynamic output feedback control is investigated for a class of networked nonlinear systems with mixed delays and packet dropouts. By applying the cone complementary linearization technique, sufficient conditions are developed such that the resulting closed‐loop system dynamics is mean square asymptotically stable with a desired performance level. The effectiveness of the proposed method is demonstrated via an illustrative example.

Asymptotic stability analysis and model reduction for spatially interconnected time-delay systems

This paper deals with problems of asymptotic stability analysis and model reduction for spatially interconnected continuous time-delay systems. The well-posedness, asymptotic stability, and contractiveness of spatially interconnected continuous-time state-delay systems are appropriately defined. The Lyapunov–Krasovskii method is extended for asymptotic stability analysis of spatially interconnected continuous time-delay systems in infinite-dimensional space. A sufficient condition based on the given system matrices is presented in terms of linear matrix inequalities to check the well-posedness, asymptotic stability, and contractiveness. We then obtain a sufficient condition for the existence of a delay-free reduced-order system for a given spatially interconnected continuous time-delay system. Employing the elimination lemma and the cone complementary linearization algorithm, we can obtain a delay-free reduced-order system. Finally, two examples are used to demonstrate the effectiveness and applicability of the proposed method.

Consensus Control of Nonlinear Multiagent Systems with Incremental Quadratic Constraints and Time Delays

This paper considers the problem of consensus control for a class of nonlinear multiagent systems with incremental quadratic constraints and time delays. Each agent exchanges state information through a strongly connected communication topology. Based on the information obtained from neighboring agents, a distributed consensus protocol is designed. A delay-independent consensus condition is formed for the protocol to solve the consensus problem by employing Lyapunov–Krasovskii functional method. In order to deal with the nonlinear terms in matrix inequalities, an iterative algorithm is proposed by using the Schur complement lemma and the cone complementary linearization method. The nonlinearities under consideration are more general than many other nonlinearities considered in related literature studies since the incremental quadratic constraints include many other known nonlinearities as some special cases. Finally, we give a numerical example to illustrate the effectiveness of the proposed consensus control protocol.

Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework.

This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction is to simplify the high-order complex systems by reducing the order of the original system. The aim of this article is to reduce the order of the original stochastic discrete-time IT2 fuzzy system into lower order system without ignoring the influence of IT2 membership functions. First, the Hankel-norm performance of the stochastic discrete-time IT2 fuzzy model is analyzed. Then, based on the projection theorem and cone complementary linearization approach, a convex Hankel-norm-based model reduction approach subject to conditions in the form of linear matrix inequalities (LMIs) is obtained. A membership-functions-dependent (MFD) technique is applied to capture the information of IT2 membership functions and further reduce the conservativeness. A numerical example is presented to illustrate the effectiveness of the proposed results.

Static output feedback problem for Lipschitz nonlinear systems

The output feedback stabilization of Lipschitz nonlinear systems is addressed. The synthesis of reduced-order controller is formulated as static output feedback problem. Based on coupled algebraic Riccati inequalities, the stability analysis of closed loop dynamic is presented. By utilizing some structural knowledge of Lipschitz nonlinearity, the sufficient conditions to obtain static as well as dynamic output feedback gains are given. For the class of Lipschitz nonlinearity, it is shown that the proposed condition is a necessary and sufficient condition to achieve static gain. The cone complementary linearization method is then applied to satisfy the proposed stability condition and to obtain an output feedback regulator. The effectiveness of proposed method is finally demonstrated through simulation results on some practical systems.

Novel results on observer-based control of one-sided Lipschitz systems under input saturation

This paper addresses the design of an observer-based control system for the one-sided Lipschitz (OSL) nonlinear systems under input saturation. A nonlinear matrix inequality-based control law for the nonlinear systems under input saturation and unavailable states is derived to ensure convergence of the state vector to the origin. A decoupling approach is provided for attaining simple design constraints for computing the controller and observer gains through a cone complementary linearization algorithm. In contrast to the conventional decoupling methods, the proposed approach considers OSL nonlinearity and saturation function to demonstrate both the necessity and sufficiency of the decoupled design constraints for the nonlinear matrix inequality-based main condition. To the best of our knowledge, observer-based stabilization of OSL systems under input saturation has been addressed for the first time. Novel results for the observer-based control of input-constrained Lipschitz nonlinear systems are provided as specific scenarios of the proposed results. Simulation results of the proposed control scheme to a flexible-joint robot and a complex nonlinear circuit are presented.

Finite-time sensor fault diagnosis observer design for attitude control systems of satellite based on sampled-data descriptor systems

In this paper, a finite-time robust sensor fault diagnosis observer with non-singular structure is proposed for Attitude Control Systems of satellite based on Lipschitz non-linear sampled-data descriptor systems with state time-varying delay. Firstly, an Attitude Control Systems model based on sampled-data descriptor system with time-varying delay is proposed and transformed into a discrete-time non-singular one. Then, a sensor fault diagnosis observer is designed upon on the state estimation error and the measurement residual. The finite-time stability and robustness of the augmented error dynamic model is analyzed, the H infinity performance index in finite-time is satisfied. As the confining matrices of the observer parameters do not meet the Linear Matrix Inequality, a cone complementary linearization iteration algorithm is proposed to solve this problem. Residual evaluation function and the threshold are introduced for judging if the faults occur. At the end, simulation examples are given to illustrate the effectiveness of this method.

Consensus of One-Sided Lipschitz Multiagents Under Switching Topologies

This paper considers the leader-following consensus of multiagents with one-sided Lipschitz nonlinear dynamics by considering switching topologies. For the suitable selection of the consensus control gain matrix and coupling weight, a new condition for consensus is achieved for switching communication links with a directed spanning tree in the topology by constraining the dwell time. Employing a communication restoration mechanism allows a method to be obtained for the case in which a topology violates a permanent directed spanning tree. Computationally straightforward consensus controller design conditions that are necessary and sufficient for the former conditions are also developed for both cases. These simpler conditions can be used to obtain consensus protocol gains directly through convex routines. An algorithm is also provided to solve nonlinear constraints using the cone complementary linearization approach by considering a nonlinear objective function optimization problem. A numerical simulation is provided for multiagents that demonstrates the proposed control schemes’ efficiency.

Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

This paper focuses on the synchronization of uncertain coronary artery chaos systems (CACSs) with the state and input time-varying delays under input saturation. First, the stability of the closed-loop system is established to ensure the synchronization between the diseased and healthy CACSs under input saturation by utilizing the local sector condition and the Lyapunov–Krasovskii functional (LKF) method. The use of Wirtinger inequality and the reciprocally convex method further reduces the conservatism. Second, by making use of the cone complementary linearization approach to deal with nonlinear terms, we obtained a state feedback controller. Finally, a robust state feedback controller is formulated to achieve the synchronization of the CACS under disturbances bounded by $L_{2}$ norm. The simulation results of the CACS synchronization are presented to demonstrate the effectiveness of the derived results, which provides a certain theoretical basis for curing diseases related to the coronary artery vessel.

Robust Antiwindup for One-Sided Lipschitz Systems Subject to Input Saturation and Applications

This paper presents the robust nonlinear dynamic antiwindup compensator (AWC) design for nonlinear systems with parametric uncertainties and one-sided Lipschitz nonlinearities under actuator saturation. A decoupling architecture for a full-order AWC is proposed for the case of parametric uncertainties. AWC synthesis scheme is derived by employing the quadratic Lyapunov function, the notion of quadratic inner-boundedness, the one-sided Lipschitz condition, sector condition, and ${{\mathcal L}_2}$ gain minimization. An algorithm, based on the convex routines, by employing the cone complementary linearization, recursive computation, and a bilinear term resolving approach is provided for obtaining the AWC parameters. In contrast to the existing nonlinear AWC designs, our results provide a remedy to the input saturation for a widespread class of nonlinear systems and can effectively deal with the parametric uncertainties. The suggested AWC methodology is employed to compensate windup in the buck–boost converter and one-link flexible robot with revolute joint.

Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures

ABSTRACTThis paper investigates the problem of adaptive sliding mode control for a class of interval type-2 Itô stochastic fuzzy systems, where the actuator failures may happen. The sliding function is firstly constructed, whose key feature is its dependence on the upper membership functions. And then, an adaptive scheme is proposed to estimate the effectiveness lose values of faulty actuators, and a sliding mode controller based on estimating scheme is designed such that the reachability of the specified sliding surface can be guaranteed even in the presence of actuator failures, in which the lower and upper membership functions are involved. Moreover, the stability conditions of sliding mode dynamics are derived, which involve some coupling terms of Lyapunov matrix and the sliding matrix. By introducing additional matrix variables and employing the cone complementary linearisation algorithm, the above nonlinear stability criterions are decoupled and lastly converted to a minimisation problem with linear constraints. Finally, a numerical example demonstrates the validity of the proposed method.

Quantized Output Feedback Control of Networked Control Systems with Packet Dropout

This paper considers the quantized dynamic output feedback control of networked control system(NCS) with random packet dropout in both sensor-to-controller and controller-to-actuator channels. The packet losses in the two links are modeled as two independent Markov chains and the NCS is modeled as a Markov jump system. The stochastic switching signal for the quantized output feedback controller is designed to be a function of the number of successive packet loss in both of the two channels. Quantization density varies with the networked load condition. Then a sufficient condition of the stochastic stability with a prescribed H∞ performance level is established based on the Lyapunov-Krasovskii function approach. Furthermore, a quantized output feedback controller is obtained via the cone complement linearization method. Finally, simulation results are provided to verify the effectiveness of the proposed method.

Observer‐Based H∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

AbstractThe paper investigates the observer‐based H∞ synchronization for coronary artery time‐delay system under the state immeasurement and external uncertainty. A Luenberger‐like state observer, the observation system, is designed to realize the state reconstruction of the master system. Based on the Lyapunov stability theory and Lyapunov‐Krasovskii functional (LKF), the observer‐based synchronization control condition is derived for a coronary artery system subjected to the external uncertainty bounded by L2 norm. By introducing the delay‐interval bounds and delay‐derivative limits in LKF, the time‐delays are handled by the delay‐range‐dependent strategy. The tighter upper bound of inequality can be obtained to reduce the conservation by employing further improved result of Jensen inequality and reciprocally convex approach. Furthermore, a decoupling technique is utilized to render the separate and simple controller and observer synthesis condition, which can be further solved by applying the cone complementary linearization approach respectively. Numerical simulations are listed to exhibit the effectiveness of the presented methodology.

Finite-time stability and stabilization for Itô-type stochastic Markovian jump systems with generally uncertain transition rates

This paper investigates the problems of finite-time stability and stabilization for stochastic Markovian jump systems with generally uncertain transition rates (SMJSwGUTRs). Firstly, a less conservative stability criterion is presented by a mode-dependent approach. Then, the state feedback controller and observer-based controller are designed by a cone complementary linearization method, and two specific algorithms are presented. Finally, an example is used to illustrate our results.

Observer-Based Control for Piecewise-Affine Systems With Both Input and Output Quantization

This technical note is concerned with the problem of simultaneous design of observers and controllers for a class of piecewise-affine systems against signal quantization occurring in both measurement output and control input channels. The general scenario is considered that system state and estimated state may not be in the same operating region. By a novel quantization-error-dependent Lyapunov function, the stability and $\mathcal {H}_{\infty }$ performance criteria are first established for the augmented system composed of a closed-loop control system and an estimation error system with the aid of $S$ -procedure involving the region partition information of the original system. Then, by the cone complementary linearization algorithm, the desired observer and controller gains are solved simultaneously such that the resulting closed-loop system is asymptotically stable with a prescribed $\mathcal {H}_{\infty }$ performance index. Finally, a networked single-link robot arm is utilized to demonstrate the effectiveness of the proposed control strategy.

Asynchronous observer-based [formula omitted] control for switched stochastic systems with mixed delays under quantization and packet dropouts

In this paper, the observer-based H∞ control problem is investigated for a class of discrete-time switched stochastic systems with mixed delays comprising both discrete and distributed delays. The measurement output of the addressed system is subject to quantizations and packet dropouts. The observer/controller switching is allowed to be asynchronous with the subsystem switching. An observer-based controller is designed such that, in the simultaneous presence of system switches, mixed delays, quantizations and packet dropouts, the closed-loop system is guaranteed to be mean-square exponentially stable while achieving the prescribed H∞ performance constraints. Based on the piecewise Lyapunov-like functionals and the average dwell-time switching, sufficient conditions are first established under which the closed-loop system is mean-square exponentially stable with a weighted disturbance attenuation level. Then, the explicit characterizations of the observer/controller gains are obtained by means of certain nonlinear matrix inequalities that can be effectively solved by applying the cone complementary linearization algorithm. Finally, a numerical example is given to show the effectiveness of the proposed design scheme.

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Reliable Filter Design for Sensor Networks Using Type-2 Fuzzy Framework

This paper studies the problem of reliable filter problem for a category of sensor networks in the framework of interval type-2 fuzzy model. In the filter design, the random link failures, which are caused possibly by missing measurements as well as by probabilistic communication failures, are considered to illustrate more realistic dynamical behaviors of sensor networks. In order to tackle the uncertainties existing in systems, interval type-2 (IT2) fuzzy approach is utilized to establish the model, wherein upper and lower membership functions together with weighting coefficients are employed to express the uncertainties. An distributed IT2 fuzzy filter model is constructed to estimate system states. Using the Lyapunov theory, sufficient conditions have been given to ensure that the filtering error system is mean-square asymptotically stable and satisfies the predefined average $ \mathcal {H}_{\infty }$ performance level. Moreover, the criteria to design the filter parameters are developed through using cone complementary linearization approach. Finally, a practical example is given to validate the proposed method.

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

This paper addresses the filtering problem for the one-sided Lipschitz nonlinear systems under measurement delays and disturbances using a generalized observer. A generalized architecture for filtering of the one-sided Lipschitz nonlinear systems with output delays is explored, which exhibits diverging manifolds, namely, the conventional static-gain filter and the dynamical filter, and can be employed to render robust stability of the filtering error dynamics. A matrix inequality based framework is obtained by employing a Lyapunov−Krasovskii (LK) functional, whose derivative is exploited through Jensen's inequality, one-sided Lipschitz condition, quadratic inner-boundedness inequality and range of the measurement delay, resulting into L2 stability for the filtering error system. Generalized filter design for the Lipschitz nonlinear systems with delayed outputs and specific results for the delay-dependent and delay-rate-independent filtering schemes for the one-sided Lipschitz nonlinear systems are deduced from the proposed approach. Convex optimization techniques are employed to achieve a solution for the nonlinear constraints through linear matrix inequalities by employing cone complementary linearization approach. Illustrative numerical examples to demonstrate the effectiveness of proposed method are provided.