One-sided Lipschitz Nonlinear Systems Research Articles

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.

Observer-Based Distributed Adaptive Consensus Tracking of Nonlinear Multi-agent Systems on Directed Graphs

This paper studies the leader-following consensus problem of nonlinear multi-agent systems (MAS) with one-sided Lipschitz conditions under the directed graph, and a novel observer-based distributed tracking protocol that only utilizes the relative output information of adjacent agents is proposed. To avoid the disadvantage of solving Laplace matrix eigenvalues, a fully distributed adaptive consensus scheme is constructed. The sufficient conditions for linear matrix inequalities (LMIs) for the consensus of MAS systems are derived using the Lyapunov function and the properties of one-sided Lipschitz nonlinear systems. Finally, the effectiveness of the proposed control method can be verified by two examples-based simulations with a leader and five followers.

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Joint Estimation of State and Unknown Input for Nonlinear Interconnected Systems Based on Multiple Intermediate Estimator

This brief investigates the issue of state estimation and unbounded unknown input reconstruction for a class of one-sided Lipschitz nonlinear interconnected systems with uncertain output and mismatched unknown input distribution matrix. Based on descriptor augmentation strategy and coordinate transformation, the effect of measurement noise and matched unknown input parts are firstly decoupled. Then, a novel multi-intermediate estimator-assisted unknown input observer is constructed to estimate state and mismatched unknown input. In addition, sufficient conditions in linear matrix inequality (LMI) form is derived to guarantee the stability of the observer and to facilitate observer parameter tuning. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed methods.

Finite-time dissipative control design for one-sided Lipschitz nonlinear singular Caputo fractional order systems

ABSTRACT This paper presents an efficient analytical approach for solving the problem of dissipative control in one-sided Lipschitz singular Caputo fractional-order systems subject to nonlinear perturbations. The approach is based on mathematical transformations, and fractional calculus. A state feedback controller is designed to ensure that the closed-loop system is regular, impulse-free, and finite-time bounded with a dissipativity performance index. The results are established using tractable strict linear matrix inequalities (LMIs) without any equality constraint. Two numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Observer-based time-varying group formation tracking for one-sided Lipschitz nonlinear second-order multi-agent systems

This paper discusses the observer-based time-varying group formation tracking (TVGFT) control problem for one-sided Lipschitz nonlinear second-order multi-agent systems (MASs). The followers in the MASs are divided into multiple groups, where only one follower in each group knows the leaders information, and a control protocol is designed through the interactions among the followers. Based on the one-sided Lipschitz definition and the properties of Laplacian matrices, sufficient conditions are provided to achieve the TVGFT for one-sided Lipschitz nonlinear MASs. By solving the linear matrix inequality (LMI), sufficient criteria for achieving TVGFT can be obtained. Finally, it is demonstrated from simulations that the designed control protocol can achieve TVGFT effectively.

A new event-triggered distributed state estimation approach for one-sided Lipschitz nonlinear discrete-time systems and its application to wireless sensor networks

This article proposes the design of a distributed state estimator for a class of one-sided Lipschitz nonlinear systems over wireless sensor networks. The suggested estimation scheme utilizes the one-sided Lipschitz constraint in conjunction with quadratic inner-boundedness, which makes it applicable to a broader class of nonlinear systems. The proposed estimator design is evaluated under a conventional event-triggered mechanism both in the absence and presence of external perturbations. Furthermore, a novel event-triggering condition is introduced that ensures error convergence to the origin in the absence of external perturbations. It is further established that the inclusion of new triggering condition reduces the estimation error upper bounds in the presence of external disturbances and noises. Sufficient conditions for boundedness of estimation errors are derived for each case, and matrix inequalities are developed for the calculation of estimator gains. Finally, a numerical example is considered to illustrate the efficacy of the proposed estimator.

Robust observer-based dissipative control designs for fractional-order one-sided Lipschitz nonlinear systems

Robust observer-based dissipative control designs for fractional-order one-sided Lipschitz nonlinear systems

State-Based Dynamic Event-Triggered Observer for One-Sided Lipschitz Nonlinear Systems With Disturbances

Considering that the communication networks usually suffer from limited communication resources with detrimental consequences, this brief considers the state-based dynamic event-triggered observer issue for one-sided Lipschitz nonlinear systems (OLNSs) with disturbances. To reduce the supervision time, a discrete-time event-triggering mechanism (DETM) is proposed in accordance with sampled signals (SSs) and a dynamic function, which not only significantly reduces the utilization of communication resources but also maintains the desired system performance. Then, by resorting to an input-delay protocol, sufficient conditions are derived to guarantee that the state observer can availably estimate the state of the system. An illustrative example is provided to verify the merit of the achieved strategy.

Consensus in discrete-time one-sided Lipschitz nonlinear multi-agent systems with time-varying communication delay

This paper discusses consensus in discrete-time nonlinear multi-agent systems with time-varying delay in a directed communication topology. Since each agent can obtain information only from its neighbouring agents, for the purpose of analysis, a consensus protocol is proposed that considers the relative position information between the leader and followers and between neighbouring followers under time-varying communication delay. This nonlinear problem is solved by employing nonlinear behaviour based on the one-sided Lipschitz method. By constructing an appropriate Lyapunov-Krasovskii function, the consensus criterion for the leader-following problem is established in terms of the linear matrix inequality (LMI) framework. Furthermore, the solution of gain matrix is addressed by utilizing the cone complementarity linearization (CCL) algorithm. The results of a numerical simulation indicate that this method can be used to effectively solve this problem.

Fault-Tolerant Control of One-Sided Lipschitz Nonlinear Systems

In this short paper, development of an adaptive fault tolerant control (FTC) using a virtual actuator framework is presented for one-sided Lipschitz nonlinear systems subjected to time-varying loss of effectiveness and additive actuator faults. The proposed controller does not require to have a separate unit to detect, isolate, and identify a fault, and it is completely independent from the nominal controller. Due to this important property, the virtual actuator can easily added between the faulty plant and the nominal controller and it can guarantee that the deviation of states from the nominal behavior of the system in the presence of actuator faults can be made arbitrary small. Simulation results are provided to show the efficacy of the proposed adaptive fault tolerant controller.

Non-fragile observer-based quantized control for a class of one-sided Lipschitz systems

The topic of nonfragile observer design for a class of one-sided Lipschitz nonlinear systems with quantized inputs is investigated in this study. The one-sided Lipschitz and quadratically inner-bounded conditions were used to obtain less conservative synthesis requirements for the observer design. Sufficient conditions, stated in terms of linear matrix inequalities, are supplied using auxiliary variables and a decoupling method to ensure the resilience of the quantized closed-loop. The controller and observer gains may then be found in the same process. An example generated from a nonlinear DC motor model is provided to demonstrate the efficiency of the suggested technique.

Observer-Based $$H_\infty $$ Control for One-Sided Lipschitz Nonlinear Systems with Uncertain Input Matrix

Observer-Based $$H_\infty $$ Control for One-Sided Lipschitz Nonlinear Systems with Uncertain Input Matrix

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.

Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity. The uncertainty is assumed to be of a norm bound parametric type. Moreover, transient response shaping using the concept of ‘return time’ is also proposed. The controller design relies on the solution of Linear Matrix Inequalities (LMIs) and hence is computationally efficient. The proposed control law is linear in states, and thus the implementation is often straightforward. To illustrate the capability and simplicity of the proposed theory, three design examples are included.

Impulsive consensus of one-sided Lipschitz nonlinear multi-agent systems with Semi-Markov switching topologies

Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov chain is adopted to describe this kind of randomly occurring changes reasonably. To cope with the communication and control cost constraints in the multi-agent systems, the distributed impulsive control method is applied to address the leader–follower consensus problem. Beyond that, to obtain a wider nonlinear application range, the one-sided condition is delicately developed to the controller design, and the results are different from the ones obtained in the traditional method with the Lipschitz condition (note that the existing results are usually only applicable to the case with small Lipschitz constant). Based on the characteristics of cumulative distribution functions, the theory of Lyapunov-like function and impulsive differential equation, the asymptotically mean square consensus of multi-agent systems is maintained with the proposed impulsive control protocol. Finally, an explanatory simulation is presented to validate the correctness of the proposed approach conclusively.

Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

This paper investigates the problem of finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties. The system is subjected to event-triggered scheme, which can automatically monitor the data transmission. Firstly, a zero-order-hold is employed to guarantee the control signal to be continuous, and an observer is proposed to estimate the system states. Then, some sufficient conditions are given to ensure the FTB of the resulting closed-loop system under consideration. Based on these, an observer and an observer-based sliding mode controller can be simultaneously involved in the design at one step in terms of linear matrix inequalities (LMIs). Two convex optimization problems subjected to LMIs are formulated to optimize the desired performance indices of interest to us. Finally, two practical examples are provided to verify the effectiveness of the proposed method.

Distributed filtering for Markov jump systems with randomly occurring one-sided Lipschitz nonlinearities under Round-Robin scheduling

This paper focuses on distributed filter design for Markov jump one-sided Lipschitz nonlinear systems over a sensor network by applying Round-Robin scheduling scheme. The nonlinear perturbations occur randomly and satisfy the so-called one-sided Lipschitz constraint that is more general than the conventional Lipschitz restraint. Two categories of exogenous noises, i.e., the persistent bounded noise and square additive noise in l2 space, are taken into investigation, respectively. Meanwhile, the well-known Round-Robin scheduling protocol is employed to regulate the data transmission through the shared communication media. The exponential mean-square ultimate boundedness and stochastic bounded real lemma (BRL) are obtained for the filtering error dynamics, and then two distributed filters are correspondingly designed. Finally, an illustrative example shows the effectiveness of the proposed results.

Observer-based Time-varying Formation Tracking for One-sided Lipschitz Nonlinear Systems via Adaptive Protocol

In this paper, we investigate the problem of observer-based time-varying leader-following formation tracking for multi-agent systems with the one-sided Lipschitz and quadratic inner-boundedness nonlinear dynamics. An idea of the observer-based protocol with an edge-based adaptive law is designed for nonlinear systems, which enable agents to achieve a desired formation tracking when it cannot obtain the full state of the nonlinear system. In contrast to the previous nonlinear formation systems, the advantage of the developed method is that it is less conservative and more general for the nonlinear system with large Lipschitz constants. Besides, under the proposed adaptive law, the design of the protocol does not rely on the known communication topology. Finally, the simulation results for one leader and six followers are proposed to show the feasibility and effectiveness of the proposed method in the nonlinear time-varying formation system.

A novel approach for static anti-windup compensation of one-sided Lipschitz systems under input saturation

This paper illustrates a new strategy for designing the local static anti-windup (AW) compensator for nonlinear systems with one-sided Lipschitz (OSL) nonlinearities under saturating actuators and exogenous disturbances. The static AW strategy is designed such that the resulting closed-loop system with OSL nonlinearity, actuator saturation, and exogenous disturbance is stable and the region of attraction can be maximized. Inequalities based conditions are formulated for the static AW gain design by using Lyapunov stability theory, sector condition, L2 gain reduction, OSL inequality, and quadratic inner-bounded (QIB) condition. The proposed AW technique is simpler to design, straightforward to implement and deals with a broader class of systems in contrast to conventional methods. An application example demonstrates that the proposed static AW can successfully mitigate the saturation consequences in OSL nonlinear systems.