One-sided Lipschitz Nonlinearities 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.

Precise tracking control via iterative learning for one-sided Lipschitz Caputo fractional-order systems.

This paper investigates iterative learning control for Caputo fractional-order systems with one-sided Lipschitz nonlinearity. Both open- and closed-loop P-type learning algorithms are proposed to achieve perfect tracking for the desired trajectory, and their convergence conditions are established. It is shown that the algorithms can make the output tracking error converge to zero along the iteration axis. A simulation example illustrates the application of the theoretical findings, and shows the effectiveness of the proposed approach.

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

Observer-Based Adaptive Consensus Protocol Design for Multi-Agent Systems with One-Sided Lipschitz Nonlinearity

This paper considers the observer-based leader–follower consensus problem of multi-agent systems with one-sided Lipschitz conditions and quadratic inner-boundedness nonlinearity. Based on the relative outputs of neighboring agents, an adaptive protocol over a directed graph is designed via assigning a time-varying coupling weight to each node. Compared with the existing protocols, the proposed protocol can not only be utilized in the unidirectional flow of information, but it does not require any global graph information for its design. It has been shown that the established criteria can not only make the observer error tendency zero, but one can also achieve the leader–follower consensus of such nonlinear multi-agent systems. Furthermore, the gains of observer and protocol parameters can be constructed by solving the linear matrix inequalities (LMIs), which are conveniently checked. The results are illustrated by numerical simulations.

Consensus of multi-Agent systems with one-Sided lipschitz nonlinearity via nonidentical double event-Triggered control subject to deception attacks

As for the multi-agent systems (MASs) with time-varying switching subject to deception attacks, the leader-following consensus problem is studied in this article. The one-sided Lipschitz (OSL) condition is utilized for the nonlinear functions, which makes the results more general and relaxed than those obtained by Lipschitz condition. The nonidentical double event-triggering mechanisms (ETMs) are adopted for only a fraction of agents, and each agent transmits the data according to its own necessity. Semi-Markov process modeling with time-varying switching probability is adopted for switching topology and deception attacks occurring in transmission channel are considered. By using the cumulative distribution function (CDF) and the linear matrix inequality (LMI) technology, sufficient conditions for MASs to achieve consensus in mean square are obtained. An effective algorithm is presented to obtain the event-based control gains. The merits of the proposed control scheme are demonstrated via a simulation example.

Observer-Based Relative-Output Feedback Consensus of One-Sided Lipschitz Multi-Agent Systems Subjected to Switching Graphs

This article addresses a multiple Lyapunov functions approach for investigating an observer-based protocol for the consensus of nonlinear multiagent systems (MASs). Consensus protocol designs using relative-output feedback are developed by considering leader-following consensus and one-sided Lipschitz nonlinearity (OSL) under switching topologies. Switching occurrences are modeled using a relaxed average dwell time constraint. Consensus protocol designs have been provided for switching communication topologies that have a permanent or frequent directed spanning tree (DST) with respect to the leader. In contrast to conventional methods, a more practical and complicated output feedback approach for the consensus of OSL agents under switching topologies has been addressed. In addition, the scenario of frequent DST in a switching network is addressed for the first time to the best of our knowledge for the observer-based control protocol for MASs with OSL nonlinearities. Numerical simulations are provided for MASs to confirm observer-based protocol's proficiency at synchronization under switching graphs.

Robust leader-following consensus control of one-sided Lipschitz multi-agent systems over heterogeneous matching uncertainties

This paper presents a novel consensus control methodology for the multi-agent systems (MASs) with one-sided Lipschitz (OSL) nonlinearities under heterogeneous matching uncertainties, non-zero input to the leader, and external perturbations. A leader-following consensus control scheme is considered, and a control law is provided to assure that the followers track the leader successfully to deal with the uncertainties. The present work considers heterogeneous matching uncertainties, and a new approach with different Lyapunov function, rather than using Laplacian matrix term in the Lyapunov function, has been considered for complete elimination of the uncertainties. The proposed strategy is extended to the case where exogenous disturbances are also acting (to deal with un-matching uncertainties) on the nonlinear dynamics, and a robust consensus control approach is revealed. To overcome the chattering problem, a continuous-time consensus control law is also presented to guarantee the convergence of the consensus error to a small bounded set in the presence of external disturbance. To the best of the authors’ knowledge, consensus control of a generalized form of OSL agents for the complete elimination of heterogeneous matching uncertainties and for considering non-zero input to the leader has been explored for the first time. The developed treatment is different from the conventional methods on the linear or Lipschitz nonlinear multi-agents under heterogeneous uncertainties. Finally, an application of the proposed methods to moving agents is furnished to illustrate the strength of the resultant consensualization protocol.

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.

Robust sliding mode control for stochastic singular Markovian jump systems with unmatched one-sided Lipschitz nonlinearities

This paper investigates sliding mode control of stochastic singular Markovian jump systems with nonlinearity. The unmatched nonlinearity satisfies one-sided Lipschitz condition and quadratically inner-boundedness. In term of a new technical variable transformation, sufficient conditions are developed for nonlinear stochastic singular Markovian jump systems constrained on sliding manifold to guarantee stochastic admissibility and uniqueness of solution based on implicit function theorem. The sliding mode control law by which the trajectories of system can be compelled to the predefined sliding surface in finite time no matter what initial state value is, is synthesized. The derivative singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily.The technical treatment of the nonlinear matrix term avoids the classification discussion of sliding mode controller design. Convex optimization problems subject to linear matrix inequalities are formulated to optimize the desired indexes of interest. Finally, the effectiveness of the proposed approach is illustrated by a numerical example and a practical example.

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

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.

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 Delay-Dependent Approach to Finite-Time H∞ Control of Nonlinear Descriptor Systems with State Delay via Observer-Based Control

This paper proposes a finite-time observer-based controller for time-delay descriptor systems with time-varying disturbances, model uncertainties, and one-sided Lipschitz nonlinearities. For this purpose, first, a nonlinear descriptor observer is designed, and the observer error system is calculated. Then, the observer-based control law is proposed to provide the conditions for robust stabilization of the closed-loop descriptor system by selecting an appropriate Lyapunov–Krasovskii functional. According to the delay-dependent stability criterion, LMI-based sufficient conditions are derived and the gains of the controller and the observer are calculated. The proposed controller guarantees the finite-time boundedness and H∞ disturbance attenuation of the closed-loop descriptor system. Finally, the effectiveness of the proposed technique is investigated through computer simulations.

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.

Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

This paper investigates the problem of sliding mode control (SMC) for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates. Unmatched norm-bounded uncertainties of state matrices and output matrices are considered. First, a suitable integral-type sliding surface is proposed and a sufficient condition is given such that the sliding mode dynamics is stochastically stable with an H ∞ performance level γ. Next, an SMC law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, two simulation examples are provided to prove the effectiveness of the proposed approach.

Robust stabilization of one-sided Lipschitz nonlinear systems via adaptive sliding mode control

In this paper, the problem of adaptive sliding mode control for varied one-sided Lipschitz nonlinear systems with uncertainties is investigated. In contrast to existing sliding mode control design methods, the considered models, in the current study, are affected by nonlinear control inputs, one-sided Lipschitz nonlinearities, unknown disturbances and parameter uncertainties. At first, to design the sliding surface, a specific switching function is defined. The corresponding nonlinear equivalent control is extracted and the resulting sliding mode dynamic is given. Novel synthesis conditions of asymptotic stability are derived in terms of linear matrix inequalities. Thereafter, to ensure the reachability of system states and the occurrence of the sliding mode, the sliding mode controller is designed. Any knowledge of the upper bound on the perturbation is not required and an adaptation law is proposed. At last, two illustrative examples are introduced.

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.

Robust generalized observer design for uncertain one-sided Lipschitz systems

This paper develops a novel generalized observer design approach for the uncertain descriptor systems with one-sided Lipschitz nonlinearities, parametric uncertainties, and external perturbations. The nonlinearities, uncertainties, and external perturbations are considered both in input and output equations to consider a matter-of-fact observer design. A generalized structure for the observer is employed to deal with a large number of systems, considering both non-singular and singular systems. The proposed observer scheme is based on non-strict and strict linear matrix inequalities (LMIs), which are derived using the concepts of generalized Lyapunov theory, uncertainty bounds, quadratic inner-boundedness, one-sided Lipschitz condition, matrix transformations, and L2 gain minimization criteria. The proposed state filtering approach is robust for disturbances with asymptotically stable estimation error dynamics under zero external perturbations and attenuation of disturbance effects to keep the estimation error within prescribed limits. In comparison to the conventional observer designs for the one-sided Lipschitz systems, the presented scheme is based on a generalized observer and can deal with parametric uncertainties. A numerical simulation example and an application example of spring-mass-damper system are provided to verify the effectiveness of the suggested filtering schemes.

P-type Iterative Learning Control with Initial State Learning for One-sided Lipschitz Nonlinear Systems

In this paper, the problem of iterative learning control is considered for a class of one-sided Lipschitz nonlinear systems. For such nonlinear systems, open-loop and closed-loop P-type learning algorithms with initial state learning are adopted, respectively. Furthermore, the convergence conditions of the P-type learning algorithms are established. It is shown that both algorithms can guarantee the system output converges to the desired one on the whole time interval. A numerical example is constructed to illustrate the effectiveness of the proposed learning algorithms.