Global Robust Asymptotic Stability Research Articles

Global Stabilization of Antipodal Points on $n$-Sphere With Application to Attitude Tracking

Existing approaches to robust global asymptotic stabilization of a pair of antipodal points on unit $n$-sphere $\mathbb{S}^n$ typically involve the non-centrally synergistic hybrid controllers for attitude tracking on unit quaternion space. However, when switching faults occur due to parameter errors, the non-centrally synergistic property can lead to the unwinding problem or in some cases, destabilize the desired set. In this work, a hybrid controller is first proposed based on a novel centrally synergistic family of potential functions on $\mathbb{S}^n$, which is generated from a basic potential function through angular warping. The synergistic parameter can be explicitly expressed if the warping angle has a positive lower bound at the undesired critical points of the family. Next, the proposed approach induces a new quaternion-based controller for global attitude tracking. It has three advantageous features over existing synergistic designs: 1) it is consistent, i.e., free from the ambiguity of unit quaternion representation; 2) it is switching-fault-tolerant, i.e., the desired closed-loop equilibria remain asymptotically stable even when the switching mechanism does not work; 3) it relaxes the assumption on the parameter of the basic potential function in literature. Comprehensive simulation confirms the high robustness of the proposed centrally synergistic approach compared with existing non-centrally synergistic approaches.

Global robust stability of fuzzy cellular neural networks with parameter uncertainties

<abstract><p>The global robust stability of uncertain delayed fuzzy cellular neural networks (UDFCNNs) was analyzed in this paper. The major results of this paper provided some new criteria for the existence and uniqueness of the equilibrium point of UDFCNN. Furthermore, suitable Lyapunov-Krasovskii functionals was designed for obtaining the adequate conditions for the global asymptotic robust stability and global exponential robust stability of UDFCNN. Finally, several numerical examples was provided to verify the validity of the results.</p></abstract>

Synchronization of chaotic satellite systems with an unknown parameter

Spacecraft (satellite) formation has several applications in space exploration. Synchronization controllers are essential in satellite formation systems. This article proposes a novel robust adaptive synchronization control (RASC) technique for two identical three-dimensional chaotic satellite systems attitude synchronization with an unknown system parameter, unknown bounded model uncertainties, unknown external disturbances, and nonlinear terms. This controller achieves smooth error vector convergence to zero. The closed-loop has a robust performance as the controller avoids plant nonlinear terms cancellation. This controller has two parts. (i) A nonlinear controller for keeping the closed-loop stable; it flourishes robust and faster error vector convergence to zero with reduced fluctuations. (ii) An adaptive nonlinear controller that compensates exogenous disturbances and model uncertainties using online estimations of model uncertainties and bounds. The Lyapunov stability theory assures the closed-loop's global asymptotic robust stability. Computer simulation results-based analysis verifies the theoretical findings. The article includes a comparative study and discusses the control effort saturation effects.

Weighted input-to-output practical stability of non-autonomous infinite-dimensional systems with disturbances

In this paper, we introduce a new concept of weighted input-to-output practical stability (WIOpS) and weighted integral-input-to-output practically stable (WiIOpS) for non-autonomous infinite-dimensional systems with disturbances. By using the notion of practical stable scalar functions, sufficient conditions for WIOpS and WiIOpS are derived. As a result, the robust global asymptotic output practical stability criteria of non-autonomous infinite-dimensional systems with zero input is also established via an indefinite Lyapunov function. Thus, we study the UWISpS of non-autonomous nonlinear evolution equations. Moreover, we discuss UWISS and UWiISS for linear non-autonomous infinite-dimensional control systems. A feedback law is provided for a class of semi-linear evolution equations by which the closed-loop system is uniform input-to-state practical stable (UISpS) with respect to disturbances acting in the input. Two examples are given throughout the paper to illustrate the theoretical results.

Robust Global Asymptotic Stabilization of Linear Cascaded Systems With Hysteretic Interconnection

We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

New Global Asymptotic Robust Stability of Dynamical Delayed Neural Networks via Intervalized Interconnection Matrices.

This article identifies a new upper bound norm for the intervalized interconnection matrices pertaining to delayed dynamical neural networks under the parameter uncertainties. By formulating the appropriate Lyapunov functional and slope-bounded activation functions, the derived new upper bound norms provide new sufficient conditions corresponding to the equilibrium point of the globally asymptotic robust stability with respect to the delayed neural networks. The new upper bound norm also yields the optimized minimum results as compared with some existing methods. Numerical examples are given to demonstrate the effectiveness of the proposed results obtained through the new upper bound norm method.

Novel criteria for robust stability of Cohen-Grossberg neural networks with multiple time delays

<p style='text-indent:20px;'>This research paper deals with the investigation of global robust stability results for Cohen-Grossberg neural networks involving the multiple constant time delays. The activation functions in this neural network model are supposed to be in the set of non-decreasing slope-bounded nonlinear functions and the uncertainties in the constant network parameters are considered to have bounded upper norms. By employing a proper positive definite Lyapunov-type functional and using homeomorphism mapping theory, we propose some novel sets of novel conditions that assure both existence, uniqueness and global robust asymptotic stability of equilibrium points of this nonlinear Cohen-Grossberg-type neural network model involving the multiple time delays. The derived robustly stable conditions mainly rely on examining some proper relationships that are imposed on constant valued interconnection matrices of this delayed neural network. These stability conditions can be certainly verified by employing various simple and useful properties of real interval matrices. Some comparisons are made to address the key advantages of these novel criteria over previously reported corresponding results. An instructive example is also examined to observe novelty of these proposed criteria.</p>

Robust attitude control of the three-dimensional unknown chaotic satellite system

This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

Novel criteria for global robust stability of dynamical neural networks with multiple time delays

This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.

Disturbance decoupling by state feedback for uncertain impulsive linear systems

AbstractThe problem of making the output of a linear system with polytopic uncertainties and discontinuities in the state evolution totally insensitive to an unknown disturbance input by state feedback is investigated. Suitable geometric notions are introduced and used to provide a structural, constructive solvability condition. The requirement of achieving global robust asymptotic stability of the compensated dynamics is then added and further solvability conditions are provided by requiring that the time instants at which discontinuities in the state evolution, or jumps, occur are sufficiently far from each other.

Enhanced two-loop model predictive control design for linear uncertain systems

Model predictive controllers (MPC) with the two-loop scheme are successful approaches practically and can be classified into two main categories, tube-based MPC and MPC-based reference governors (RG). In this paper, an enhanced two-loop MPC design is proposed for a pre-stabilized system with the bounded uncertainty subject to the input and state constraints. The proposed method offers less conservatism than the tube-based MPC methods by enlarging the restricted input constraint. Contrary to the MPC-based RGs, the investigated method improves tracking performance of the pre-stabilized system while satisfying the constraints. Additionally, the robust global asymptotic stability of the closed-loop system is guaranteed in a novel procedure with terminal constraint relaxation. Simulation of the proposed method on a servo system shows its effectiveness in comparison to the others.

Observer-Based Adaptive Hybrid Feedback for Robust Global Attitude Stabilization of a Rigid Body

In this article, an observer-based adaptive hybrid attitude controller is presented that overcomes the topological obstructions associated with the global attitude stabilization. This hybrid controller consists of two major parts: an adaptive trimodal hybrid controller to eliminate unwinding phenomenon, and a centrally synergistic potential function. In the adaptive trimodal hybrid controller, the first logic variable selects, which quaternion representation of the desired attitude should be tracked. Furthermore, an adaptive technique is introduced to collaborate with the second logic variable to adapt the hysteresis width. The third logic variable controls the mismatch between the auxiliary dynamical system and the actual attitude. Moreover, an auxiliary dynamical system and a nonlinear angular velocity observer are presented whose outputs are utilized in the proposed feedback control law to attain the necessary damping. Furthermore, a new centrally synergistic potential function is presented to cooperate with the trimodal hybrid controller to overcome the topological obstruction associated with the vector bundle structure. The robust global asymptotic stability of the consequent closed-loop system is guaranteed through a Lyapunov analysis. A comparative analysis in simulations illustrates the effectiveness and superiority of the proposed control scheme.

Enhancement of High-Fidelity Haptic Feedback Through Multimodal Adaptive Robust Control for Teleoperated Systems

Achieving high-fidelity haptic feedback in teleoperated robotic systems is crucial, particularly in applications, such as medical, industrial, military, space, and underwater explorations. The quality of haptic feedback depends to a great extent on the controller design objectives, such as stability and transparency. In addition to the time delay, the most challenging issues that affect haptic feedback are model uncertainties, parametric variations, and external disturbances. In this article, such issues have been addressed by developing a novel multimodal adaptive robust control algorithm for teleoperated systems with time-varying delay. Here, parametric convergence is achieved swiftly with a milder condition than a stronger persistent excitation condition on the regressor signal, resulting in the enhancement of transient performance. The proposed method ensures the robustness of the system against bounded perturbations and high-frequency unmodeled dynamics using a modified terminal sliding-mode controller alongside the adaptive scheme. The proposed method promises high-fidelity haptic feedback to the operator by ensuring improved robust global asymptotic stability, synchronization, and transparency, addressing parametric variations and disturbances. The validity of the proposed adaptive robust control law is substantiated through simulations and comparisons with the existing methods for a 2-R teleoperation system. The experimental results for a 1-R teleoperation system are also presented.

Robust stability of moving horizon estimation for non‐linear systems with bounded disturbances using adaptive arrival cost

Fil: Deniz, Nestor Nahuel. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas. Instituto de Investigacion en Senales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional del Litoral. Facultad de Ingenieria y Ciencias Hidricas; Argentina

Global Stability Analysis of Neural Networks with Constant Time Delay via Frobenius Norm

This paper deals with the global asymptotic robust stability (GARS) of neural networks (NNs) with constant time delay via Frobenius norm. The Frobenius norm result has been utilized to find a new sufficient condition for the existence, uniqueness, and GARS of equilibrium point of the NNs. Some suitable Lyapunov functional and the slope bounded functions have been employed to find the new sufficient condition for GARS of NNs. Finally, we give some comparative study of numerical examples for explaining the advantageous of the proposed result along with the existing GARS results in terms of network parameters.

Explicit Construction of Stabilizing Robust Avoidance Controllers for Linear Systems With Drift

We propose a constructive design method for linear systems with a nontrivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, is investigated via numerical examples.

Novel Results on Global Robust Stability Analysis for Dynamical Delayed Neural Networks Under Parameter Uncertainties

In this paper, we focus on the global stability analysis with respect to dynamical delayed neural networks (NNs) that contain parameter uncertainties. Many investigations on the sufficient conditions utilizing different upper bounds for the norm of interconnection matrices pertaining to the global asymptotic robust stability of delayed NNs have been conducted. In this study, a new upper bound of the norm of connection weight matrices is derived for the delayed NNs under parameter uncertainties. The key focus is on how the new upper bound is able to yield minimum result with respects to some of the existing upper bounds. We demonstrate that the new upper bound can lead to some new sufficient conditions with respect to the global asymptotic robust stability of equilibrium point of the delayed NNs. The slope bounded activation functions and Lyapunov-Krasovskii functionals (LKFs) are employed for formulating the sufficient conditions of the equilibrium point of NNs. Moreover, the derived sufficient conditions are independent on the time delay parameter. Numerical examples are provided and the outcomes obtained are compared with those of the existing results subject to different network parameters.

Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

In this paper, the global robust asymptotic stability problem for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. The proposed generalized neural networks model includes reaction–diffusion local field neural networks and reaction–diffusion static neural networks as its special cases. By using stochastic analysis approaches and constructing a suitable Lyapunov–Krasovskii functional, some simple and useful criteria for global robust asymptotic stability of the neural networks are obtained. According to the theoretical results, the influences of diffusion coefficients, diffusion spaces, stochastic perturbation, and uncertain parameters are analyzed. Finally, numerical examples are provided to show the feasibility and efficiency of the proposed methods, and by choosing different diffusion coefficients and diffusion spaces, different stability states can be achieved.

A Nonsmooth Hybrid Invariance Principle Applied to Robust Event-Triggered Design

We first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone, and complete jumping solutions cannot jump outside the jump and flow sets. We then show an application consisting in the design of event-triggered rules to stabilize a class of uncertain linear control systems. The event-triggering rule depends only on local information, that is it uses only the output signals available to the controller. The approach proposed combines hybrid and sampled-data tools. The proposed design conditions are formulated in terms of linear matrix inequalities (LMIs) ensuring global robust asymptotic stability of the closed-loop system. A tunable parameter is also available to guarantee an adjustable dwell-time property of the solutions. The effectiveness of the approach is evaluated through an example borrowed from the literature.

Nonlinear moving horizon estimation in the presence of bounded disturbances

In this paper, we propose a new moving horizon estimator for nonlinear detectable systems. Similar to a recently proposed full information estimator, the corresponding cost function contains an additional max-term compared to more standard least-squares type approaches. We show that robust global asymptotic stability in case of bounded disturbances and convergence of the estimation error in case of vanishing disturbances can be established. Second, we show that the same results hold for a standard least-squares type moving horizon estimator, which so far has not been proven even in the full information estimation case. An additional advantage of the proposed estimators is that a suitable prior weighting appearing in the cost function can explicitly be determined offline, which is not the case in various existing approaches.