Stabilization Of Uncertain Nonlinear Systems Research Articles

Semi-globally practical finite-time stability for uncertain nonlinear systems based on dynamic surface control

ABSTRACT In this paper, a semi-globally practical finite-time stability (SGPFS) problem is investigated for a class of uncertain nonlinear systems. Two well-known control techniques, dynamic surface control (DSC) and adding a power integrator (AAPI), are combined to obtain the semi-globally practical finite-time controller. With the aid of DSC, a less-complex finite-time control algorithm is presented, which makes the closed-loop system SGPF-stable. Two examples are provided to explain the feasibility and effectiveness of the proposed design technique.

Adaptive fuzzy finite-time stability of uncertain nonlinear systems based on prescribed performance

The semi-globally practical finite-time stability (SGPFS) problem for a class of uncertain strict-feedback nonlinear systems is discussed in this paper. A novel performance function called finite-time performance function (FTPF) is first defined. Moreover, this paper is the first to solve an adaptive semi-globally practical finite-time control issue by combining with backstepping, prescribed performance control (PPC) and fuzzy logic systems. Furthermore, it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite-time, but also all the signals of the closed-loop systems are SGPF-stable. Simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method.

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

AbstractA new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.

Constrained extremum seeking stabilization of systems not affine in control

SummaryRecently, a form of extremum seeking for control (ESC) was developed for the stabilization of uncertain nonlinear systems. In ESC, the extremum seeker itself directly controls the systems through feedback rather than fine tuning a controller. The ESC results, and other related results, apply only to systems affine in control. However, in most physical systems, the control effort enters the system's dynamics through a nonlinear function, such as an input with deadzone and saturation. In this work, we use our previous results on ESC to develop constrained extremum seeking stabilizing controllers for systems of practical interest that are nonaffine in control. Considering that any odd function can be approximated arbitrarily well by an odd polynomial, we present analytic results for designing controllers for systems in which control enters the system dynamics through an odd polynomial. Furthermore, we study the robustness of the scheme to uncertainty in the odd polynomial degree as well as robustness to even‐powered perturbations.

Finite-Time Stability of Uncertain Nonlinear Systems with Time-Varying Delay

The problem of finite-time stability for a class of uncertain nonlinear systems with time-varying delay and external disturbances is investigated. By using the Lyapunov stability theory, sufficient conditions for the existence of finite-time state feedback controller for this class of systems are derived. The results can be applied to finite-time stability problems of linear time-delay systems with parameter uncertainties and external disturbances. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.

Output Feedback Stabilization and Estimation of the Region of Attraction for Nonlinear Systems: A Vector Control Lyapunov Function Perspective

This technical note deals with (local) asymptotic stabilization of uncertain nonlinear systems by output feedback control. Our study provides a new design technique from a vector control Lyapunov function perspective. A comparison principle is developed and as a major consequence, an effective estimation method of the region of attraction (ROA) is established. Application to a class of minimum-phase strict-feedback nonlinear systems gives rise to a constructive stabilization design as well as an estimate of the resulting ROA.

Study of the Stabilization of Uncertain Nonlinear Systems Controlled by State Feedback

Study of the Stabilization of Uncertain Nonlinear Systems Controlled by State Feedback

Robust finite-time stabilization of uncertain nonlinear systems based on partial stability

This paper presents a new approach to design a robust finite-time partial stabilization for uncertain nonlinear systems. The main contribution of this paper is to divide system state into two subsystems based on their required stability properties, and to stabilize just one of them in finite-time. First, integral sliding mode control is applied and the system is converted to a chain of integrators. Then, a finite-time state feedback controller with dynamical gains is utilized. Since guidance issue is an appropriate example in which stabilization of all of the state variables is not desirable, the proposed approach is employed to design a robust finite-time convergent guidance law. Simulation results justify that the proposed method is reliable in terms of robustness and effectiveness.

Stabilization of nonlinear uncertain systems with stochastic actuator failures and time-varying delay

Summary In this paper, we investigate the adaptive state-feedback stabilization problem for a class of nonlinear systems subject to parametric uncertainties, time-varying delay, and Markovian jumping actuator failures. First, some fundamental results, including the infinitesimal generator and conditions for the existence and uniqueness of the solution, are established for nonlinear systems w.r.t. Markovian vector and time-varying delay. Subsequently, corresponding stability criterion is generalized to the considered systems. By employing the backstepping method and the tuning function technique, a systematic adaptive fault-tolerant control scheme is proposed, which guarantees the boundedness in probability of all the closed-loop signals. It is noted that no fault detection and diagnostic block are needed, and the control law can be adapted automatically by taking account of the innovative state information. The efficiency of the designed controller is demonstrated by an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.

Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control

This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique.

Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system

Design of a novel global sliding mode control law for the stabilization of uncertain nonlinear systems is presented in this article. A sufficient condition is derived using the Lyapunov theorem and linear matrix inequality to guarantee the asymptotical stability of the states and to improve the stability of the system. Under the uncertainty and nonlinearity effects, the reaching phase is eliminated and the chattering is reduced effectively and then, the robustness and performance of the system are improved. Lastly, the proposed method is applied on Genesio's chaotic system and the simulation results demonstrate the effectiveness of this technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 94–98, 2015

Adaptive Backstepping Stabilization of Nonlinear Uncertain Systems With Quantized Input Signal

In this paper, we study a general class of strict feedback nonlinear systems, where the input signal takes quantized values. We consider a stabilization problem for nonlinear uncertain systems via adaptive backstepping approach. The control design is achieved by introducing a hysteretic quantizer to avoid chattering and using backstepping technique. A guideline is derived to select the parameters of the quantizer. The designed controller together with the quantizer ensures the stability of the closed-loop system in the sense of signal boundedness.

Global Asymptotic Stabilization of Uncertain Nonlinear Systems via System Reconfiguration and Lyapunov Equation Utilization

Global Asymptotic Stabilization of Uncertain Nonlinear Systems via System Reconfiguration and Lyapunov Equation Utilization

Global adaptive output stabilization of uncertain nonlinear systems with polynomial output depending growth rate

SUMMARYThis paper investigates the problem of global output stabilization for a family of uncertain nonlinear systems, which are dominated by a triangular‐type condition. The distinguishing feature of such a class of systems is the presence of unmeasured states growth with growth rate polynomial of output‐input multiplying an unknown constant. We show by an example that the power of the input in the growth rate seems to be optimal.Copyright © 2013 John Wiley & Sons, Ltd.

Delay-Dependent Robust Stability Analysis for Uncertain Nonlinear Systems

As a popular topic, robust stability for uncertain systems with time delay have been widely studied in various engineering, biological, economical, electronic and dynamical systems, nerve network and so on. Recently, many researchers have paid a lot of attentions on the problem of robust stability for uncertain nonlinear systems with time delay. In this paper, a type of uncertain nonlinear delay systems has been considered in robust stability analysis. A novel robust stability criterion of the system is derived by using Lyapunov method and quadratic stability theory. A new upper bound with high-level infinite small on time delay based on Hariwity matrix and a solvable algebraic Riccati equation is presented. The main results are as follows: Through Lyapunov function and a solvable algebraic Riccati equation, we obtain the criterion of robust stability (exponential stability) for uncertain nonlinear systems with time delay.

Exponential stabilization of nonlinear uncertain systems with time-varying delay

The problem of robust exponential stabilization for dynamical nonlinear systems with uncertainties and time-varying delay is investigated. Based on the Razumikhin theorem and the Lyapunov function method, the continuous state feedback controllers for the studied systems are proposed and the robust exponential stabilization criterion is established in terms of solutions to the standard Riccati differential equations. Furthermore, a delay-dependent stabilization criterion is derived in terms of a linear matrix inequality and the restriction on the derivative of the delay function is removed. Finally, two numerical examples are presented to demonstrate the validity of the proposed method.

Partial stabilization of uncertain nonlinear systems

In this paper, the problem of robust partial stabilization is considered and two approaches for partial stabilization of uncertain nonlinear systems are presented. In these approaches, the nonlinear dynamical system is divided into two subsystems, which are called the first and the second subsystems. This division is done based on the required stability properties of the system’s states. The reduced input vector (the vector that includes components of the input vector appearing in the first subsystem) is designed to asymptotically stabilize the first subsystem. In the first approach, a new partial stabilization technique, based on the first order sliding mode control idea is proposed. In the proposed method, hereafter called the partial sliding mode, a sliding surface is designed such that restricting the motion on this surface guarantees the stability of only the first part of the system’s state. In the second approach, a Lyapunov-based controller is proposed for partial stabilization and then an additional feedback control is designed so that the overall feedback law guarantees a robust manner in the presence of uncertainties.

Robust partial control design for non-linear control systems: a guidance application

In this paper, a general approach for robust partial stabilization of uncertain non-linear systems is presented. In this approach, the non-linear dynamic system is divided into two subsystems, called the first and the second subsystems. This division is done based on the required stability properties of the system’s states. The reduced input vector (the vector that includes components of the input vector appearing in the first subsystem) is designed to asymptotically stabilize the first subsystem. The proposed scheme is then applied for designing a guidance law as a potential application. Indeed, the paper presents a new approach to the missile guidance problem and shows that asymptotic stability behaviour is not realistic for all states of the guidance system. The effectiveness of the proposed guidance law in interception of manoeuvring targets is demonstrated analytically and through computer simulations.

On the Practical Output Feedback Stabilization for Nonlinear Uncertain Systems

In this paper, we treat the problem of output feedback stabilization of nonlinear uncertain systems. We propose an output feedback controller that guarantees global uniform practical stability of the closed loop system.

Robust global stabilization by means of discrete-delay output feedback

In this work, sufficient conditions for global stabilization of nonlinear uncertain systems by means of discrete-delay static output feedback are presented. Examples illustrate the efficiency of the proposed control strategy.