Problem Of Semi-global Stabilization Research Articles

Semi-Global Stabilization of Discrete-Time Linear Systems Subject to Infinite Distributed Input Delays and Actuator Saturations.

The semi-global stabilization problem of discrete-time systems subject to infinite distributed input delays and actuator saturations is investigated in this article. This article develops two low-gain feedback control laws for two types of systems, respectively. It is shown that the resulting system is semi-globally exponentially stabilized. Our results include those existing results on systems subject to only input saturations and systems subject to bounded delays and input saturations as special cases. Compared with existing results on infinite delays and actuator saturations, this article develops a more accurate scaling utilizing a more general framework. Furthermore, a novel converse Lyapunov theorem for discrete-time linear infinite-delayed systems and a novel stability analysis theorem for perturbed discrete-time linear infinite-delayed systems are developed to handle the nonlinearity induced by saturations. Finally, this article provides two numerical examples to illustrate the effectiveness of the developed theorems.

Robust Output Feedback Control of Single-Link Flexible-Joint Robot Manipulator with Matched Disturbances Using High Gain Observer.

This article focuses on the output feedback control of single-link flexible-joint robot manipulators (SFJRMs) with matched disturbances and parametric uncertainties. Formally, four sensing elements are required to design the controller for single-link manipulators. We have designed a robust control technique for the semiglobal stabilization problem of the angular position of the link in the SFJRM system, with the availability of only a position sensing device. The sliding mode control (SMC) based output feedback controller is devised for SFJRM dynamics. The nonlinear model of SFJRM is considered to estimate the unknown states utilizing the high-gain observer (HGO). It is shown that the output under SMC using HGO-based estimated states coincides with that using original states when the gains of HGO are sufficiently high. Finally, the results are presented showing that the designed control technique works well when the SFJRM model is uncertain and matched perturbations are expected.

Semiglobal output feedback control for uncertain nontriangular nonlinear systems with sector‐bounded unknown measurement

SummaryThe problem of semiglobal stabilization for nontriangular nonlinear systems with unknown control coefficients and uncertain output function is investigated in this paper. By virtue of homogeneous domination technique, a novel nonrecursive design approach is presented to construct the semiglobal controller. To that end, a new output‐driven reduce‐order observer is developed to estimate the unmeasurable states. Moreover, it has been shown that we can determine the maximal sector bound of output function, in which an output feedback controller can be designed to render the closed‐loop system semiglobally stable. The effectiveness of controller is demonstrated by a ship simulation.

Semi-global stabilization of linear systems with distributed infinite input delays and actuator saturations

This paper addresses the semi-global stabilization problem of linear systems with simultaneous presence of distributed infinite input delays and actuator saturations. Two low gain controllers are proposed, respectively, for two classes of linear systems with both infinite input delays and actuator saturations. It is shown that under our first controller, the semi-global stabilization problem can be solved for the first class of systems where all eigenvalues of the open loop system have no positive real parts. It is also shown that under our second controller, which is much simpler, the semi-global stabilization problem can be solved for the second class of systems where all eigenvalues of the open loop system are zero. Another contribution of this paper is that the bounds for the peak magnitude of the control signals can be explicitly given. Furthermore, our results include relevant results on bounded distributed delays and constant delays as their special cases. Simulation examples are finally provided to illustrate the effectiveness of the proposed controllers.

Semi-global output feedback cooperative control for nonlinear multi-agent systems via internal model approach

In this paper, we present an internal model based output feedback control for the cooperative semi-global output regulation of nonlinear strict-feedback multi-agent systems with arbitrary non-identical relative degrees and switching network topologies. The problem is first converted into a cooperative semi-global stabilization problem by introducing a distributed internal model. We then propose a distributed output feedback stabilizer that is determined by a novel distributed observer composed of a distributed dynamic compensator and a modified reduced order high gain observer. It is shown that this novel observer is capable of estimating the states of nonlinear subsystems with arbitrary non-identical relative degrees. A semi-global common Lyapunov function is then developed for conducting the stability analysis of nonlinear switched closed-loop system. The benefit of our design also lies in that it has removed the average dwell time assumption in some existing literatures.

An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems

This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches.

An Internal Model Based Semi-global Output Feedback Control for Nonlinear Multi-agent Systems

In this paper, we present an internal model based output feedback control for the cooperative semi-global output regulation of nonlinear strict-feedback multi-agent systems with arbitrary non-identical relative degrees. The problem is first converted into a cooperative semi-global stabilization problem by introducing a distributed internal model. We then propose a distributed output feedback stabilizer that is determined by a distributed high-gain observer. It is shown that this novel observer is capable of estimating the states of nonlinear subsystems with arbitrary non-identical relative degrees.

Semi-global stabilization via homogeneous output feedback for a class of nonlinear time-delay systems

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. By using Lyapunov-Krasovskii functional method and homogeneous domination approach, a homogeneous observer and an output feedback controller with a scaling gain are designed. Then the scaling gain is adjusted such that the closed-loop system is semi-global asymptotically stable. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

Cooperative Semi-Global Output Regulation of Nonlinear Strict-Feedback Multi-Agent Systems With Nonidentical Relative Degrees.

In this paper, we study the cooperative semi-global output regulation problem for a class of nonlinear strict-feedback multi-agent systems, where the subsystems are assumed to have nonidentical relative degrees. We first introduce the so-called distributed internal model that converts our problem into the cooperative semi-global stabilization problem of the corresponding augmented system composed of the original multi-agent system and the internal model. We then put this augmented system into the general block lower triangular form, and develop the block semi-global backstepping technique to stabilize it. Comparing with some existing literatures, our design has removed the identical relative degree assumption, and hence applies to a much larger group of nonlinear multi-agent systems.

On semi-global stabilization of linear periodic systems with control magnitude and energy saturations

This paper establishes a systematic approach to solve the L∞(l∞) and L2(l2) semi-global stabilization problem of linear periodic systems with controls having bounded magnitude and energy, respectively. The developed approach will be referred to as L∞(l∞) and L2(l2) low gain feedback. Definitions, properties, and characterizations of this new concept are also provided, and particularly, the characterizations are based upon differential (difference) Lyapunov inequalities. Design of L∞(l∞) and L2(l2) low gain feedback by solving differential (difference) Riccati equations is proposed. Both continuous-time and discrete-time linear periodic systems are studied and both state feedback and observer based output feedback are considered. In the discrete-time setting, a linear matrix inequalities (LMIs) based solution to the l∞ and l2 semi-global stabilization problem is also established and the LMIs conditions are shown to be always solvable. Applications of the proposed approach to the elliptical spacecraft rendezvous system show the effectiveness of the established theory.

Semi-Global Stabilization for a Class of Nonlinear Time-Delay Systems by Linear Output Feedback

The semi-global stabilization problem for a class of nonlinear systems with state time-delay is addressed in this paper. Sufficient conditions are derived by using Lyapunov-Krasovskii functional method and adjusting the scaling gain to guarantee the systems as well as the resulted closed-loop systems under a linear output feedback controller to be semi-globally stable. Numerical example is presented to illustrate the effectiveness of the obtained results in this paper.

Output feedback gain scheduled control of actuator saturated linear systems with applications to the spacecraft rendezvous

The problem of stabilization of a linear system that is asymptotic null controllable with bounded control is studied in this paper. By combining the parametric Lyapunov equation approach and the gain scheduling technique, a new observer-based output feedback gain scheduling controller is proposed to solve the semi-global stabilization problem for a linear system subject to actuator saturation. By scheduling the design parameters online the convergence rate of the state can be improved. Numerical simulations for a spacecraft rendezvous system show the effectiveness of the proposed approaches.

Stabilization of Discrete-Time Linear Systems Subject to Input Saturation and Multiple Unknown Constant Delays

In this technical note, we study the semi-global stabilization of general linear discrete-time critically unstable systems subject to input saturation and multiple unknown input delays. Based on a simple frequency-domain stability criterion, we find upper bounds for delays that are inversely proportional to the argument of open-loop eigenvalues on the unit circle. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problems.

Cooperative semi-global robust output regulation for a class of nonlinear uncertain multi-agent systems

In this paper, we study the cooperative semi-global robust output regulation problem for a class of minimum phase nonlinear uncertain multi-agent systems. This problem is a generalization of the leader-following tracking problem in the sense that it further addresses such issues as disturbance rejection, robustness with respect to parameter uncertainties. To solve this problem, we first introduce a type of distributed internal model that converts the cooperative semi-global robust output regulation problem into a cooperative semi-global robust stabilization problem of the so-called augmented system. We then solve the semi-global stabilization problem via distributed dynamic output control law by utilizing and combining a block semi-global backstepping technique, a simultaneous high gain feedback control technique, and a distributed high gain observer technique.

Semiglobal stabilization of saturated linear systems via multiple parametric Lyapunov equations

SUMMARYThis paper investigates the problem of semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems. To retain the advantages of the parametric Lyapunov equation, matrix‐partitioning idea is used to derive a new pole shift lemma. Starting from system matrix transformations, a recursive algorithm is proposed to shift every eigenvalue of a linear system separately without mode decomposition in each step. A new method introducing various parameters to every Lyapunov equation in each step is presented. As an application, the semiglobal stabilization with guaranteed flexible pole placement for saturated linear systems can be achieved by this method. Finally, its effectiveness and advantages are demonstrated via a simulation example. Copyright © 2013 John Wiley & Sons, Ltd.

Stabilization of linear system with input saturation and unknown constant delays

In this paper, we study the stabilization of linear critically unstable systems subject to input saturation and multiple unknown input delays. We find tight upper bounds for delays which are inversely proportional to the maximal magnitude of open-loop eigenvalues on the imaginary axis. For delays satisfying these upper bounds, linear low-gain state and finite dimensional dynamic measurement feedbacks are constructed to solve the semi-global stabilization problem. The effectiveness of the proposed design is illustrated by an example.

Robust supervisory control for uniting two output-feedback hybrid controllers with different objectives

The problem of robustly, asymptotically stabilizing a point (or a set) with two output-feedback hybrid controllers is considered. These control laws may have different objectives, e.g., the closed-loop systems resulting with each controller may have different attractors. We provide a control algorithm that combines the two hybrid controllers to accomplish the stabilization task. The algorithm consists of a hybrid supervisor that, based on the values of plant’s outputs and (norm) state estimates, selects the hybrid controller that should be applied to the plant. The accomplishment of the stabilization task relies on an output-to-state stability property induced by the controllers, which enables the construction of an estimator for the norm of the plant’s state. The algorithm is motivated by and applied to robust, semi-global stabilization problems uniting two controllers.

Semi-global output feedback stabilization for a class of nonlinear systems using homogeneous domination approach

This paper investigates the problem of semi-global stabilization by output feedback for a class of nonlinear systems using homogeneous domination approach. For each subsystem, we first design an output feedback stabilizer for the nominal system without the perturbing nonlinearities. Then, based on the ideas of the homogeneous systems theory and the adding a power integrator technique, a series of homogeneous output feedback stabilizers are constructed recursively for each subsystem and the closed-loop system is rendered semi-globally asymptotically stable. The efficiency of the output feedback stabilizers is demonstrated by a simulation example.

Semiglobal Stabilization for Nonholonomic Mobile Robots Based on Dynamic Feedback With Inputs Saturation

This paper investigates the semiglobal stabilization problem for nonholonomic mobile robots based on dynamic feedback with inputs saturation. A bounded, continuous, time-varying controller is presented such that the closed-loop system is semiglobally asymptotically stable. The systematic strategy combines finite-time control technique with the virtual-controller-tracked method, which is similar to the back-stepping procedure. First, the bound-constrained smooth controller is presented for the kinematic model. Second, the dynamic feedback controller is designed to make the generalized velocity converge to the prespecified kinematic (virtual) controller in a finite time. Furthermore, the rigorous proof is given for the stability analysis of the closed-loop system. In the mean time, the position and torque inputs of robots are proved to be bounded at any time. Finally, the simulation results show the effectiveness of the proposed control approach.

Semi-Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi-global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block-backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed-loop system is rendered semi-globally asymptotically stable.