Prescribed-time Stabilization Research Articles

Prescribed-time and output feedback stabilization of heat equation with an intermediate-point heat source and boundary control

This paper addresses the problem of prescribed-time stabilization for the heat equation with an interior point heat source under output feedback. The study employs a two-step backstepping approach along with time-varying feedback techniques. A prescribed-time state observer and an observer-based boundary control law are developed. The proposed method extends the applicability of the prescribed time-stabilizing algorithm to heat equations with non-strict feedback terms. Numerical simulations validate its effectiveness.

Adaptive Event-Triggered Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Asymmetric Time-Varying Output Constraint

Adaptive Event-Triggered Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Asymmetric Time-Varying Output Constraint

Event-triggered prescribed-time control for a class of uncertain nonlinear systems using finite time-varying gain

This paper addresses the event-triggered prescribed-time control problem for a class of high-order nonlinear systems based on finite time-varying gain. Due to the existence of unknown gain functions and system uncertainties, the resultant control with prescribed-time convergence performance becomes nontrivial. The problem becomes even more complex due to the use of event-based communication instead of continuous communication. To tackle the aforementioned challenges, this paper proposes an event-triggered prescribed-time stabilization approach with the following key steps. Firstly, we establish a new prescribed-time stability lemma to overcome the technical difficulty arising from the prescribed-time controller design, and stability analysis. Secondly, we give the controller design procedure upon using the backstepping technique. Thirdly, we redesign the event-triggering threshold condition based on time-varying functions, which allows the controller terminal jitter to be mitigated and the controller to be implemented straightforwardly in practice. Furthermore, the proposed control scheme avoids Zeno behavior. The numerical simulation confirms the effectiveness of the proposed control scheme.

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Practical Prescribed-Time Stabilization of a Class of Nonlinear Systems by Event-Triggered and Self-Triggered Control

Practical Prescribed-Time Stabilization of a Class of Nonlinear Systems by Event-Triggered and Self-Triggered Control

Prescribed-Time Stabilization of Complex Networks With Intermittent Control

Prescribed-Time Stabilization of Complex Networks With Intermittent Control

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

Fixed/Prescribed stability criterions of stochastic system with time-delay

<abstract><p>In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.</p></abstract>

Global Prescribed-Time Stabilization of a Class of Uncertain Linear Systems With Applications to Aerospace Systems

Global Prescribed-Time Stabilization of a Class of Uncertain Linear Systems With Applications to Aerospace Systems

Prescribed-time stabilization of nonlinear systems with uncertainties/disturbances by improved time-varying feedback control

<p>We address the prescribed-time stability of a class of nonlinear system with uncertainty/disturbance. With the help of the parametric Lyapunov equation (PLE), we designed a state feedback control to regulate the full-state of a controlled system within prescribed time, independent of initial conditions. The result illustrated that the controlled state converges to zero as $t$ approaches the settling time and remains zero thereafter. It was further proved that the controller is bounded by a constant that depends on the system state. A numerical example is presented to verify the validity of the theoretical results.</p>

Achieving Prescribed-Time Stabilization in Nonlinear TCP/AQM Systems With Input Saturation

Achieving Prescribed-Time Stabilization in Nonlinear TCP/AQM Systems With Input Saturation

Prescribed-time stabilization and optimization of CPS-based microgrids with event-triggered interactions

Prescribed-time stabilization and optimization of CPS-based microgrids with event-triggered interactions

Conditions and Synthesis of Adaptive Prescribed-Time Controllers

This paper addresses conditions and synthesis of adaptive prescribed-time controllers. The sufficient condition says that a system can achieve prescribed-time stabilization if its certain variant can be made globally bounded (on infinite time interval). From the condition one can know far more varieties of (uncertain nonlinear) systems can achieve prescribed-time control, rather than just special varieties in the related literature. The necessary condition states that a system can achieve prescribed-time stabilization attached global uniform boundedness (GUB) on finite time interval only if it, by some feedback type, can achieve GUB on infinite time interval. From the condition, or rather, its converse-negative version, one can see that what kind of systems cannot virtually achieve the prescribed-time stabilization attached GUB for some feedback type. The sufficient condition builds on two crucial transformations which change prescribed-time convergence on finite-time interval into global boundedness on infinite-time interval. With the aid of the conditions and transformations, we conduct the synthesis of adaptive prescribed-time controllers for general uncertain nonlinear systems typically with unknown control directions. By integrating time-varying factors into Lyapunov functions, an adaptive smooth controller is devised such that the system states converge to zero before an arbitrarily prescribed time, while the controller and its dynamic gains are bounded.

Controller Design and Stability Analysis for a Class of Leader-Type Stochastic Nonlinear Systems

In this paper, the non-scaling backstepping approach is used to examine the controller design process and stability analysis of a class of leader-type stochastic nonlinear systems. By utilizing the non-scaling backstepping design method and Lyapunov method, the controller of the leader-type stochastic nonlinear system is derived. Different from the previous literature on controller design, we develop a more computationally efficient way for designing controllers because the scaling function in the coordinate transformation is not included. Meanwhile, the prescribed-time mean-square stabilization on the equilibrium and two important estimates are derived by combining the Lyapunov method with the matrix norm. Compared to the finite-time stabilization in other studies, the prescribed-time stabilization can determine the convergence time without relying on the initial value and has more real-world applicability. To illustrate the effectiveness of the controller derived in this paper, numerical examples are provided finally.

Event-Triggered Control for Nonlinear Uncertain Systems via a Prescribed-Time Approach

The event-triggered control problem is investigated for nonlinear uncertain systems via a prescribed-time approach. Different from the existing event-triggered control methods that can only achieve bounded or finite-time stability, this paper focuses on the prescribed-time stability under the event-based design method. First, a novel prescribed-time stability criterion is presented, which provides explicit theoretical supports and systematic guidelines for addressing the studied problem. Then, we put forward a new method for co-designing the controller and event-triggering mechanism by utilizing the idea of backstepping design. Based on the proposed stability criterion, it is proved that the controller constructed with the new method can regulate the system states to zero in the prescribed-time interval while avoiding the Zeno phenomenon, thus improving the previous prescribed-time stabilization results that are all based on the real-time control signals. Finally, a simulation example is given to show the effectiveness of proposed control strategy.

Event-triggered adaptive prescribed-time control for nonlinear systems with uncertain time-varying parameters

The problem of event-based adaptive prescribed-time control for a class of nonlinear systems with uncertain time-varying parameters is considered in this paper. The existence of uncertain time-varying parameters makes the system in question intrinsically different from that in prescribed-time stabilization or event-triggered control. Moreover, the existing prescribed-time control methods require the real-time continuous control input. For this reason, a novel event-based adaptive prescribed-time control strategy is presented by skillfully utilizing a key scaling technique and a new event-triggering mechanism. It is proved that the proposed event-triggering mechanism can enlarge the trigger time interval and effectively reduce the number of trigger moments compared with the existing event-triggered control methods. An important stability criterion is proposed based on the defined prescribed-time adjustment function. Furthermore, the proposed control algorithm can effectively reduce the computational burden and save the control effort. Finally, a numerical simulation verifies the effectiveness of the proposed prescribed-time control algorithm.

Global Prescribed-Time Stabilization of Input-Quantized Nonlinear Systems via State-Scale Transformation

The problem of global prescribed-time stabilization is reported in this paper for a kind of uncertain nonlinear system in power normal form. Compared with related work, the distinct characteristics of this study are that the system under consideration has an input-quantized actuator, and the prescribed time convergence of the system states is wanted. To meet these special requirements, a novel state-scaling transformation (SST) is firstly given to convert the prescribed-time stabilization of original systems to the asymptotic stabilization of the transformed one. Then, under the new framework of equivalent transformation, a quantized state feedback controller that ensures the achievement of the performance requirements is developed by using a power integrator (API) technique. Finally, the simulation results of a liquid-level system are provided to confirm the efficacy of the proposed approach.

Adaptive Prescribed-Time Control of Time-Delay Nonlinear Systems via a Double Time-Varying Gain Approach.

This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov-Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.

Prescribed-time stabilization control for p-norm stochastic nonlinear systems based on homogeneous dominant technique

In this article, a prescribed-time state-feedback stabilization design strategy is proposed for a class of p-norm stochastic nonlinear strict feedback systems. In previous work on prescribed-time stabilization of stochastic systems, only stochastic nonlinear systems with fractional power less than or equal to one are considered. To overcome this problem, we improve the existing method and discuss the issue of prescribed-time stabilization of stochastic nonlinear systems with fractional power is arbitrary positive odd rational number. First, a prescribed-time controller is designed by combining the Lyapunov function with adding a power integrator technique. It should be pointed out that the homogeneous domination approach is adopted when dealing with the nonlinear terms of the system. Then, according to the stochastic prescribed-time stability theorem, it is proved that the designed controller can ensure the closed-loop system is prescribed-time mean-square stable. Finally, three simulation examples are given to investigate the validity of the presented method, in which the last one is an electromechanical system example.