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This paper addresses the stability issues of delayed nonlinear systems of the form x(t) = A(t, x(t), x(t − d(t)))x(t)+B(t, x(t), x(t − d(t)))x (t − d(t)), that is, the system matrices depend on time and the present and past states. By means of a trajectory-based comparison approach, the stability of original nonlinear system is transformed into that of a positive linear system called comparison system...
The paper provides new results for testing the flow-invariance of time-dependent sets with arbitrary shapes, with respect to trajectories of continuous-time nonlinear systems. The approach represents a generalization of a criterion used in the qualitative analysis of ordinary differential equations with solutions in closed sets with hyper-rectangular form. Given a nonlinear dynamical system for investigation,...
Because most systems are nonlinear in practical applications, output tracking for nonlinear system is of great interest to engineers and scientists. As a specific class of nonlinear system, fractional power system arises in many problems, yet little progress is made on this topic. Inspired by Zhang et al., this paper presents a simple but powerful method of controller design, i.e., generating the...
This paper investigates the coupled disturbance reconstruction, state estimation and trajectory tracking problems for a class of nonlinear systems. The sliding mode observer and the state feedback approaches are utilized to solve these problems. Considering only a partial of the system states are measured but the disturbances couple with time-varying parameters that the observer is designed by transforming...
An adaptive tracking control is proposed for a class of constrained nonlinear systems with hysteresis and uncertainty. Hysteresis and uncertainty may limit system performance such as giving rise to undesirable accuracy or oscillations, even leading to instability. First, Bouc-Wen model is used to describe the hysteresis, and the upper bound is derived. Then, a Barrier Lyapunov Function (BLF) is adopted...
Adaptive iterative learning control is a popular approach to control parametric time-varying systems over finite time interval. However, initial resetting condition limits the application of a large amount of learning control algorithms. In this paper, we propose a suboptimal iterative learning control for a class of dynamic parametric systems to solve this problem. An error-tracking control strategy...
Differential equation is a useful way to describe nonlinear systems. In general, integration is used to solve them, which is a forward method using current information to get the future information. In some special occasions where the system has a fix final condition and a free initial condition, a new kind of integration method with a backward direction is needed. This paper presents a new kind of...
In this paper, the research on the stabilization of time-varying linear (TVL) system is conducted with pseudo division-by-zero (PDBZ) phenomenon shown. We not only adopt zeroing dynamics (also called Zhang dynamics, ZD) method to design ZD stabilization controller, but also adopt zeroing-gradient (also called Zhang-gradient, ZG) method to design ZG stabilization controller. Through numerical experiments,...
A method of stability analysis of nonlinear systems using Lyapunov densities has been proposed by Rantzer: almost all trajectories of the system are guaranteed to converge to the equilibrium point if a Lyapunov density exists for the nonlinear system. However, only the convergence of trajectories is considered in the Rantzer's original result and the speed of convergence has never been taken care...
How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing...
This paper focuses on the control of dynamical systems under the case that actual reference signals can not be available in real time. In such case, although predicted values are used as reference signals, the prediction errors degrade the control performance of the systems. To overcome this problem, the previous work presented the prediction governor which shapes predicted values. However, the previous...
Optimal control has been a very attractive and desirable feature for many dynamic and static systems, An effective online technique for finite-horizon nonlinear control problem is offered in this paper. The idea of the proposed technique is to combine the differential State Dependent Riccati equation filter algorithm and the finite-horizon SDRE technique. Genetic algorithm is used to calculate the...
Constant-Power Load (CPL) introduces destabilizing effect to dc-dc converters, which may lead to voltage oscillation or collapse. To mitigate the destabilizing problem brought by CPL, a nonlinear boundary controller is proposed in this paper, which has a nonlinear switching line. The converters' dynamics on the state space plane is analyzed through phase portrait. The proposed controller is verified...
This paper investigates the issue of fuzzy dynamic integral sliding-mode controllers for nonlinear descriptor systems based on Takagi-Sugeno (T-S) fuzzy models. A fuzzy dynamic integral sliding-mode control (DISMC) scheme is developed for the nonlinear descriptor systems to remove the restrictive assumption that all local models share a common input matrix, which is required in most existing fuzzy...
The adaptive iterative learning control for the variable trajectories driven by a deterministic finite state machine (DFSM) are addressed in this paper. The DFSM is repressed by a linear state equation with linear-inequalities, and a state feedback controller is designed to stabilize the DFSM at an equilibrium set. Then, the variable trajectories are driven by this DFSM. Combined the Backstepping...
The convergence of PIβDα-type fractional-order iterative learning control(FOILC) is discussed for a class of fractional-order linear time-invariant system in the sense of Lp norm. First, by taking advantage of the generalized Young inequality of convolution integral, the sufficient conditions for the monotone convergence of first and second-order PIβDα-type control laws are analyzed in the sense of...
This paper considers distributed coordinated control for multi-agent systems composed of multiple heterogeneous leaders and a class of uncertain nonlinear systems with external disturbances. What makes our problem more interesting and challenging is that the control direction of each nonlinear subsystem is unknown. Inspired by output regulation theory, based on the distributed internal model technique,...
This paper investigates the problem of attitude stabilization for a rigid body subject to external disturbance with unknown bound. A fixed-time based finite time controller is proposed to guarantee that the closed-loop system gets stable in fixed time, which means the bound of the settling time is independent of the initial conditions. Moreover, the adaptive method is adopted to deal with the external...
A novel data-driven iterative learning control (ILC) based on the adaptive tuning of the 2D learning gain, is proposed in this paper for a class of general discrete-time nonlinear SISO systems. Based on an equivalent compact form dynamic linearization data model of the controlled nonlinear system in the iteration domain, an iterative learning law is formulated by using a recursive search algorithm...
In this paper we are interested in distributed control for dynamically decoupled nonlinear systems with coupled objective function. An event-triggered distributed MPC is designed to stabilize systems and optimize local and cooperative objective function. Different from existing time-triggered approaches, in this work, a contraction constraint is used to ensure stability so that the cooperation matrix...
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