State bounding for nonlinear time-varying systems with delay and disturbance

A robust tracking control algorithm based mainly on the theory of variable structure systems and Lyapunov's direct method is developed in this paper, to treat the tracking control problem of a class of non-linear time-varying systems with uncertain dynamics. A nominal model is used instead of an exact one. together with a description of the bounds of plant uncertainty. The objective is to design a control law such that all the plants lying within a specified band of uncertainly will be driven to reach the goal. The modelling error, time-varying system dynamics, system uncertainties, and disturbances are all treated as general disturbances to the nominal system. This algorithm greatly eases the difficulties present in requiring a precise model of the physical system for the control purpose and for handling the non-linear time-varying system. The non-linear time-varying system is first linearized to a linear time-varying system (with time-varying coefficients completely defined) via the method of variable s...

Interval state observer for nonlinear time varying systems

Motivated by the recent advance in adaptive output feedback control of affine nonlinear systems [8-10], an adaptive variable structure controller is proposed in this paper for solving the model reference adaptive control of nonlinear time-varying systems. Asymptotic output tracking performance can be achieved for relative degree one case. When the relative degree of the nonlinear system is greater than one, a systematic design procedure is given under a modified sector-type condition so that the closed-loop stability and the tracking performance are achieved similar to that in relative degree one case.

In previous papers we have introduced a sufficient condition for uniform attractivity of the origin of a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform /spl delta/-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u/spl delta/-PE which is conceptually equivalent to but technically different from its predecessors. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems.

A novel neural network controller architecture is explored for the speed control of a DC motor-driven four bar linkage system which represents a class of time-varying nonlinear systems. Simulation and experimental implementation show the viability and effectiveness of this promising tool for nonlinear systems. Identification and control, as well as real-time implementation issues are considered. Comparative studies with two other neural network architectures are also reported. Importantly, they also perform well in real-time control studies for the system considered.

An identification approach for linear and nonlinear time-variant structural systems via harmonic wavelets

The stability and behavior of continuous-time nonlinear time-varying (NTV), nonlinear time-invariant (NTI) and linear time-varying (LTV) systems are generally very difficult to ascertain using current analytical tools. This paper presents sufficient conditions under which a NTV system with a bounded system matrix, A(t,X), is globally exponentially stable (GES). The continuous-time NTV system is modeled as an uncertain polytopic system even though A(t,X) may be reasonably known. It is shown that if all polytope-vertex matrices are Hurwitz, then the system is GES. Also, a method for determining the boundary estimate of a NTV system state-trajectory norm is developed. Presented is a unified stability analysis approach for a large class of NTV, NTI, and LTV systems. Even for large systems, application of the GES theorem presented is straight forward using readily available software and computational power. Examples are given that illustrate the application of the theorem offered.

For a class of time-varying nonlinear systems described by the equation $$\dot x = f(x,t) + g(x,t)u$$ , the precalculating control is not available if the input matrixg(x,t) is not invertible. With Lyapunov's second method, a stabilizing controller which makes the system practically stable is constructed in this paper. It is shown that the implementation of this scheme depends on some so-called posi-invertibility conditions forg(x,t). In case the system is partly stable, the method, named part-calculating control, can simplify the on-line computations. Without the assumption that the nominal system is asymptotically stable, the method is applied to the problems of control for the corresponding uncertain system that satisfies the matching condition. When the matching condition is not satisfied, the mismatching control problem is also studied with Lyapunov's second method.

EP-based adaptive tracker with observer and fault estimator for nonlinear time-varying sampled-data systems against actuator failures

Global stabilization for linear continuous time-varying systems

Iterative learning control (ILC) is a simple and effective method for the control of systems that perform same task repetitively. In this paper, open-closed-loop D-type ILC problem is investigated for a class of nonlinear time-varying systems. Under a few reasonable assumptions, sufficient condition for guaranteeing the convergence of the learning scheme is given and then proved with linear operator theory. The condition is independent of the specific form of the state space model, also it is weaker than known results for D-type ILC scheme.

Cooperative regulation based on virtual vector triangles asymptotically compressed in multidimensional space for time-varying nonlinear multi-agent systems.

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

Closure to “Discussion of ‘On the Global Stability of a Class of Nonlinear Time-Varying Systems’” (1966, ASME J. Basic Eng., 88, pp. 406–407)

A variable structure control (VSC) algorithm is proposed with a nonlinear time-varying (NTV) sliding sector for a class of nonlinear time-variant systems represented in a state-dependent linear time-variant form. The NTV sliding sector, a subset of the state space is designed by the state-dependent differential Riccati equation (SDDRE). A VSC law is designed such that the system enters the sliding sector in finite time and a Lyapunov function candidate decreases inside the NTV sliding sector. An NTV control and a sliding mode control algorithms are proposed based on the solution of the SDDRE as well.