Ho-Lim Choi

Output Feedback Regulation of a Chain of Integrators With an Unbounded Time-Varying Delay in the Input

We consider a problem of global regulation of a chain of integrators that has an unknown time-varying delay in the input. In contrast to the previous works in the literature, the upper bound of delay is not known. Moreover, there is no given information on the time-varying rate of delay, either. Using the dynamic gain approach inspired by the method in and the control structure of together, we construct an adaptive output feedback controller to solve the considered control problem. The only requirement is that the time-varying delay is bounded.

Asymptotic stabilization of an input-delayed chain of integrators with nonlinearity

In this paper, we consider a stabilization problem of an input-delayed chain of integrators with nonlinearity. In this system, the nonlinear part cannot be directly canceled by the input due to time-delay. We design a stabilizing controller and show that the system stability is determined by the types of nonlinear functions.

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

Abstract We consider a global regulation problem of a class of feedforward nonlinear systems with uncertain delays by output feedback. The considered system is a generalized feedforward time-delay nonlinear system in the sense that an additional uncertain constant delay exists in the main control input to the system and feedforward nonlinearity includes states and input which have uncertain time-varying delays. Moreover, when feedforward nonlinearity satisfies some restrictive condition, we extend our control problem to the case such that the delay in the main control input is also a time-varying delay. To globally regulate the considered system, we develop an output feedback controller whose gain-scaling factor involves an adaptive dynamic. Two examples are given for illustration.

Global regulation of a class of feedforward and non-feedforward nonlinear systems with a delay in the input

In this paper, we propose a new state feedback controller using dynamic gain for input-delayed systems with high-order nonlinearity terms in both feedforward and non-feedforward forms. The controller design is based on a reduction method to remove the input delay and a gain scaling technique involving appropriate powers of high-order nonlinearity. As a result, more generalized systems containing feedforward and nonfeedforward terms with an input delay are regulated when the proposed power order condition of the nonlinear function is satisfied. An example is given to show the generality of our result over existing results.

Stabilisation of non-linear systems with unknown growth rate by adaptive output feedback

In recent years, several results have been proposed on the global stabilisation of non-linear systems with unknown linear growth rate. However, these works are limited in the sense that they consider only one particular form of non-linear systems–mostly either triangular or feedforward form. We propose an adaptive output feedback control scheme which can deal with both triangular or feedforward non-linear systems with unknown linear growth rate in a unified framework. Thus, our result broadens the class of non-linear systems under consideration over the existing results.

Global Regulation of a Class of Uncertain Nonlinear Systems by Switching Adaptive Controller

There are several results on the stabilization or regulation of nonlinear systems with either triangular or feedforward nonlinearity. However, the existing results are applicable to their considered systems when the nonlinearity structure is known a priori. In this technical note, we propose a switching adaptive controller which tunes the dynamic gain depending on the nonlinearity structure. Thus, as a benefit over the existing results, the structural information on the nonlinearity is not needed. Although the linear growth condition is assumed, the rate of growth is unknown and arbitrary large with our control scheme.

On stability of linear time-delay systems with multiple delays

In this article, delay-dependent stability criteria for linear retarded and neutral systems with multiple delays are proposed by employing the Lyapunov-Krasovskii functional approach and integral inequality. By the N-segmentation of delay length, we obtain more relaxed results on the delay bounds which guarantee the asymptotic stability of the linear retarded and neutral systems with multiple delays. Simulation results show that the stability boundary calculated by the proposed stability criteria are very near to the real stability boundary of the example systems. Moreover, it is shown that the proposed stability criteria are less conservative than several other existing criteria.

Universal control of nonlinear systems with unknown nonlinearity and growth rate by adaptive output feedback

Over the past several years, triangular or feedforward nonlinear systems have received considerable attention and there are many independent results for stabilization or regulation problems. These results are often specifically targeted for only one of these systems and they are applicable when the system nonlinearity is known a priori. In this paper, we propose an adaptive output feedback controller coupled with switching logic to universally regulate both triangular and feedforward systems without recognizing the system nonlinearity. Moreover, with our control scheme, the linear growth rate is not required to be known.

Global asymptotic stabilization of a chain of integrators with a time-varying delay in the input by output feedback

In this paper, we consider a stabilization problem of a chain of integrators which allows a time-varying delay in the input. Among the plethora of papers on the stabilization of input-delayed chain of integrators, the existing results are only with constant delays. We show that with the proposed output feedback controller, the considered system can be globally asymptotically stabilized as long as the time-varying delay is bounded by a finite constant. That is, the time-varying rate is irrelevant in the stability result.

Sliding mode control design under partial state feedback for ball and beam system

In this paper, we develop a state observer in order to estimate the velocity of a ball and angular velocity of a motor. With the observer, we propose a sliding mode controller where sliding surface consists of some measured and estimated states. Then, a new rigorous analysis will be done to show the behavior of the system on the sliding surface. We show the stability analysis and convergence analysis of the partial state observer. In addition, the experimental results show the validity of the proposed controller.