Jin H. Seo

Semi-global observer for multi-output nonlinear systems

Abstract We present an explicit form of nonlinear observers for a class of multi-input multi-output systems. Observer construction for multi-output nonlinear systems is not a trivial extension of single output case, especially when the global error convergence is of interest. In this paper, we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself, and the overall system has a block triangular form for each subsystem. Hence, the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed. The construction is based on the saturation of some estimates, which is originated by Khalil and Esfandiari for the use of semi-global output feedback control.

Nonlinear observer design by dynamic observer error linearization

In this note, we address the problem of transforming a nonlinear system into nonlinear observer canonical form in the extended state-space with the aid of dynamic system extension and introduction of virtual outputs. As an intermediate step for the general problem, we consider a restricted structure of dynamic extension, which is obtained, roughly speaking, by adding the chains of integrators to the outputs of original system. We propose sufficient conditions which can be verified using the system dynamics expressed in their original coordinates. An illustrative example is included that demonstrates the advantage of the proposed method over the conventional method.

A state observer for nonlinear systems and its application to ball and beam system

In this paper, we present a state observer for single-input/single-output nonlinear systems which fail to have well defined relative degree. It is shown that there exists a local state observer for a nonlinear system if it has robust relative degree n. The proposed observer utilizes the coordinate change which transforms a system into an approximate normal form. The proposed method is applied to a ball and beam system, and simulation results show that substantial improvement in the performance was achieved compared with other local observers.

Compensation of actuator dynamics in nonlinear missile control

This brief presents an approach to the compensation of the actuator dynamics in nonlinear missile control. In general, actuator dynamics are not considered in nonlinear missile control systems. Here, we analyzed the influences of actuator dynamics on the nonlinear missile controller and found that the second-order actuator dynamics showed risks of potentially destabilizing the overall system. Thus, to accommodate for the influence of the actuator dynamics, a compensator is proposed where the information of the nonlinear control input and the actual fin deflection is incorporated. We also conducted performance and stability analysis for the proposed control system, including actuator dynamics. We were able to confirm the validity of the proposed approach based on simulation results for the first- and second-order actuator dynamics.

Sliding mode tracking control of nonholonomic wheeled mobile robots

This paper proposes a sliding mode control method for wheeled mobile robots. Due to the nonholonomic property and restricted mobility, the trajectory tracking of this system has been one of the challenging class of control problems. A new sliding mode control method is presented as a sliding mode controller by representing the kinematic equation of a mobile robot as two-dimensional polar coordinates. The proposed method, compared with previous studies based on a polar coordinate representation, can effectively improve the trajectory tracking performance and reduce the constraints on the posture of the robot. The stability and performance analyses are performed and also simulations are included to demonstrate the practical application of our scheme.

Observer design for non-linear systems that are not uniformly observable

The observer design problem is studied for a class of single-output non-linear systems that are not necessarily uniformly observable. In the first part of this paper, the non-linear observer canonical form is generalized to the partial non-linear observer canonical form which is quite similar to the decomposition of a linear system into its observable and unobservable states. A necessary and sufficient condition is given for a non-linear system to be transformable into this canonical form by the change of coordinates. Based on this canonical form, a sufficient condition is given for the existence of observers. In the second part, a high gain observer for a class of non-linear systems that are not uniformly observable will be developed in order to relax the system structure of the partial non-linear observer canonical form. To this end, a new canonical form is proposed that generalizes the canonical form of uniform observability and a sufficient condition is provided based on the proposed canonical form.

The realization of the three dimensional guidance law using modified augmented proportional navigation

This paper deals with 3D missile guidance law and presents the general optimal solution of the state equation which includes the target maneuver as Gauss-Markov processing, and the solution has the form of the augmented proportional navigation guidance. The main result is about the transformation between the Cartesian coordinates on which both the guidance law and the filter are based and the polar coordinates in real missile guidance and radar measurement information. The adjustment of estimated target acceleration by trigonometric functions and extended Kalman filter is proposed as a solution to this problem. It is shown that this proposed transformation is valid in real 3D guidance problem by comparison with the conventional method through computer simulation.

Local separation principle for non-linear systems

In this paper, we consider the problem of locally stabilizing non-linear systems by output feedback control. To be precise, the separation principle for non-linear systems are studied, which allows the design of the control law and the observer to be carried out independently. While the previous results assumed the existence of Lyapunov function for the observation error, we assume the existence of a state observer which asymptotically estimates the true state. As a matter of fact, it turns out that the latter condition is necessary for the former condition, but the converse is not true. The separation principle with the reduced order observer is also presented. Under the assumption that a non-linear system has asymptotically stable zero dynamics and is locally detectable, it is shown that the asymptotic output tracking by output feedback control can be achieved.

Passivity framework for nonlinear state observer

We solve the general problem of reconstructing the state of a plant with the input and output information of the plant only, referred to as the observer problem. Our strategy of observer design is the output feedback passification to the error dynamics. In order to describe the passivity of the error dynamics effectively, the standard passivity is reformed for the augmented error dynamics which also include the plant dynamics. The proposed framework includes the precise definition of passivity-based state observer (PSO) and the design scheme of PSO. It is also shown that a PSO has its potential robustness to the measurement disturbance and that the framework of PSO unifies the earlier works in the literature.

A constructive algorithm for system immersion into nonlinear observer form

Abstract This paper investigates when n dimensional nonlinear systems can be immersed into n + m dimensional observer form using output diffeomorphism. We provide a necessary and sufficient condition which involves a differential equation with n + m + 1 unknowns; n + m unknowns for the state transformation, one for the output diffeomorphism. The algebraic structure of the characteristic equation is investigated, and an algorithm is presented to check the immersibility iteratively.