Robust observer‐based stabilization of Lipschitz nonlinear uncertain systems via LMIs ‐ discussions and new design procedure

Linear multicellular system is a type of differential inclusion system, which can be deemed as an extension of linear control system with set‐valued mapping. As an important issue in existing control systems, interval state estimation has been widely applied in engineering practices. Over the years, the objects of the studies on interval state estimation have been extended from the initial linear time‐invariant systems to linear time‐varying systems, chaotic systems, feedback linearization systems, and nonlinear Lipschitz systems. However, there is no report on the design of interval observer for linear multicellular system. To make up for this gap, this chapter attempts to explore the design of an interval observer for linear multicellular systems.

Enhanced catalyst performance using integrated structured functionalities

This paper proposes a composite state observer structure that combines the sliding mode and cubic observers for state estimation of linear time-invariant and nonlinear Lipschitz systems. The proposed observer generalises the aforementioned ones and can be reduced by the proper assignment of parameters. Convergence criteria and performance advantages are given for the proposed observer structure. The paper also provides a simple structural parameter selection framework for the design of the sliding mode and sliding mode cubic observers. Simulation examples show the superiority of the proposed observer to the existing ones.

Observer-based control for time-delayed quasi-one-sided Lipschitz nonlinear systems under input saturation

Generalized filtering of one-sided Lipschitz nonlinear systems under measurement delays

Laser welding application for car body manufacturing has many advantages in the stiffness and the lightness of vehicle, the productivity of assembly line, and the degree of freedom in design. This presentation will express the innovation of car body manufacturing including parameter optimization, process modeling, and system integration. In this application the investment for systems was cut down dramatically by real time switching over the laser path between two welding stations. Points of technical discussion are as follows: optimization of parameters such as laser power, robot speed and trajectory, compact and useful design of jig & fixture to assure welding quality for 3 sheet-layer zinc-coated steel, system integration between 4kW Nd:YAG laser device and the other systems, on-line real time welding quality monitoring system, perfect safety standards for high power laser, minimization of consumption costs such as arc lamp, protective glass for optic, etc.Laser welding has found a place on Hyundai’s production plant in conjunction with the startup of mass production of new sports car, and this production system is the result of a collaboration of its engineers. Outer side sheets are joined to inner side sheets by 122 stitch welds totally. And the length is about 2.4meter.Laser welding application for car body manufacturing has many advantages in the stiffness and the lightness of vehicle, the productivity of assembly line, and the degree of freedom in design. This presentation will express the innovation of car body manufacturing including parameter optimization, process modeling, and system integration. In this application the investment for systems was cut down dramatically by real time switching over the laser path between two welding stations. Points of technical discussion are as follows: optimization of parameters such as laser power, robot speed and trajectory, compact and useful design of jig & fixture to assure welding quality for 3 sheet-layer zinc-coated steel, system integration between 4kW Nd:YAG laser device and the other systems, on-line real time welding quality monitoring system, perfect safety standards for high power laser, minimization of consumption cos...

The purpose of this paper is to give four new applications of the Quillen-Suslin theorem to mathematical systems theory. Using a constructive version of the Quillen-Suslin theorem, also known as Serre's conjecture, we show how to effectively compute flat outputs and injective parametrizations of flat multidimensional linear systems. We prove that a flat multidimensional linear system is algebraically equivalent to the controllable 1-D dimensional linear systems obtained by setting all but one functional operator to zero in the polynomial matrix defining the system. In particular, we show that a flat ordinary differential time-delay linear system is algebraically equivalent to the corresponding ordinary differential system without delay, i.e., the controllable ordinary differential linear system obtained by setting all the delay amplitudes to zero. We also give a constructive proof of a generalization of Serre's conjecture known as Lin-Bose's conjecture. Moreover, we show how to constructively compute (weakly) left-/right-/doubly coprime factorizations of rational transfer matrices over a commutative polynomial ring. The Quillen-Suslin theorem also plays a central part in the so-called decomposition problem of linear functional systems studied in the literature of symbolic computation. In particular, we show how the basis computation of certain free modules, coming from projectors of the endomorphism ring of the module associated with the system, allows us to obtain unimodular matrices which transform the system matrix into an equivalent block-triangular or a block-diagonal form. Finally, we demonstrate the package QuillenSuslin which, to our knowledge, contains the first implementation of the Quillen-Suslin theorem in a computer algebra system as well as the different algorithms developed in the paper.

The parameter adaptive control problem of linear stochastic distributed-parameter systems is considered and treated by invoking the partitioning/non-linear separation approach. Both continuous-time and discrete-time systems are studied, with volume and/or boundary control and disturbance inputs. The following cases are considered: spatially-continuous and point-wise measurements/control actions, continuous and quantized parameter space, non-gaussian initial state, uncertainty in continuous and point-wise measurements, cost-function with spatial-derivative penalties, systems with pure time delays, composite distributed- and lumped-parameter systems, scanning-type control, and simultaneous adaptive system and measurement control. The uncertain parameters are assumed to be time-and-space independent, but the spatial independence can be alleviated as will be shown elsewhere.

The regulator problem for linear uncertain continuous-time systems having control constraints is considered. Necessary and sufficient conditions of positive invariance of polyhedral domains are extended to the case of continuous-time uncertain systems. Robust constrained regulators are then derived. An application to the control of a stirred tank pH is then achieved. First, the process is modeled as models studied hereafter, then a robust constrained regulator is calculated. Simulation results show that this control law is easy to implement and guarantees robust asymptotic stability and control admissibility.

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper presents a state observer for linear systems and Lipschitz nonlinear systems with delayed output measurements, which are affected by a known and bounded time-varying delay. The structure of the proposed observer is based on a proportional-integral term, which allows to compensate the time-varying delay. The observer gain depends on the maximum bounded delay. This gain is computed by a Linear Matrix Inequality (LMI) approach. The observer exhibits good performance for state estimation of the system despite the presence of significantly long delay. A Lyapunov-Krasovskii functional is used to prove the asymptotical convergence to zero of the observation error. This observer is applied to the case of systems with time-varying delay whose dynamic is described by a piecewise differentiable function. Examples and numerical simulations are provided in order to support the validity of the main results.

Efficient approximate solution of sparse linear systems

The model reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the model reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve model reduction problems in the presence of constraints on the reduced model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies.

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.