Impulse analysis for nonlinear singular system via Differential Mean Value Theorem

International audience

This paper discusses feedback control problems for affine nonlinear singular systems. Namely, the problems of regularization (regular singular systems have for a particular initial state and input, a unique solution), non-interaction and exact linearization. First, an algorithm providing necessary and sufficient conditions for the regularizability of the affine nonlinear singular systems is introduced. This algorithm resembles the well-known constrained dynamics algorithm for affine nonlinear systems. For regularizable affine nonlinear singular systems, necessary and sufficient conditions for the solvability of the non-interacting control problem are derived. They are based on another algorithm producing a sequence of integers, the generalization of the well known notion of relative degree for usual affine nonlinear systems. Finally, the problem of feedback exact linearization of the dynamic part of singular systems is briefly addressed. An example is provided to illustrate the main results.

ROBUST OUTPUT REGULATION OF SINGULAR NONLINEAR SYSTEMS

In this paper we develop dissipativity results for continual nonlinear and linear singular systems. To the best knowledge of author results are nonexistent. We generalize dissipativity theory to nonlinear continuous singular dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to singular dynamical systems providing a generalized system energy interpretation in terms of stored energy and dissipated energy over the continuous-time system dynamics. Furthermore, extended Kalman-Yakubovich-Popov conditions in terms of the singular system dynamics characterizing dissipativeness via system storage functions are derived. Finally, the framework is specialized to passive and nonexpansive singular systems to provide a generalization of the classical notions of passivity and nonexpansivity for nonlinear singular systems.

In this note, we investigate a new approach for observer synthesis of nonlinear time delay systems. This approach is based on the differential mean value theorem (DMVT). Using the Lyapunov-Krasovskii functionals and the DMVT, we give new sufficient synthesis conditions for the observer design problem. These conditions are formulated as matrix inequalities which become linear whenever an unknown scalar variable is chosen a priori

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time-delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H ∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.

The theoretical foundation of differential aspect in real analysis is the differential mean value theorem, which connects to both the local and total properties of the copula function. The link between the copula function's local and overall properties is differential calculus. The maximum value, minimum value, extreme value, monotonicity, and other difficulties may all be resolved with the help of these differential mean value theorems. Additionally, they aid in the computation of limits, the demonstration of inequality, and the identification of the curve's inflection point and concave-convex interval. They are also capable of mapping the function and locating the equation's root. To tackle these issues, one can apply a number of significant findings from the differential mean value theorem. This study gives the formulae for solving three distinct mean value theorems. The Cauchy, Lagrange, and Roller theorems are examples of these mean value theorems. Understanding the connections between the three mean value theorems is made easier by these studies, which also provide an explanation of the theory underlying the theorems and provide examples and visuals of their practical application.

The differential mean value theorem is one of the important basic theorems in differential calculus and a powerful tool to study the properties of the Han script. It reflects the relationship between functions and derivatives. Many proof questions encountered in the study of calculus need to use the relevant knowledge of the differential mean value theorem, and students are often at a loss. In this paper, several types of differential mean value theorems are discussed in depth, and it is found that the key point and difficulty in proving many propositions related to differential mean value theorems is to construct appropriate auxiliary functions. By constructing auxiliary functions, abstract and seemingly unrelated conclusions can be transformed into relatively straightforward views, which can easily find the path that meets the conditions of differential mean value theorems, and then solve the problem. Through these types of questions, this paper summarizes the common skills to find auxiliary functions, hoping to provide some help for students in learning, postgraduate entrance examination, etc.

Exponential admissibility and [formula omitted] control for nonlinear singular discrete systems with mixed time-varying delays

Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays

The leader-following consensus problem for a type of second-order nonlinear multi-agent systems (MASs) with input saturation, actuator faults, and sensor faults is examined in this study. An adaptive control strategy based on neural networks (NNs) is suggested to overcome the difficulties brought on by unknown nonlinear dynamics and real-world limitations. To handle the unknown nonlinear factors more precisely and flexibly than traditional approaches that depend on global Lipschitz requirements, we use the differential mean value theorem. This improvement enhances the system's capacity to deal with nonlinear behaviors that change quickly. Additionally, sensor faults that affect location and velocity readings and actuator faults that may decrease or deform the input signal are taken into consideration in the control design. The suggested design also clearly addresses input saturation, which may restrict the control authority. Complete state measurements are not required because a distributed adaptive NN-based controller is created only on relative location and velocity data. Using stability theory and appropriate Lyapunov function construction, we rigorously demonstrate that the suggested approach leads to leader-following consensus. The efficiency and resilience of the suggested control strategy against nonlinear uncertainty, actuator and sensor failures, and saturation effects in complicated multi-agent networks are confirmed by simulation results.

During the 20th century, the electronics industry has evolved from radio, television, and audio systems to computer systems. The trace of evolution is clearly from linear systems to nonlinear systems. This is by no means accidental, and is due to the fact that nonlinear systems are more versatile than linear systems. As of now, the successful commercial optical instruments are all linear systems. From the entropy point of view, as the knowledge of human beings further expands, we need more powerful computing capabilities such as memory association and self organization. Based on the fundamental differences between the electron and the photon, this paper presents the argument that optical computing will provide memory association and self organization ability (which compliments the current electronic logical computing). Thus, one can infer that the main future thrust of the optical industry will be in nonlinear optical systems and hybrid combinations with nonlinear electronic systems in order to provide both self organization and logical computing (to emulate, more or less, the computing power of the human brain). Currently, the stat of the ar has already demonstrated successful combinations of linear optical system with nonlinear electronic systems (computers). These kinds of hybrid systems are called electro-photonic systems in the following curriculum. Based on the above vision for the future and taking into account the need for immediate employment, the following curriculum is designed to provide a core training to the students who are interested in choosing optics or electro-photonics as their career. This curriculum is being offered in the upper years at the Physics Department of Chung Yuan University. Electronics, Optics, Electro-photonic System Design and Analysis, Optical System Design and Analysis, Introduction to Optical Computing, Holography, Nonlinear Optics, The Experimental Technology for Electro- photonics (I), The Experimental Technology for Electro-photonics (II). The main thrust among all these courses is the system modeling and analysis. In this paper, the design of this curriculum will be elaborated and the topics for each course will be listed in detail.

Observability and observable degree, which are derived from modern control theory and relative to control and estimation performances, are both important concepts for state estimation. For linear time-invariant systems, judgement of observability and evaluation of observable degree are irrelevant to filtering process and parameters. Thereby, it has limited application ability. Different from linear systems, observability and observable degree becomes more complex and are seldom studied deeply and integrally for nonlinear systems. Due to the complexity of nonlinear filtering, the observable degree depends strongly on filtering process, filter class and associated parameters. Thereby, we study the observable degree analysis of nonlinear estimation systems by using unscented information filter (UIF). A way to evaluate observable degree using singular value decomposition (SVD) of observability matrix is presented based on the UIF and the influencing factors are deeply analyzed. Moreover, differences of observable degree analysis are distinctly discussed between linear and nonlinear systems. The results reveal that evaluation of the observable degree for nonlinear systems can be affected by filtering estimate at last time, initial estimate and filter's parameters such as covariances of process and measurement noises. Some simulations are demonstrated to validate the results.

Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method

Theory of nonlinear control