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Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and suggests a way to improve the teaching of the methodology...
Existing reachability theory and optimal control theory are applied to a class of nonlinear systems with ellipsoidal initial reachability sets, reflecting information typically provided by industry-standard optimal estimation methods. Analytical expressions for position-and velocity-extrema are developed, yielding necessary conditions for reachability as well as tools for significant reduction in...
Iterative methods for linear systems with a symmetric positive definite coefficient matrix are designed from a control-theoretic viewpoint. In particular, it is shown that a control-theoretic approach loosely based on m-step dead beat control of the error or residual system, with a suitable definition of error norm can be utilized to design new iterative methods that are competitive with the popular...
In this paper we analyze the inverted pendulum system and use variable structure theory in controlling the car position and pendulum angle. We use Lyapunov theory getting the sliding mode function and output expression of the controller. At the same time we prove the astringency of sliding mode. The simulation and inverted pendulum system experiment both prove that the nonlinear variable structure...
We study the solution properties of a family of inverted pendulum systems driven by odd periodic forcing. Using the Schauder fixed point theorem, we show that the inverted pendulum with an odd periodic driving acceleration at the pivot always possesses an odd periodic solution. Fundamental to the production of good estimates is the development of a Green's function for an unstable harmonic oscillator...
A new observation procedure is proposed for a wide class of single output observable nonlinear systems written in lower triangular form. First, we give the n-th order time-varying differentiator that robustly estimates, in asymptotic manner, the higher derivatives of any model-free continuously differentiable signal. This n-th order differentiator is a generalization of the time-varying differentiator...
In this paper, we propose a new iterative learning control (ILC) scheme, which is devoted to dealing with unknown parameters that are both time varying and iteration varying. In particular, we consider iteration-varying parameters that are generated by a second-order internal model. By incorporating the internal model into the parametric learning law, the ILC scheme can handle more generic nonlinear...
This paper considers the problem of output regulation for nonlinear, possibly non-minimum phase, systems, in the presence of parameter-uncertain exosystems. The proposed result relies upon a framework recently proposed by the authors to deal with the presence of unstable zero dynamics in nonlinear output regulation. An interesting aspect of the theory presented in the paper is given by the fact that...
In this paper, we present a systematic approach inspired from the ergodic theory of dynamical system for the optimal control of complex fluid flows. The infinite dimensional Navier Stokes equation describing the complex fluid flow is first reduced to a finite set of coupled ordinary differential equations. We utilize Proper Orthogonal Decomposition techniques to obtain a reduced order model. The linear...
This work presents a set of cascade high gain observers for triangular nonlinear systems with delayed output measurement. A sufficient condition ensuring the exponential convergence of the observation error towards zero is given. This result is illustrated by some simulations.
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
This paper considers the optimal tracking control (OTC) problem for bilinear systems affected by sinusoidal disturbances, and gives a successive approximation approach to solve analogous problems for general bilinear systems. For a given bilinear OTC problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By iteratively solving the...
Feedback linearization technique is a relative mature design technique in nonlinear control system theory, the backstepping technique is a controller design technique which recently gets much favor. The feedback linearization based on backstepping technique is the combination of the two techniques mentioned, it uses backstepping design process, designs a sequence of ??virtual?? systems of relative...
This paper proposes the analysis and design of robust fuzzy control to nonlinear systems with time delay. The nonlinear system to be controlled, is studied in the context of Linear Parameters Varying (LPV) systems, it is partitioned into several linear sub-models of second order with time delay, in terms of transfer function, forming a convex polytope. Once defined the linear sub-models of the plant,...
The rotation mechanical vibration system is a certainty complex nonlinear system, in this paper, we research this system based on chaotic theory, the nonlinear rotation system will be in chaotic state when the rotation speed changed, the dynamic behavior of the system at stable oscillation, according to the values of frequency and amplitude of the steer signal, we can get the basic character s of...
The purpose of this paper is to present a new systematic procedure for decoupling and command tracking of multivariable, nonlinear, and unstable systems. The design methodology is based on stabilization of the multivariable system followed by generating its describing function models; two algebraic procedures for decoupling and tracking are utilized. Finally, the design must be verified by a nonlinear...
Adaptive observer design procedure is proposed for nonlinear locally Lipschitz systems. Possible presence of disturbances is taken into account. The solution is based on logic-based control approach applicable to nonlinear systems with bounded solutions. Efficacy of the proposed observer is demonstrated by computer simulation for a mechanical oscillating system.
For sampled data controller design of nonlinear continuous time systems, it is important to derive a good approximate sampled data model because the exact sampled data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed a more accurate approximate model than the simple Euler model in the case of a zero-order hold. This paper derives...
It is important content that the studying connective stability among the stability studying of the large-scale interconnected systems. The many results recently have been given for the normal systems, the studying result of the singular large scale systems, however, is a little. The paper discussed the connective stability of a kind of nonlinear singular large-scale dynamical systems by means of singular...
This paper presents a method to compute sub-optimal control strategies of discrete time large scale nonlinear systems by neural networks. The method is based on the principle of decomposition of the global system into interconnected subsystems for which we consider that non-linearities are located in the interconnection terms. Then, a mixed method is considered to coordinate between different subsystems...
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