Class Of Affine Nonlinear Systems Research Articles

Robust and adaptive backstepping control for nonlinear systems using RBF neural networks.

In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.

TRACKING CONTROL OF NONLINEAR SYSTEMS: A SLIDING MODE DESIGN VIA CHAOTIC OPTIMIZATION

The output tracking for a general family of nonlinear systems presents formidable technical challenges. In this paper, we present a novel scheme for tracking control of a class of affine nonlinear systems with multi-inputs. This effective procedure is based on a new sliding mode design for tracking control of such nonlinear systems. The construction of an optimal sliding mode is a difficult problem and no systematic and efficient method is currently available. Here, we develop an innovative approach that utilizes a chaotic optimizing algorithm, which is then successfully applied to obtain the optimal sliding manifold. The existing efficient reaching law approach is then utilized to synthesize the sliding mode control law. The sliding mode control scheme proposed here is particularly appropriate for robust tracking of the chaotic motion trajectory.

On minimum quadratic functional control of affine nonlinear systems

The minimization control problem of the quadratic functionals for the class of affine nonlinear systems in the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control correspondent to the first-, second- and third-order nilpotent operator is determined. H. Bourdache-Siguerdinljane has applied the method of Lie algebras to the study of optimal control regulation of satellites. S. Banks and M. Yew have studied the optimal control of energy consumption minimization for a class of bilinear systems and J.S. Liu et al., have generalized this result for the class of affine nonlinear systems. The optimal control determination of nonlinear system with a nilpotent structure minimizing the quadratic functionals generalizes the results of J.S. Liu, K. Yuan, W.S. Lin, and S.P. Banks, and M.K. Yew regarding the energy minimization of the affine nonlinear and bilinear systems.

Nonregular feedback linearization: A nonsmooth approach

In this note, we address the problem of exact linearization via nonsmooth nonregular feedback. A criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs, and its application to nonholonomic systems is briefly discussed.

SEPARATION PRINCIPLE FOR A CLASS OF NONLINEAR SYSTEMS

We address the problem of global output feedback stabilization for a class of nonlinear affine systems. For affine systems that admit an exponentially stable observer it is shown that a global separation principle holds. Our stabilization results are also presented for general nonlinear systems. An output feedback controller is designed for a flexible one-link robot arm as an illustrative example.

Direct adaptive NN control of a class of nonlinear systems

In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.

Stiffening control of a class of nonlinear affine systems

A control procedure is proposed for dealing with the active stiffening motion of a class of flexible structures characterized by nonlinear affine dynamics. Based on recent developments in the area of differential geometry, the procedure allows for determining the critical area for placing a sensor on a given flexible structure beyond which a centralized controller located on the rigid part becomes ineffective. This is used subsequently for locating instrumentation devices and hardware components on the elastic parts of the system. Numerical simulations are carried out to assess the validity of the theoretical framework. Several meaningful results are obtained, and propositions for further findings are outlined.

Essential orders and the non-linear decoupling problem

Abstract The concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems (Commauit et al. 1986, De Luca et al. 1985). This paper presents a non-trivial extension to the class of non-linear affine systems of some of these definitions and results. It is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right-invertible system.