M. A. Zohdy

A robust optimal model matching control

A deductive design approach is proposed to develop an optimal feedback control, while preserving quantitative robustness and noise rejection properties. The design procedure involves the minimization of a suitably selected performance index to reflect a required model matching (following) objective. Gradient projection schemes, applied to the performance index and feasible constraints, are used to accomplish the design tradeoff. A mechanical manipulator control system example is employed as a vehicle to illustrate the overall design selection and optimization. Uncertainty of the system description is included as a feature of the example.

Robust control of biped robots

Demonstrates a strategy for the design and implementation of robust controllers for robots. The design technique is based on constructing an error vector between the robot measurable states and the desired states, then forcing the gradient of this error vector to be negative via the use of a suitable Lyapunov function. The controller is robust in the sense that it accommodates unstructured uncertainties inherent in robotics. Different robots having different degrees of complexities are used to simulate the response of the proposed controller and compare it to existing ones. The simulation is made in a MATLAB environment. A few practical considerations are then addressed to investigate the causality of the proposed controller and its applicability to real-time situations. A conclusion is submitted with a few comments regarding both adaptivity and real-time compatibility of the proposed controller.

Nonlinear recursive chaos control

A nonlinear recursive chaos and bifurcation control approach, based on a backstepping technique, is presented to control bifurcation and chaos in engineering applications. Modern nonlinear system theory in bifurcation and chaos is used to study the dynamics of a 3rd order nonlinear system. The study considers the system when experiencing bifurcation and chaos state. In order to control it, a recursive backstepping controller is designed. We show how such a controller is effective in controlling the unstable bifurcation region.

Robust model-reference control for a class of non-linear and piece-wise linear systems

This paper demonstrates a strategy for designing model-reference controllers. The design technique is based on using Backstepping techniques as an extension to Lyapunov-based designs. The proposed controller has the capability of accomplishing both asymptotic stability and satisfactory transient performance. LMI techniques are used to investigate the stability of the proposed controller when the model could be expressed in an affine-based form. Two different approaches are used to deal with nonlinear systems. The first one is by using different affine models for the system with a scheduling parameter to switch between the models. The second one is by directly using the nonlinear system while adding pole-placement structure to the closed loop system. Full state feedback, output feedback and robustness problems are addressed in the existence of uncertainties. A simulated one-degree of freedom robot arm, in a MATLAB/SIMULINK environment, is used to exemplify the suggested techniques along with the LMI toolbox. Tradeoffs between stability and performance are carefully studied.

Variable structure control using system decomposition

An approach to the design of large variable structure systems subject to control bounds is introduced. The method includes a switching hyperplane design based on generalized inverses and system decomposition. To ensure reaching the hyperplane and achieving a sliding condition, the control is switched between local equivalent control and bounded corrective control. The design of the corrective control component is completed using system decomposition into smaller subsystems. An estimate of the domain of attraction corresponding to the bounded control is obtained and used to select the appropriate controller bounds. The method is illustrated using a fifth-order numerical example. >

Discrete-time optimal feedback controllers with time-multiplied performance indexes

A class of optimal state and output feedback control laws for discrete-time time-invariant linear systems which minimizes a class of discrete-time time-multiplied performance indexes is presented. A necessary condition, an existence condition, and a sufficient condition for the control laws are derived. A simple example is given to illustrate the effectiveness of the proposed control laws.

A neural network approach to least squares estimation

The authors present a new neural network approach to the problem of least squares parameter estimation and identification in engineering applications. First, they define the fundamental estimation problems, which is reformulated into a form suitable for a neural network realization. After introducing the interconnected neural network architecture, the required inputs and the values of the connectivities among the processing elements are derived. A numerical example is presented to illustrate the detrimental effects of inevitable parameter variations and noise.<<ETX>>

Robust Estimation-Based Control of Chaotic Behavior in an Oscillator with Inertial and Elastic Symmetric Nonlinearities

In this paper, we study the dynamics of a forced nonlinear oscillator with inertial and elastic symmetric nonlinearities using modern nonlinear, bifurcation and chaos theories. The results for the response have shown that, for a certain combination of physical parameters, this oscillator exhibits a chaotic behavior or a transition to chaos through a sequence of period doubling bifurcations. The main objective of this paper is to control the chaotic behavior for this type of oscillator. A nonlinear estimation-based controller is proposed and the transient performance is investigated. The design of the parameter update mechanism is analyzed while discussing ways to extend its performance to further account for other types of uncertainties. We examine robustness problems as well as ways to tune the controller parameters. Simulation results are presented for the uncontrolled and controlled cases, verifying the effectiveness and the capability of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.

A joint frequency-position domain structure identification of nonlinear discrete-time systems by neural networks

A new technique is proposed to identify the structure and the parameters of nonlinear discrete-time system models. The structure is represented in a frequency-position domain of Gabor basis functions (GBFs). A simplification to the GBF is also presented, where the spatial Gaussian envelope of GBF is replaced with a triangular one. A modification to the GBF has also been introduced in order to suppress the effects of noise on the procedure. A three-layered neural network, augmented with nonuniform sampling, is described for solving the system identification problem. >

A genetic algorithm for selection of noisy sensor data in multisensor data fusion

Irrespective of the specifics of a given application, multisensor data fusion problem is mainly composed of three sub-problems: selection, fusion and estimation. Sensor measurements inherently incorporate varying degrees of uncertainty and are, occasionally, spurious and incorrect This, coupled with the practical reality of occasional sensor failure greatly compromises reliability and reduces confidence in sensor measurements. In order to avoid any false inferences, we need data pre-processing methods to make sure that the data to be merged is consistent. Selection of noisy sensor data is a preprocessing of data before merging and is referred to as choosing a representative subset of the sensors that are consistent. In this paper, we use genetic search and optimization approach to develop a genetic algorithm for qualifying the data.