ADAPTIVE DYNAMICAL FEEDBACK REGULATION STRATEGIES FOR LINEARIZABLE UNCERTAIN SYSTEMS

In this paper we address the design of adaptive dynamical feedback strategies of the continuous and discontinuous, types for the output stabilization of nonlinear systems. The class of systems considered corresponds to nonlinear controlled systems exhibiting linear parametric uncertainty. Dynamical feedback controllers, ideally achieving output stabilization via exact linearization, are obtained by means of repeated output differentiation and, either, pole placement, or, sliding mode control techniques. The adaptive versions of the dynamical stabilizing controllers are then obtainable through standard, direct, overparamemzed adaptive control strategies available for linearizable systems. Illustrative examples are provided which deal with the regulation of electromechanical systems

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated

High-gain nonlinear observer for simple genetic regulation process

High-gain nonlinear observers occur in the nonlinear automatic control theory and are in standard usage in chemical engineering processes. We apply such a type of analysis in the context of a very simple one-gene regulation circuit. In general, an observer combines an analytical differential-equation-based model with partial measurement of the system in order to estimate the non-measured state variables. We use one of the simplest observers, that of Gauthier et al., which is a copy of the original system plus a correction term which is easy to calculate. For the illustration of this procedure, we employ a biological model, recently adapted from Goodwin's old book by De Jong, in which one plays with the dynamics of the concentrations of the messenger RNA coding for a given protein, the protein itself, and a single metabolite. Using the observer instead of the metabolite, it is possible to rebuild the non-measured concentrations of the mRNA and the proteinComment: 9 pages, one figur

Sliding Mode for User Equilibrium Dynamic Traffic Routing Control

Presents a solution to the user equilibrium dynamic traffic routing (DTR) problem for a point diversion case using feedback control methodology. The sliding mode control technique which is a robust control methodology applicable to nonlinear systems in canonical form is employed to solve the user equilibrium DTR problem. The canonical form for this problem is obtained by using a feedback linearization technique, and the uncertainties of the system are countered by using the sliding mode principle. Simulation results show promising results