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Robust output regulation of uncertain chaotic systems with input magnitude and rate constraints

Velosa C. M. N., Bousson K.

Acta Mechanica et Automatica

2015

Vol. 9, no. 4

252--258

The problem of output regulation deserves a special attention particularly when it comes to the regulation of nonlinear systems. It is well-known that the problem is not always solvable even for linear systems and the fact that some demanding applications require not only magnitude but also rate actuator constraints makes the problem even more challenging. In addition, real physical systems might have parameters whose values can be known only with a specified accuracy and these uncertainties must also be considered to ensure robustness and on the other hand because they can be crucial for the type of behaviour exhibited by the system as it happens with the celebrated chaotic systems. The present paper proposes a robust control method for output regulation of chaotic systems with parameter uncertainties and subjected to magnitude and rate actuator constraints. The method is an extension of a work recently addressed by the same authors and consists in decomposing the nonlinear system into a stabilizable linear part plus a nonlinear part and in finding a control law based on the small-gain principle. Numerical simulations are performed to validate the effectiveness and robustness of the method using an aeronautical application. The output regulation is successfully achieved without exceeding the input constraints and stability is assured when the parameters are within the specified intervals. Furthermore, the proposed method does not require much computational effort because all the control parameters are computed offline.

Efficient global optimization based on dynamic canonical descent

Bousson K.

Systems Science

2000

Vol. 26, nr 4

61-78

Stochastic methods have gained some popularity in global optimization in that most of them do not assume the cost functions to be differentiable, have capabilities to avoid being trapped by local optima, and may converge even faster than gradient-based optimization methods on some problems. The present paper briefly reviews the advantages and the limitations of some classical stochastic optimization algorithms such as genetic algorithms (GA) and simulated annealing (SA), and then proposes a faster derivative-free and deterministic (non-stochastic) global optimization algorithm which retains their advantages while avoiding their disadvantages.