No abstract

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.

This chapter proposes a robust control approach for the class of chaotic systems subject to magnitude and rate actuator constraints. The approach consists of decomposing the chaotic system into a linear part plus a nonlinear part to form an augmented system comprising the system itself and the integral of the output error. The resulting system is posteriorly seen as a linear system plus a bounded disturbance, and two robust controllers are applied: first, a controller based on a generalization of the Lyapunov function, then a Linear-Quadratic Regulator (LQR) with a prescribed degree of stability. Numerical simulations are performed to validate the approach applying it to the Lorenz chaotic system and to a chaotic aeroelastic system, and parameter uncertainties are also considered to prove its robustness. The results confirm the effectiveness of the approach, and the constraints are guaranteed as opposed to other control techniques which do not consider any kind of constraints.