Sergey Dashkovskiy

Constructive Design of Adaptive Controllers for Nonlinear MIMO Systems With Arbitrary Switchings

This technical note is devoted to the problem of global adaptive stabilization of switched triangular form systems with unknown parameters. The switching signal is assumed to be unknown and the input-output maps of the triangular form are assumed to be right-invertible. A scheme to find a stabilizing controller is provided.

Uniform Stabilization of Nonlinear Systems With Arbitrary Switchings and Dynamic Uncertainties

We solve the problem of global uniform input-to-state stabilization of nonlinear switched systems with time-varying and periodic dynamics, with dynamic uncertainties, and with external disturbances. The switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form (GTF) with non-invertible input-output maps. In our first and most general result, we prove that, if the dynamic uncertainty is treated as external disturbance, then the general triangular form system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty by means of a switching-independent, smooth and periodic feedback. Hence, using a suitable extension of the well-known small gain theorem to our case of switched systems with arbitrary switchings, we obtain the uniform input-to-state stabilization of the entire interconnected system. The second part of the paper addresses a more special case of triangular form (TF) switched systems with right-invertible input-output (I-O) maps with unknown switchings and with dynamic uncertainties. We show that the design becomes simpler and more constructive and the controllers become time-invariant if the dynamics is autonomous in this special case. Finally, we consider an example with explicit design of the stabilizing controllers.

Integrator backstepping for uncertain nonlinear systems with non-smooth dynamics

Abstract We solve the problem of global input-to-state stabilization with respect to external disturbances for a class of nonlinear systems with unknown parameters. For this class, the classical backstepping framework is not applicable and needs to be redesigned because of the following obstacles: (a) the systems under consideration are not in strict-feedback form, are not feedback linearizable and their input-output maps are not invertible, and (b) the dynamics is non-smooth and the trajectories starting from an initial point are not necessarily uniquely defined.