arXiv subjects

Andrew R. Teel

Publications and source records attributed to Andrew R. Teel.

22 records · Page 2Linked to original sources

arXiv2015

Lyapunov-based sufficient conditions for stability of hybrid systems with memory

Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals. Examples are provided to illustrate these conditions.

math.DS↗

arXiv2013

On generalized terminal state constraints for model predictive control

This manuscript contains technical results related to a particular approach for the design of Model Predictive Control (MPC) laws. The approach, named "generalized" terminal state constraint, induces the recursive feasibility of the underlying optimization problem and recursive satisfaction of state and input constraints, and it can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to existing approaches, given the same computational complexity. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by three examples.

eess.SY↗

arXiv2003

Matrosov's theorem using a family of auxiliary functions: an analysis tool to aid time-varying nonlinear control design

We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskii-LaSalle invariance principle to the case of general nonlinear time-varying systems. We show the utility of our theorem by addressing a control problem of port interconnected driftless systems. The latter includes as special case, the control of chained-form nonholonomic systems which has been extensively studied in the literature.

math.OC↗

arXiv2003

Persistency of excitation for uniform convergence in nonlinear control systems

In previous papers we have introduced a sufficient condition for uniform attractivity of the origin for a class of nonlinear time-varying systems which is stated in terms of persistency of excitation (PE), a concept well known in the adaptive control and systems identification literature. The novelty of our condition, called uniform delta-PE, is that it is tailored for nonlinear functions of time and state and it allows us to prove uniform asymptotic stability. In this paper we present a new definition of u-delta-PE which is conceptually similar to but technically different from its predecessors and give several useful characterizations. We make connections between this property and similar properties previously used in the literature. We also show when this condition is necessary and sufficient for uniform (global) asymptotic stability for a large class of nonlinear time-varying systems. Finally, we show the utility of our main results on some control applications regarding feedforward systems and systems with matching nonlinearities.

math.OC↗