This paper presents a formulation of differential flatness—a concept originally introduced by Fliess, Levine, Martin, and Rouchon—in terms of absolute equivalence between exterior differential systems. Systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was g...

Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi timescale systems. In this paper a contraction theory based framework is proposed for stabilization of singularly perturbed systems. The primary objective is to design a feedback controller to achieve bounded tracking error for both standard an...

This paper presents a formulation of diierential atness|a concept originally introduced by Fliess, Levine, Martin, and Rouchon|in terms of absolute equivalence between exterior diierential systems. Systems which are diierentially at have several useful properties which can be exploited to generate eeective control strategies for nonlinear systems. The original deenition of atness was given in t...

This paper presents a formulation of diierential atness|a concept originally introduced by Fliess, Levine, Martin, and Rouchon|in terms of absolute equivalence between exterior diierential systems. Systems which are diierentially at have several useful properties which can be exploited to generate eeective control strategies for nonlinear systems. The original deenition of atness was given in t...

Numerous papers were published during the last decade on the normal forms of nonlinear control systems with applications in bifurcation and its control. The approach is motivated by Poincaré’s theory of normal forms for classical dynamical systems using homogeneous transformations. In this paper, we summarize a variety of control system normal forms published in the literature so that the norma...

We consider special cases of the quadratic assignment problem (QAP) that are linearizable in the sense of Bookhold. We provide combinatorial characterizations of the linearizable instances of the weighted feedback arc set QAP, and of the linearizable instances of the traveling salesman QAP. As a by-product, this yields a new well-solvable special case of the weighted feedback arc set problem.

Robust controllers for nonlinear systems with uncertain parameters can be reliably designed using probabilistic methods. In this chapter, a design approach based on the combination of stochastic robustness and dynamic inversion is presented for general systems that have a feedback-linearizable nominal system. The efficacy of this control approach is illustrated through the design of flight cont...

In this work, we consider nonlinear singularly perturbed systems with time-varying uncertain variables, for which the fast subsystem is asymptotically stable and the slow subsystem is input/output linearizable and possesses input-to-state stable (ISS) inverse dynamics. For these systems, we synthesize a robust output feedback controller that ensures boundedness of the state and enforces robust ...