Provably asymptotically stable running gaits are developed for the five-link, four-actuator bipedal robot, RABBIT. A controller is designed so that the Poincaré return map associated with periodic running gaits can be computed on the basis of a model with impulse effects that, previously, had been used only for the design of walking gaits. This feedback design leads to the notion of a hybrid ze...

The stability of the trivial equilibrium position of certain classes of mechanical systems with time-varying delay is studied. The considered systems are described by the second order differential equations in the Lagrange form. It is assumed that velocity forces are linear, whereas for positional forces both linear case and essentially nonlinear one are investigated. On the basis of the decomp...

This paper presents results for stability and robustness of hybrid systems consisting of nonlinear subsystems. Present stability results that are extensions of classical Lyapunov theory are restricted to certain kinds of hybrid systems. For example, it is required that all subsystems have the same equilibrium point. In this paper, existing results are generalized; but more importantly, it is sh...

In this paper we analyze a class of hybrid systems known as Witsenhausen systems, or switched systems. We study the existence of a solution to the state trajec-tory equation as well as conditions for global existence of solutions. We also present a discussion about the continuity of the solutions with respect to the initial condition. Then we prove some facts about the stability of equilibria a...

This paper addresses the two-agent safety control problem for piecewise continuous systemswith disturbances and imperfect state information. In particular, we focus on a class of systemsthat evolve on a partial order and whose dynamics preserve the ordering. While the safety con-trol problem with imperfect state information is prohibitive for general classes of nonlinear andhybr...

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated “dynamic walking” biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not k...

Reachability analysis has recently proved to be a useful technique for analysing the behaviour of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bounded interval containing the time at which the system can reach a target set from an initial set. Then this estimation can be directly integ...

A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinear hybrid systems. In this paper, we propose a new barrier certificate condition, called Exponential Conditio...

We develop algorithms for computing Craig interpolants for first-order formulas over real numbers with a wide range of nonlinear functions, including transcendental functions and differential equations. We transform proof traces from δ-complete decision procedures into interpolants that consist of Boolean combinations of linear constraints. The algorithms are guaranteed to find the interpolants...

This paper presents the qualitative heterogeneous control framework, a methodology for the design of a controlled hybrid system based on attractors and transitions between them. This framework designs a robust controller that can accommodate bounded amounts of parametric and structural uncertainty. This framework provides a number of advantages over other similar techniques. The local models us...