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Invited Paper Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential(More)
Theories about sexual selection can be traced back to Darwin in 1871. He proposed that males fertilize as many females as possible with inexpensive sperm, whereas females, with a limited supply of large eggs, select the genetically highest quality males to endow their offspring with superior capabilities. Since its proposal, problems with this narrative(More)
We address systems which have multiple objectives: broadly speaking, these objectives can be thought of as safety and performance goals. Guaranteeing safety is our rst priority, satisfying performance criteria our second. In this paper, we compute the system's safe operating space and represent it in closed form, and then, within this space, we compute(More)
We present a connection between the viability kernel and maximal reachable sets. Current numerical schemes that compute the viability kernel suffer from a complexity that is exponential in the dimension of the state space. In contrast, extremely efficient and scalable techniques are available that compute maximal reachable sets. We show that under certain(More)
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been applied to stochastic hybrid systems, little work has been done on the equally important problem of reachability under(More)
We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative approximation of the discriminating kernel using robust maximal reachable sets—an extension of our earlier work on(More)
—Hybrid systems combine discrete state dynamics which model mode switching, with continuous state dynamics which model physical processes. Hybrid systems can be controlled by affecting both their discrete mode logic and continuous dynamics: in many systems, such as commercial aircraft, these can be controlled both automatically and using manual control. A(More)
While a number of Lagrangian algorithms to approximate reachability in dozens or even hundreds of dimensions for systems with linear dynamics have recently appeared in the literature, no similarly scalable algorithms for approximating viable sets have been developed. In this paper we describe a connection between reachability and viability that enables us(More)
— A human interacting with a hybrid system is often presented, through information displays, with a simplified representation of the underlying system. This interface should not overwhelm the human with unnecessary information, and thus usually contains only a subset of information about the true system model, yet, if properly designed, represents an(More)