We address the invertibility problem for switched systems, which is the problem of recovering the switching signal and the input uniquely given an output and an initial state. In the context of hybrid systems, this corresponds to recovering the discrete state and the input from partial measurements of the continuous state. In solving the invertibility problem, we introduce the concept of singul...

We show how to automatically learn the class of Hybrid Automata called Cycle-Linear Hybrid Automata (CLHA) in order to model the behavior of excitable cells. Such cells, whose main purpose is to amplify and propagate an electrical signal known as the action potential (AP), serve as the “biologic transistors” of living organisms. The learning algorithm we propose comprises the following three ph...

We consider observability for a class of piecewise-affine hybrid systems without inputs. The aim is to give verifiable conditions for observability in terms of linear equations and inequalities. We first discuss a number of important concepts, such as discrete-event detectability and trajectory observability. We give sufficient conditions for observability, observability in infinitesimal time, ...

We show how different functional interpretations can be combined via a multi-modal linear logic. A concrete hybrid of Kreisel’s modified realizability and Gödel’s Dialectica is presented, and several small applications are given. We also discuss how the hybrid interpretation relates to variants of Dialectica and modified realizability with non-computational quantifiers.

Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.

In this paper we compute the root-mean-square (RMS) gain of a switched linear system when the interval between consecutive switchings is large. The algorithm proposed is based on the fact that a given constant γ provides an upper bound on the RMS gain whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of γ-dependent algebraic Riccati equations. The...

This paper proposes an event-driven model predictive control scheme with guaranteed closed-loop convergence properties for the class of integral continuous-time hybrid automata (icHA). After converting icHA to a corresponding event-driven representation that allows one to compute the model predictive control action by mixed integer programming, sufficient conditions ensuring event-asymptotic an...

We analyze the observability of the continuous and discrete states of a class of continuous-time linear hybrid systems. We derive necessary and sufficient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces generated ...

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL) as a common ground and they admit (cut-free) complete focused proof systems. The difference relies on the way modalities are handled. In HyLL, truth judgmen...

This paper presents a new approach to the solution of nonsymmetric linear systems that uses hybrid techniques based on both direct and iterative methods An implicitly preconditioned modi ed system is obtained by applying projections onto block rows of the original system Our technique provides the exibility of using either direct or iter ative methods for the solution of the preconditioned syst...