A geometric approach to structural model matching by output feedback in linear impulsive systems

AbstractThis paper provides a complete characterization of solvability of the problem of structural model matching by output feedback in linear impulsive systems with nonuniformly spaced state jumps. Namely, given a linear impulsive plant and a linear impulsive model, both subject to sequences of state jumps which are assumed to be simultaneous and measurable, the problem consists in finding a linear impulsive compensator that achieves exact matching between the respective forced responses of the linear impulsive plant and of the linear impulsive model, by means of a dynamic feedback of the plant output, for all the admissible input functions and for all the admissible sequences of jump times. The solution of the stated problem is achieved by reducing it to an equivalent problem of structural disturbance decoupling by dynamic feedforward. Indeed, this latter problem is formulated for the so-called extended linear impulsive system, which consists of a suitable connection between the given plant and a modified model. A necessary and sufficient condition for the solution of the structural disturbance decoupling problem is first shown. The proof of sufficiency is constructive, since it is based on the synthesis of the compensator that solves the problem. The proof of necessity is based on the definition and the geometric properties of the unobservable subspace of a linear impulsive system subject to unequally spaced state jumps. Finally, the equivalence between the two structural problems is formally established and proven

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Equivalence of switching linear systems by bisimulation

A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input–output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud \u

Learning and Designing Stochastic Processes from Logical Constraints

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are {\it qualitative} properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation

Fast, Autonomous Flight in GPS-Denied and Cluttered Environments

One of the most challenging tasks for a flying robot is to autonomously navigate between target locations quickly and reliably while avoiding obstacles in its path, and with little to no a-priori knowledge of the operating environment. This challenge is addressed in the present paper. We describe the system design and software architecture of our proposed solution, and showcase how all the distinct components can be integrated to enable smooth robot operation. We provide critical insight on hardware and software component selection and development, and present results from extensive experimental testing in real-world warehouse environments. Experimental testing reveals that our proposed solution can deliver fast and robust aerial robot autonomous navigation in cluttered, GPS-denied environments.Comment: Pre-peer reviewed version of the article accepted in Journal of Field Robotic