Observability of user-interfaces for linear hybrid systems under collaborative control

Human interaction with automation is ubiquitous, occurring in many cyberphysical systems such as cell phones, automobiles, and commercial aircraft. When interacting with such systems, human users are only exposed to a simplified representation the complex system structure in the form of an interface. The human can observe system outputs and make control inputs via this interface. Problems with human-automation interaction occur when the interface does not provide enough information or provides misinformation about the underlying system, such that the human cannot determine the current state of the automation. The user\u27s knowledge of the current system state and prediction of the next system state is required for effective operation of an automated system. In this work, formal methods are employed to analyze user-interfaces of such cyberphysical systems in order to reveal state observability problems. The cyberphysical systems are modeled as hybrid systems, for which continuous behavior emerges from the laws of physics and discrete behavior results from logical conditions and rules governing the automation. Hybrid systems with LTI continuous dynamics under collaborative control are considered, where collaborative control indicates that some events and inputs are controlled by a human operator while other events and inputs are controlled by the automation. The human user is assumed to be a special type of state observer, with additional requirements beyond a standard (automated) state observer. To reflect these additional requirements, sufficient conditions for user-observability and user-predictability of linear hybrid systems under collaborative control are developed. Algorithms are generated to evaluate a user-interface based on these conditions for user-observability and user-predictability. Then, the algorithms are applied to a hybrid system model abstraction of the longitudinal dynamics of an aircraft flight management system

Identification of Piecewise Linear Models of Complex Dynamical Systems

The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivated by applications in systems biology

Observability of Switched Linear Systems in Continuous Time

We study continuous-time switched linear systems with unobserved and exogeneous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both autonomous and non-autonomous cases

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version