We are designing, perhaps for the first time, closed-loop fault-tolerant control for uncertain nonlinear systems. Our solution is based on a new algebraic estimation technique of the derivatives of a time signal, which • yields good estimates of the unknown parameters and of the residuals, i.e., of the fault indicators, • is easily implementable in real time, • is robust with respect to a large...

We propose HyDICE, Hybrid DIscrete Continuous Exploration, a multilayered approach for hybrid-system falsification that combines motion planning with discrete search and discovers safety violations by computing witness trajectories to unsafe states. The discrete search uses discrete transitions and a state-space decomposition to guide the motion planner during the search for witness trajectorie...

The present paper investigates the behaviour of nonlinear discrete-time dynamics over several steps as a particular case of multi-input dynamics. Introducing for these dynamics a differential representation with jumps, it is shown that the input-to-state or input-to-output behaviours can be represented as suitable compositions of exponential series. Some benefits of these representations are di...

This paper considers the state observer problem for a class of nonlinear systems, which present multiple non commensurate time delays as well as distributed delay terms. The proposed algorithm is an extension of the observer for nonlinear delayless systems proposed in 1993 by Ciccarella, Dalla Mora, Germani. It is proved that a suitable gain can be easily chosen such that the observation error ...

This paper discusses several recent results by the author and collaborators, which are united by the common goal of making nonlinear control theory more robust to imperfect information. These results are also united by common technical tools, centering around input-to-state stability (ISS), small-gain theorems, Lyapunov functions, and hybrid systems. The goal of this paper is to present an over...

We present a new method for the automated synthesis of safe and robust Proportional-Integral-Derivative (PID) controllers for stochastic hybrid systems. Despite their widespread use in industry, no automated method currently exists for deriving a PID controller (or any other type of controller, for that matter) with safety and performance guarantees for such a general class of systems. In parti...

dReach is a bounded reachability analysis tool for nonlinear hybrid systems. It encodes reachability problems of hybrid systems to first-order formulas over real numbers, which are solved by delta-decision procedures in the SMT solver dReal. In this way, dReach is able to handle a wide range of highly nonlinear hybrid systems. It has scaled well on various realistic models from biomedical and r...

Hybrid systems are systems consisting of discrete changes and continuous changes over time. Problems in various fields such as physics can be modeled as hybrid systems. In a simulation of a hybrid system, it is difficult to obtain rigorous solution of the model because of computation errors in the handling of continuous states. Our proposed method integrates interval-based techniques for initia...

Aircraft collision avoidance maneuvers are important and complex applications. Curved flight exhibits nontrivial continuous behavior. In combination with the control choices during air traffic maneuvers, this yields hybrid systems with challenging interactions of discrete and continuous dynamics. As a case study illustrating the use of a new proof assistant for a logic for nonlinear hybrid syst...

This paper investigates the problem of input-to-state stability (ISS) for the general discrete-time impulsive hybrid systems. Quasi-exponential input-to-state stability criteria are established for non-linear discrete-time impulsive hybrid systems, based on the Lyapunov function. The results are then specialized to the linear discrete-time impulsive hybrid systems and fairly simple algebraic co...