Danielle C. Tarraf

Danielle C. Tarraf

We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust control, we propose a control-oriented notion of finite state approximation for these systems, demonstrate its relevance to the control synthesis problem, and discuss its key features.

Danielle C. Tarraf, Dario Bauso

We consider logistic networks in which the control and disturbance inputs take values in finite sets. We derive a necessary and sufficient condition for the existence of robustly control invariant (hyperbox) sets. We show that a stronger version of this condition is sufficient to guarantee robust global attractivity, and we construct a counterexample demonstrating that it is not necessary. Being constructive, our proofs of sufficiency allow us to extract the corresponding robust control laws and to establish the invariance of certain sets. Finally, we highlight parallels between our results and existing results in the literature, and we conclude our study with two simple illustrative examples.

Donglei Fan, Danielle C. Tarraf

We consider a class of systems over finite alphabets with linear internal dynamics, finite-valued control inputs and finitely quantized outputs. We motivate the need for a new notion of observability and propose three new notions of output observability, thereby shifting our attention to the problem of state estimation for output prediction. We derive necessary and sufficient conditions for a system to be output observable, algorithmic procedures to verify these conditions, and a construction of finite memory output observers when certain conditions are met. We conclude with simple illustrative examples.

Donglei Fan, Danielle C. Tarraf

We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite uniform bisimulation. We derive sufficient conditions for the existence of finite uniform bisimulations, and propose and analyze algorithms to compute finite uniform bisimulations when the sufficient conditions are satisfied. We investigate the necessary conditions, and conclude with a set of illustrative examples.