A Control-Oriented Notion of Finite State Approximation

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.Comment: IEEE Transactions on Automatic Control, to appea

Finite Alphabet Control of Logistic Networks with Discrete Uncertainty

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

Control of production-distribution systems under discrete disturbances and control actions.

This paper deals with the robust control and optimization of production-distribution systems. The model used in our problem formulation is a general network flow model that describes production, logistics, and transportation applications. The novelty in our formulation is in the discrete nature of the control and disturbance inputs. We highlight three main contributions: First, we derive a necessary and sufficient condition for the existence of robustly control invariant hyperboxes. Second, we show that a stricter version of the same condition is sufficient for global convergence to an invariant set. Third, for the scalar case, we show that these results parallel existing results in the setting where the control actions and disturbances are analog. We conclude with two simple illustrative examples

STATE ESTIMATION AND OBSERVABILITY OF SYSTEMS OVER FINITE ALPHABETS

In this dissertation, the state estimation problem for systems over finite alphabets is studied, focusing in particular on a significant special instance of such systems consisting of an LTI system with a finite input set and an output quantizer. The need for new notions of observability is motivated, and a set of new notions of observability are formulated quantifying the degree to which the output of such systems can be predicted by an observer. The characterization of observability is investigated, with both necessary and sufficient conditions derived in terms of the dynamics of the system, the properties of the quantizer, and the finite alphabet sets. The use of deterministic finite state machine as observers is also explored, with a view towards understanding their advantages and limitations. Building on the notion of finite memory observability, a control design problem is formulated. Lastly, an idea inspired by the characterization of observability is applied to solve some remaining open questions in the theory of bisimulation