Naim Bajcinca

Design of robust PID controllers using decoupling at singular frequencies

Algorithms for computation of the total set of PID stabilizers based on decoupling of PID parameter space at singular frequencies are presented. Nonconvex stability regions are built up by convex polygonal slices. Two problems are thereby discriminated: (A) assertion of kP-intervals with stable polygons and (B) automatic detection of stable polygons for a fixed kP. This paper includes solutions to both problems. The methods apply also for robust PID stabilization of a multi-model uncertainty.

On the quadratic stability of switched linear systems associated with symmetric transfer function matrices

In this paper we give necessary and sufficient conditions for weak and strong quadratic stability of a class of switched linear systems consisting of two subsystems, associated with symmetric transfer function matrices. These conditions can simply be tested by checking the eigenvalues of the product of two subsystem matrices. This result is an extension of the result by Shorten and Narendra for strong quadratic stability, and the result by Shorten et?al. on weak quadratic stability for switched linear systems. Examples are given to illustrate the usefulness of our results.

A hybrid Petri net formalism and resource allocation in distributed control systems

We propose a generalized concept of hybrid Petri nets as a modeling and design tool for the distributed dynamical systems involving asynchronous event-based communication. The proposed Petri net machine represents an extension of the standard discrete-event Petri nets, but differs conceptually from the conventional hybrid Petri nets in that dynamical processes are stored in the continuous places, similarly as in hybrid automata. In particular, the firing semantics of the corresponding continuous arcs is defined to capture the information exchange between the network nodes. While being primarily a graphical modeling tool, the proposed formalism of hybrid Petri nets infers a hybrid dynamical setting of event-triggered control problems, an approach that has been missing in the literature. The usability of our approach is illustrated in the context of the distributed event-triggered LQR and consensus problems, in conjunction with a systematic methodology for designing optimal adaptive scheduling schemes, governing the communication resources.

On model-based source coding for dynamical systems

Communication latency plays a key role in time critical control applications in dynamical cyber-physical systems. It is in particular influenced by source coding algorithms which are typically developed independently of the process dynamics driven at the nodes of networked control systems. This is a note on model-based source coding, providing a state-dependent coding strategy. Therfore we confine our discussion to the simple case-study of Markov chains. Our goal is to minimize the expected codeword length of transmitted information by accounting for the process dynamics.

Optimal adaptive communication protocols subject to dynamical and topological constraints

We propose a systematic method to the design of adaptive communication protocols subject to a set of heterogeneous constraints, including continuous system dynamics, event-based communication and discrete topological constraints. To this end, we make use of a recent modeling formalism based on hybrid Petri nets, whose semantics is capable of capturing the information exchange between the nodes of a network system. The design problem is then given a hybrid dynamical formulation in form of a mixed-integer dynamical system. The proposed approach is directly applicable to the co-design problem of communication and control protocols.