Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes

We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spike-driven commodities.Comment: Mathematics of Control, Signals, and Systems, Springer Verlag (Germany), 2015, online first http://link.springer.com/article/10.1007/s00498-015-0146-

Stochastic optimization methods for the simultaneous control of parameter-dependent systems

We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the recently developed Continuous Stochastic Gradient (CSG) algorithm. We consider the problem of computing simultaneous controls through the minimization of a cost functional defined as the superposition of individual costs for each realization of the system. We compare the performances of these stochastic approaches, in terms of their computational complexity, with those of the more classical Gradient Descent (GD) and Conjugate Gradient (CG) algorithms, and we discuss the advantages and disadvantages of each methodology. In agreement with well-established results in the machine learning context, we show how the SGD and CSG algorithms can significantly reduce the computational burden when treating control problems depending on a large amount of parameters. This is corroborated by numerical experiments

Attack-Resilient Supervisory Control of Discrete-Event Systems

In this work, we study the problem of supervisory control of discrete-event systems (DES) in the presence of attacks that tamper with inputs and outputs of the plant. We consider a very general system setup as we focus on both deterministic and nondeterministic plants that we model as finite state transducers (FSTs); this also covers the conventional approach to modeling DES as deterministic finite automata. Furthermore, we cover a wide class of attacks that can nondeterministically add, remove, or rewrite a sensing and/or actuation word to any word from predefined regular languages, and show how such attacks can be modeled by nondeterministic FSTs; we also present how the use of FSTs facilitates modeling realistic (and very complex) attacks, as well as provides the foundation for design of attack-resilient supervisory controllers. Specifically, we first consider the supervisory control problem for deterministic plants with attacks (i) only on their sensors, (ii) only on their actuators, and (iii) both on their sensors and actuators. For each case, we develop new conditions for controllability in the presence of attacks, as well as synthesizing algorithms to obtain FST-based description of such attack-resilient supervisors. A derived resilient controller provides a set of all safe control words that can keep the plant work desirably even in the presence of corrupted observation and/or if the control words are subjected to actuation attacks. Then, we extend the controllability theorems and the supervisor synthesizing algorithms to nondeterministic plants that satisfy a nonblocking condition. Finally, we illustrate applicability of our methodology on several examples and numerical case-studies

Controllability Metrics on Networks with Linear Decision Process-type Interactions and Multiplicative Noise

This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a couple consisting of a Markov trend and a linear decision process for which both the "deterministic" and the noise components rely on trend-dependent matrices. We discuss approximate, approximate null and exact null-controllability. Several examples are given to illustrate the links between these concepts and to compare our results with their continuous-time counterpart (given in [16]). We introduce a class of backward stochastic Riccati difference schemes (BSRDS) and study their solvability for particular frameworks. These BSRDS allow one to introduce Gramian-like controllability metrics. As application of these metrics, we propose a minimal intervention-targeted reduction in the study of gene networks

Controllability in partial and uncertain environments

© 2014 IEEE.Controller synthesis is a well studied problem that attempts to automatically generate an operational behaviour model of the system-to-be that satisfies a given goal when deployed in a given domain model that behaves according to specified assumptions. A limitation of many controller synthesis techniques is that they require complete descriptions of the problem domain. This is limiting in the context of modern incremental development processes when a fully described problem domain is unavailable, undesirable or uneconomical. Previous work on Modal Transition Systems (MTS) control problems exists, however it is restricted to deterministic MTSs and deterministic Labelled Transition Systems (LTS) implementations. In this paper we study the Modal Transition System Control Problem in its full generality, allowing for nondeterministic MTSs modelling the environments behaviour and nondeterministic LTS implementations. Given an nondeterministic MTS we ask if all, none or some of the nondeterministic LTSs it describes admit an LTS controller that guarantees a given property. We show a technique that solves effectively the MTS realisability problem and it can be, in some cases, reduced to deterministic control problems. In all cases the MTS realisability problem is in same complexity class as the corresponding LTS problem

Checking sequences for distributed test architectures

Controllability and observability problems may manifest themselves during the application of a checking sequence in a test architecture where there are multiple remote testers. These problems often require the use of external coordination message exchanges among testers during testing. However, the use of coordination messages requires the existence of an external network that can increase the cost of testing and can be difficult to implement. In addition, the use of coordination messages introduces delays and this can cause problems where there are timing constraints. Thus, sometimes it is desired to construct a checking sequence from the specification of the system under test that will be free from controllability and observability problems without requiring the use of external coordination message exchanges. This paper gives conditions under which it is possible to produce such a checking sequence, using multiple distinguishing sequences, and an algorithm that achieves this