Papers by Maria Elena Valcher
This discussion paper introduces a modeling technique, based on Boolean Control Networks, for ass... more This discussion paper introduces a modeling technique, based on Boolean Control Networks, for assessing useful properties of Context Aware systems. Indeed, Context Aware systems are becoming useful components in autonomic and monitoring applications and the assessment of their properties is an important step towards reliable implementation, especially in safety-critical applications.
A Tutorial on Positive Systems and Large Scale Control
2018 IEEE Conference on Decision and Control (CDC), 2018
In this tutorial paper we first present some foundational results regarding the theory of positiv... more In this tutorial paper we first present some foundational results regarding the theory of positive systems. In particular, we present fundamental results regarding stability, positive realization and positive stabilization by means of state-feedback. Special attention is also paid to the system performance in terms of disturbance attenuation. Under the asymptotic stability assumption, such performance can be measured in terms of $L_{p}$-gain of the positive system. In the second part of the paper we propose some recent results about control synthesis by linear programming and semidefinite programming, under the positivity requirement on the resulting controlled system. These results highlight the value of positivity when dealing with large scale systems. Indeed, stability properties for these systems can be verified by resorting to linear (copositive) or diagonal Lyapunov functions that scale linearly with the system dimension, and such linear functions can be used also to design stabilizing feedback control laws. In addition, stabilization problems with disturbance attenuation performance can be easily solved by imposing special structures on the state feedback matrices. This is extremely valuable when dealing with large scale systems for which state feedback matrices are typically sparse, and their structure is a priori imposed by practical requirements.
On the reachable set of the controlled gene expression system
53rd IEEE Conference on Decision and Control, 2014
ABSTRACT We investigate the reachable set of the standard stochastic model of Controlled Gene Exp... more ABSTRACT We investigate the reachable set of the standard stochastic model of Controlled Gene Expression. Specifically, we explore what values of the protein mean and variance are achievable using the available external input, that is, the mRNA production rate. We proceed by constructing invariant sets in the two-dimensional projections of the state space. We then use these sets to construct an outer approximation of the reachable region for the protein mean and variance. This can be computed solving a one-dimensional optimization problem and is tight enough to show that it is not possible, using such control input, to arbitrarily reduce the variance while maintaining a high mean. The lower bound on the variance derived with our approach turns out to be much higher than the one available in the literature for the case when both the mRNA production and degradation rate are controlled.
In a recent pair of contributions [2, 3], starting from a set of results about the relationship b... more In a recent pair of contributions [2, 3], starting from a set of results about the relationship between the direct sum decomposition of (linear, time-invariant, differential) behaviors and the solvability of certain two-sided Bézout equations, it was shown that every autonomous behavior can be expressed as a direct sum of irreducible components. In this contribution, we further explore this issue, by naturally introducing an irreducibility notion for controllable behaviors and by proving that every controllable behavior can be naturally expressed as the direct sum of a finite number of irreducible controllable behaviors. As a result, we can extend the whole direct sum (irreducible) decomposition analysis to the general case of (linear, time-invariant, differential) behaviors.
2013 European Control Conference (ECC), 2013
In this paper the dead-beat control problem, by partial interconnection, of two-dimensional discr... more In this paper the dead-beat control problem, by partial interconnection, of two-dimensional discrete behaviors, defined on the grid Z+ × Z and having the time as (first) independent variable, is investigated. It turns out that the possibility of driving to zero (in a finite number of "steps") the "relevant variables" by means of a partial interconnection controller, making use of the "measurable variables", is equivalent to the reconstructibility of the relevant variables, that are not accessible for control. On the other hand, if we search for "admissible" dead-beat controllers, the only ones that provide meaningful results in practice, an additional condition has to be introduced: the zero-time-controllability of the relevant variables.
2003 European Control Conference (ECC), 2003
This paper aims at providing some new insights into the linear quadratic optimization problem in ... more This paper aims at providing some new insights into the linear quadratic optimization problem in the behavioral approach. A new problem statement is given and some comparisons with the standard LQ problem in the state space approach are provided. The problem solution is analyzed in detailed terms so that all optimal trajectories can be easily computed from the initial data. Noteworthy, the set of optimal solutions proves to be a behavior, too. The asymptotic stability of the optimal behavior as well as the finiteness of the cost function are finally discussed.
On the state-feedback stabilisation of compartmental systems
2017 IEEE 56th Annual Conference on Decision and Control (CDC), 2017
In this paper we address the state-feedback stabilisation of multi-input compartmental systems, b... more In this paper we address the state-feedback stabilisation of multi-input compartmental systems, by this meaning the design of a state-feedback matrix that preserves the compartmental property of the resulting feedback system, meanwhile achieving stability. We provide necessary and sufficient conditions for the stabilisability of compartmental systems whose state matrix is irreducible, and a sufficient condition for the problem solution when A is reducible. The results significantly improve upon existing Linear Programming conditions obtained for the general class of multi-input positive systems.
On the consensus problem with positivity constraints
2016 American Control Conference (ACC), 2016
In this paper we investigate the consensus problem for multi-agent systems, under the assumptions... more In this paper we investigate the consensus problem for multi-agent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system. Conditions that are either necessary or sufficient for the solvability of the positive consensus problem are provided. Under certain additional assumptions on the agents dynamics, equivalent conditions are derived. Several examples illustrate the paper results.
IFAC Proceedings Volumes, 2002
In this paper we afford the fault detection and isolation problem in the context of linear discre... more In this paper we afford the fault detection and isolation problem in the context of linear discrete-time state-space models whose state equation is affected both by faults and by disturbances. Model as well as measurement errors, described as zero-mean white gaussian noises, are also assumed to additively act both on the state and on the output equations. Upon introducing several deterministic and stochastic goals, which constitute the mathematical formalization of very natural and practical requirements, necessary and sufficient conditions for the existence of an observer-based fault detector and isolator, which achieves the aforementioned goals, are finally derived. Keywords: Observer-based fault detector and isolator, residual, estimation error, Moore-Penrose inverse, error covariance matrix. Keller, 1999). Indeed, we consider as causes affecting the system dynamics (besides the known control inputs) both the deterministic disturbances and the model and measurement errors, described as zero-mean white gaussian noises. Within this setting, we derive necessary and sufficient conditions for the existence of both a good state estimation filter and of a residual generator that ensures an efficient fault isolation. A comparison with other techniques or results appeared on this topic cannot be performed here, due to the page constraints. The interest reader is referred to (Parlangeli and Valcher, 2001). 2. STATEMENT OF THE PROBLEM Consider the discrete time linear system x(t + 1) = Ax(t) + Bu(t) + B d d(t) + F n(t) + w(t) y(t) = Cx(t) + v(t), t≥ 0,
E.Fornasini, M.E.Valcher, "Optimal control of Boolean control networks", IEEE Transactions on Automatic Control, vol.59, n.5, pp.1258-70, 2014
Ieee Transactions on Automatic Control, 2014
IEEE Transactions on Automatic Control, 2016
In this paper we introduce continuous-time linear compartmental switched systems and investigate ... more In this paper we introduce continuous-time linear compartmental switched systems and investigate their stability and stabilizability properties. By their nature, these systems are always stable. Necessary and sufficient conditions for asymptotic stability for arbitrary switching functions, and sufficient conditions for asymptotic stability under certain dwell-time conditions on the switching functions are proposed. Finally, stabilizability is thoroughly investigated and proved to be equivalent to the existence of a Hurwitz convex combination of the subsystem matrices, a condition that for positive switched systems is only sufficient for stabilizability.
E.Fornasini, M.E.Valcher, "2D systems: characteristic polynomial structure and state space geometry", Proc ECC93, pp. 1470-75, Groningen, 1993
M.E.Valcher, E.Fornasini"Polynomial inverses or 2D transfer matrices and finite memory realization via inverse systems", Multidim. Sys. Signal Proc., vol 4, pp.269-84, 1993
Multidimensional Systems and Signal Processing
E.Fornasini, M.E.Valcher, "Matrix pairs in 2D systems: an approach based on trace series and Hankel matrices", SIAM Journal on Contr. Optim., vol.33, pp. 1127-50, 1995
SIAM Journal on Control and Optimization
E.Fornasini, M.E.Valcher, "Algebraic aspects of 2D convolutional codes", IEEE Trans. Info. Theory, IT-40, pp.1068-82, 1994
IEEE Transactions on Information Theory
ABSTRACT
E.Fornasini, G.Marchesini and M.E.Valcher, "On the structure of finite memory and separable 2D systems", Automatica, vol.30, pp.347-50, 1994
Automatica
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E.Fornasini, M.E.Valcher, "Stability properties and periodic evolutions of bilinear systems in input/output form", IEEE Transactions on Automatic Control. vol. 44, pp. 1197-1202, 1999
IEEE Transactions on Automatic Control
E.Fornasini, M.E.Valcher, "Primitivity of positive matrix pairs: algebraic characterization, graph theoretic description and 2D systems interpretation", SIAM Journal on Matrix Analysis and Applications. Vol. 19, pp. 71-88, 1998
SIAM Journal on Matrix Analysis and Applications
E.Fornasini, M.E.Valcher, "nD polynomial matrices with applications to multidimensional systems analysis", Multidimensional Systems and Signal Processing, vol.8, pp.387-408, 1997
Multidimensional Systems and Signal Processing
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E.Fornasini, M.E.Valcher, "Combinatorial properties of nonnegative matrix pairs and behavior of 2D systems", Proc. IFAC Conf. System Structure and Control, Nantes, pp.482-87, 1995
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Papers by Maria Elena Valcher