| 1. |
- Blanchini, Franco, et al.
(författare)
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A bounded complementary sensitivity function ensures topology-independent stability of homogeneous dynamical networks
- 2017
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Ingår i: IEEE Transactions on Automatic Control. - 1558-2523. ; :99
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Tidskriftsartikel (refereegranskat)abstract
- This paper investigates the topology-independent stability of homogeneous dynamical networks, composed of interconnected equal systems. Precisely, dynamical systems with identical nominal transfer function F(s) are associated with the nodes of a directed graph whose arcs account for their dynamic interactions, described by a common nominal transfer function G(s). It is shown that topology-independent stability is guaranteed for all possible interconnections with interaction degree (defined as the maximum number of arcs leaving a node) equal at most to N if the infinity-norm of the complementary sensitivity function NF(s)G(s)/[1+NF(s)G(s)] is less than 1. This bound is non-conservative. When nodes and arcs transferences are affected by uncertainties with norm bound K>0, topology-independent stability is robustly ensured if the infinity-norm is less than 1/(1+2NK). For symmetric systems, stability is guaranteed for all topologies with interaction degree at most N if the Nyquist plot of NF(s)G(s) does not intersect the real axis to the left of -1/2. The proposed results are applied to fluid networks and platoon formation.
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| 2. |
- Blanchini, Franco, et al.
(författare)
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A convex programming approach to the inverse kinematics problem for manipulators under constraints
- 2017
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Ingår i: European Journal of Control. - : Elsevier BV. - 0947-3580. ; 33, s. 11-23
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Tidskriftsartikel (refereegranskat)abstract
- We propose a novel approach to the problem of inverse kinematics for possibly redundant planar manipulators. We show that, by considering the joints as point masses in a fictitious gravity field, and by adding proper constraints to take into account the length of the links, the kinematic inversion may be cast as a convex programming problem. Convex constraints in the decision variables (in particular, linear constraints in the workspace) are easily managed with the proposed approach. We also show how to exploit the idea for avoiding obstacles while tracking a reference end-effector trajectory and discuss how to extend the results to some kinds of non-planar manipulators. Simulation results are reported, showing the effectiveness of the approach.
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| 3. |
- Blanchini, Franco, et al.
(författare)
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Active Fault Isolation: A Duality-Based Approach via Convex Programming
- 2017
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Ingår i: SIAM Journal on Control and Optimization. - 1095-7138. ; 55:3, s. 1619-1640
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents the mathematical conditions and the associated design methodology of an active fault diagnosis technique for continuous-time linear systems. Given a set of faults known a priori, the system is modeled by a finite family of linear time-invariant systems, accounting for one healthy and several faulty configurations. By assuming bounded disturbances and using a residual generator, an invariant set and its projection in the residual space (i.e., its limit set) are computed for each system configuration. Each limit set, related to a single system configuration, is parameterized with respect to the system input. Thanks to this design, active fault isolation can be guaranteed by the computation of a test input, either constant or periodic, such that the limit sets associated with different system configurations are separated, and the residual converges toward one limit set only. In order to alleviate the complexity of the explicit computation of the limit set, an implicit dual representation is adopted, leading to efficient procedures, based on quadratic programming, for computing the test input. The developed methodology offers a competent continuous-time solution to the optimization-based computation of the test input via Hahn--Banach duality. Simulation examples illustrate the application of the proposed active fault diagnosis methods and its efficiency in providing a solution, even in relatively large state-dimensional problems.
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| 4. |
- Blanchini, Franco, et al.
(författare)
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Aggregates of Monotonic Step Response systems : a structural classification
- 2018
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Ingår i: IEEE Transactions on Control of Network Systems. - 2325-5870. ; 5:2, s. 782-792
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Tidskriftsartikel (refereegranskat)abstract
- Complex dynamical networks can often be analysed as the interconnection of subsystems, to simplify the model and better understand the global behaviour. Some biological networks can be analysed as aggregates of monotone subsystems. Yet, monotonicity is a strong requirement and relies on the knowledge of an explicit state model. Systems with a Monotonic Step Response (MSR), which include input-output monotone systems, are a broader class and have interesting features. The property of having a monotonically increasing step response can be evinced from experimental data. We consider networks that can be decomposed as aggregates of MSR subsystems and we provide a structural (parameter-free) classification of oscillatory and multistationary behaviours. The classification is based on the exclusive or concurrent presence of negative and positive cycles in the system $aggregate graph$, whose nodes are the MSR subsystems. The result is analogous to our earlier classification for aggregates of monotone subsystems. Our classification is applied to models of biomolecular networks and helps build synthetic biomolecular circuits that, by design, are well suited to exhibit the desired dynamics.
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| 5. |
- Blanchini, Franco, et al.
(författare)
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Aggregates of Positive Impulse Response systems: a decomposition approach for complex networks
- 2018
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Ingår i: Proceedings of the 56th IEEE Conference on Decision and Control.
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Konferensbidrag (refereegranskat)abstract
- To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally ensured (for any choice of the PIR subsystems) if a Metzler matrix depending on the interaction weights is Hurwitz; this condition is non-conservative. We also show how to compute an influence matrix that represents the steady-state effects of the interactions among PIR subsystems.
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| 6. |
- Blanchini, Franco, et al.
(författare)
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Discrete-Time Trials for Tuning without a Model
- 2017
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 50:1, s. 1539-1544
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Tidskriftsartikel (refereegranskat)abstract
- Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, we consider the problem of tuning the output (i.e., driving the output to a desired value), by suitably choosing the input. To this aim, we assume to have at our disposal a discrete sequence of trials only, as it happens, for instance, when we iteratively run a software, with new input data at each iteration, in order to achieve the desired output value. In this paper we prove that, if the polytope is robustly non-singular (or has full row rank, in the general non-square case), then a suitable discrete-time tuning law drives the output to the desired point. The computation of the tuning law is based on a convex-optimisation problem to be solved on-line. An application example is proposed to show the effectiveness of the approach.
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| 7. |
- Blanchini, F., et al.
(författare)
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Model-Free Plant Tuning
- 2017
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286. ; 62:6, s. 2623-2634
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Tidskriftsartikel (refereegranskat)abstract
- Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly non-singular (or has full rank, in the non-square case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well known game-theoretic result, concerning the existence of a saddle point for a minmax zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained, resorting to a different Lyapunov-like function. The case in which proper input or output constraints must be enforced during the transient is considered as well. Some application examples are proposed to show the effectiveness of the approach.
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| 8. |
- Blanchini, Franco, et al.
(författare)
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Model-free tuning of plants with parasitic dynamics
- 2017
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Ingår i: Proceedings of the 56th IEEE Conference on Decision and Control.
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Konferensbidrag (refereegranskat)abstract
- We have recently considered the problem of tuning a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope of matrices: to drive the output to a given desired value, we have suggested an integral feedback scheme, whose convergence is ensured if the polytope of matrices is robustly full row rank. The suggested tuning scheme may fail in the presence of parasitic dynamics, which may destabilize the loop if the tuning action is too aggressive. Here we show that such tuning action can be applied to dynamic plants as well if it is sufficiently “slow”, a property that we can ensure by limiting the integral action. We provide robust bounds based on the exclusive knowledge of the largest time constant and of the matrix polytope to which the system Jacobian is known to belong. We also provide similar bounds in the presence of parasitic dynamics affecting the actuators.
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| 9. |
- Blanchini, Franco, et al.
(författare)
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Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular
- 2017
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098. ; 86, s. 183-191
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Tidskriftsartikel (refereegranskat)abstract
- For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate Lyapunov function.
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| 10. |
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