| 1. |
- Abara, Precious Ugo, et al.
(författare)
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Spectral Conditions for Stability and Stabilization of Positive Equilibria for a Class of Nonlinear Cooperative Systems
- 2018
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 63:2, s. 402-417
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Tidskriftsartikel (refereegranskat)abstract
- Nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication, biological, economical, and neural network applications. For this class of positive systems, we provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system. If control inputs are available, then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant.
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| 2. |
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| 3. |
- Adib Yaghmaie, Farnaz, et al.
(författare)
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Linear Quadratic Control Using Model-Free Reinforcement Learning
- 2023
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 68:2, s. 737-752
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider linear quadratic (LQ) control problem with process and measurement noises. We analyze the LQ problem in terms of the average cost and the structure of the value function. We assume that the dynamics of the linear system is unknown and only noisy measurements of the state variable are available. Using noisy measurements of the state variable, we propose two model-free iterative algorithms to solve the LQ problem. The proposed algorithms are variants of policy iteration routine where the policy is greedy with respect to the average of all previous iterations. We rigorously analyze the properties of the proposed algorithms, including stability of the generated controllers and convergence. We analyze the effect of measurement noise on the performance of the proposed algorithms, the classical off-policy, and the classical Q-learning routines. We also investigate a model-building approach, inspired by adaptive control, where a model of the dynamical system is estimated and the optimal control problem is solved assuming that the estimated model is the true model. We use a benchmark to evaluate and compare our proposed algorithms with the classical off-policy, the classical Q-learning, and the policy gradient. We show that our model-building approach performs nearly identical to the analytical solution and our proposed policy iteration based algorithms outperform the classical off-policy and the classical Q-learning algorithms on this benchmark but do not outperform the model-building approach.
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| 4. |
- Akcay, H., et al.
(författare)
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On the choice of norms in system identification
- 1996
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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| 5. |
- Alanwar, Amr, et al.
(författare)
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Data-Driven Reachability Analysis From Noisy Data
- 2023
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 68:5, s. 3054-3069
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.
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| 6. |
- Almér, Stefan, et al.
(författare)
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Dynamic Phasor Analysis of Periodic Systems
- 2009
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 54:8, s. 2007-2012
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers stability analysis of linear time-periodic (LTP) systems based on the dynamic phasor model (DPM). The DPM exploits the periodicity of the system by expanding the system state in a Fourier series over a moving time window. This results in an L-2-equivalent representation in terms of an infinite-dimensional LTI system which describes the evolution of time varying Fourier coefficients. To prove stability, we consider quadratic time-periodic Lyapunov candidates. Using the DPM, the corresponding time-periodic Lyapunov inequality can be stated as a finite dimensional inequality and the Lyapunov function can be found by solving a linear matrix inequality.
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| 7. |
- Almér, Stefan, et al.
(författare)
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Stability analysis of a class of PWM systems
- 2007
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 52:6, s. 1072-1078
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Tidskriftsartikel (refereegranskat)abstract
- This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-de- converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).
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| 8. |
- Altafini, Claudio, et al.
(författare)
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Predictable Dynamics of Opinion Forming for Networks With Antagonistic Interactions
- 2015
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 60:2, s. 342-357
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Tidskriftsartikel (refereegranskat)abstract
- For communities of agents which are not necessarily cooperating, distributed processes of opinion forming are naturally represented by signed graphs, with positive edges representing friendly and cooperative interactions and negative edges the corresponding antagonistic counterpart. Unlike for nonnegative graphs, the outcome of a dynamical system evolving on a signed graph is not obvious and it is in general difficult to characterize, even when the dynamics are linear. In this paper, we identify a significant class of signed graphs for which the linear dynamics are however predictable and show many analogies with positive dynamical systems. These cases correspond to adjacency matrices that are eventually positive, for which the Perron-Frobenius property still holds and implies the existence of an invariant cone contained inside the positive orthant. As examples of applications, we determine cases in which it is possible to anticipate or impose unanimity of opinion in decision/voting processes even in presence of stubborn agents, and show how it is possible to extend the PageRank algorithm to include negative links.
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| 9. |
- Alur, Rajeev, et al.
(författare)
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Compositional Modeling and Analysis of Multi-Hop Control Networks
- 2011
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 56:10, s. 2345-2357
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Tidskriftsartikel (refereegranskat)abstract
- We propose a mathematical framework for modeling and analyzing multi-hop control networks designed for systems consisting of multiple control loops closed over a multi-hop (wireless) communication network. We separate control, topology, routing, and scheduling and propose formal syntax and semantics for the dynamics of the composed system, providing an explicit translation of multi-hop control networks to switched systems. We propose formal models for analyzing robustness of multi-hop control networks, where data is exchanged through a multi-hop communication network subject to disruptions. When communication disruptions are long, compared to the speed of the control system, we propose to model them as permanent link failures. We show that the complexity of analyzing such failures is NP-hard, and discuss a way to overcome this limitation for practical cases using compositional analysis. For typical packet transmission errors, we propose a transient error model where links fail for one time slot independently of the past and of other links. We provide sufficient conditions for almost sure stability in presence of transient link failures, and give efficient decision procedures. We deal with errors that have random time span and show that, under some conditions, the permanent failure model can be used as a reliable abstraction. Our approach is compositional, namely it addresses the problem of designing scalable scheduling and routing policies for multiple control loops closed on the same multi-hop control network. We describe how the translation of multi-hop control networks to switched systems can be automated, and use it to solve control and networking co-design challenges in some representative examples, and to propose a scheduling solution in a mineral floatation control problem that can be implemented on a time triggered communication protocols for wireless networks.
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| 10. |
- Andersen, Martin S., et al.
(författare)
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Robust Stability Analysis of Sparsely Interconnected Uncertain Systems
- 2014
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE. - 0018-9286 .- 1558-2523. ; 59:8, s. 2151-2156
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.
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