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| 2. |
- Demirel, Burak, et al.
(författare)
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Deterministic and stochastic approaches to supervisory control design for networked systems with time-varying communication delays
- 2013
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 10:1, s. 94-110
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Tidskriftsartikel (refereegranskat)abstract
- This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop stability conditions that can be verified by semi-definite programming, and show that the associated state feedback synthesis problem also can be solved using convex optimization tools. Extensions of the analysis and synthesis procedures to the case when the evolution of the delay mode is described by a Markov chain are also developed. Simulations on small and large-scale networked control systems are used to illustrate the effectiveness of our approach.
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| 3. |
- Konečný, Michal, et al.
(författare)
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Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point
- 2016
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Ingår i: Nonlinear Analysis. - London : Elsevier. - 1751-570X .- 1878-7460. ; 20, s. 1-20
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Tidskriftsartikel (refereegranskat)abstract
- Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution. ©2015 The Authors. Published by Elsevier Ltd.
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| 4. |
- Lindemann, Lars, et al.
(författare)
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Funnel control for fully actuated systems under a fragment of signal temporal logic specifications
- 2021
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Ingår i: Nonlinear Analysis. - : Elsevier Ltd. - 1751-570X .- 1878-7460. ; 39
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Tidskriftsartikel (refereegranskat)abstract
- Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated robust semantics. In particular, this paper provides computationally-efficient funnel-based feedback control laws for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design so that some degree of robustness is obtained. We first leverage the transient properties of a funnel-based feedback control strategy to maximize the robust semantics of some atomic temporal logic formulas. We then guarantee the satisfaction for specifications consisting of conjunctions of such atomic temporal logic formulas with overlapping time intervals by a suitable switched control system. The result is a framework that satisfies temporal logic specifications with a user-defined robustness when the specification is satisfiable. When the specification is not satisfiable, a least violating solution can be found. The theoretical findings are demonstrated in simulations of the nonlinear Lotka–Volterra equations for predator–prey models.
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| 5. |
- Matsume, Hiroki, et al.
(författare)
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Resilient self/event-triggered consensus based on ternary control
- 2021
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 42
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers the problem of multi-agent consensus in the presence of adversarial agents. Such adversaries may try to introduce undesired influence on the coordination of the regular agents and to even prevent them from reaching consensus. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the use of computation and communication resources of the agents. In particular, by employing self-and event-triggered communication, the frequencies of state updates as well as data transmissions are kept low. Moreover, the control inputs of the agents take the form of ternary signals, allowing them to further reduce the amount of information at each transmission. We will observe that in hostile environments with adversaries, the self-triggered approach can bring certain advantages over the event-triggered counterpart. Moreover, a novel switching scheme is introduced to mix the two protocols to further enhance the performance of the agents.
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| 6. |
- Melin, Jan, et al.
(författare)
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Two types of limit cycles of a resonant converter modelled by a three-dimensional system
- 2008
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Ingår i: Nonlinear Analysis. - : Elsevier. - 1751-570X .- 1878-7460. ; 2:4, s. 1275-1286
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the long-run dynamics of a controlled resonant converter, modelled as a piecewise system, is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the longrun dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.
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| 7. |
- Meyer, Pierre-Jean, et al.
(författare)
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Compositional abstraction refinement for control synthesis
- 2018
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Ingår i: Nonlinear Analysis. - : Elsevier. - 1751-570X .- 1878-7460. ; 27, s. 437-451
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a compositional approach to specification-guided abstraction refinement for control synthesis of a nonlinear system associated with a method to over-approximate its reachable sets. Given an initial coarse partition of the state space, the control specification is given as a sequence of the cells of this partition to visit at each sampling time. The dynamics are decomposed into subsystems where some states and inputs are not observed, some states are observed but not controlled and where assume-guarantee obligations are used on the uncontrolled states of each subsystem. A finite abstraction is created for each subsystem through a refinement procedure starting from a coarse partition of the state space, then proceeding backwards on the specification sequence to iteratively split the elements of the partition whose coarseness prevents the satisfaction of the specification. Each refined abstraction is associated with a controller and it is proved that combining these local controllers can enforce the specification on the original system. The efficiency of the proposed approach compared to other abstraction methods is illustrated in a numerical example.
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| 8. |
- Sharifi, Maryam, et al.
(författare)
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Compositional construction of abstractions for infinite networks of discrete-time switched systems
- 2022
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 44
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop a compositional scheme for the construction of continuous abstractions for networks of infinitely many discrete-time switched systems. In particular, the constructed abstractions are themselves also continuous-space systems with potentially lower dimensions, which can be used as replacements of the original (also known as concrete) systems in the controller design process. Having designed a controller for the abstract system, it is refined to a more detailed one for the concrete system. We use the notion of so-called simulation functions to quantify the mismatch between the original system and its approximation. Each subsystem in the concrete network and its corresponding one in the abstract network are related through a notion of local simulation functions. We show that if the local simulation functions satisfy a spectral small-gain condition, then the aggregation of the individual simulation functions provides an overall simulation function quantifying the error between the overall abstract network and the concrete one. In addition, we show that our methodology results in a scale-free compositional approach for any finite-but-arbitrarily large networks obtained from truncation of an infinite network. We provide a systematic approach to construct local abstractions and simulation functions for networks of linear switched systems. In this case, the conditions are expressed in terms of linear matrix inequalities that can be efficiently computed. We illustrate the effectiveness of our approach through an application to AC islanded microgrids.
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| 9. |
- Tiberi, U., et al.
(författare)
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A simple self-triggered sampler for perturbed nonlinear systems
- 2013
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 10:1, s. 126-140
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Tidskriftsartikel (refereegranskat)abstract
- Self-triggered control is a recent design paradigm for resource-constrained networked control systems. By allocating aperiodic sampling instances for a digital control loop, a self-triggered controller is able to utilize network resources more efficiently than conventional sampled-data systems. In this paper we propose a self-triggered sampler for perturbed nonlinear systems ensuring uniformly ultimately boundedness of trajectories. Robustness and time delays are considered. To reduce conservativeness, a disturbance observer for the self-triggered sampler is proposed. The effectiveness of the proposed method is shown by simulation.
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| 10. |
- Yamalova, Diana, et al.
(författare)
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Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
- 2021
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 41
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Tidskriftsartikel (refereegranskat)abstract
- A novel hybrid observer that estimates the states of an oscillating system composed of a linear chain structure and an intrinsic pulse-modulated feedback is considered. This particular type of plant model appears in e.g. endocrine systems with pulsatile hormone secretion. The observer reconstructs the continuous states of the model as well as the firing times and weights of the feedback impulses. Since the pulse-modulated feedback is intrinsic, no measurements of the discrete part of the plant are available to the observer. For a periodical plant solution, to reconstruct the hybrid state, the impulses in the observer have to be synchronized with those in the plant. The observer is equipped with two feedback loops driven by the output estimation error. One of these is utilized to correct the estimates of the continuous states. In contrast with previous observer designs, the estimate of the next impulse firing time is implemented by means of a finite-memory convolution operator. A pointwise mapping capturing the propagation of the continuous plant and observer states through the discrete cumulative sequence of the feedback firing instants is derived. Local stability properties of the synchronous mode are related to the spectral radius of the Jacobian of the pointwise mapping. The observer design is based on assigning a guaranteed convergence rate to the local dynamics of a synchronous mode through the output error feedback gains to the continuous and discrete part of the observer. The observation of a stable m-cycle in the plant is treated to establish a general scenario, whereas the special case of 1-cycle is worked out in detail as the most common one. A numerical example illustrates the observer performance in the case of periodic modes of low multiplicity in an impulsive model of testosterone regulation in the male. Despite the local nature of the design approach, convergence to a synchronous mode is observed for a wide range of initial conditions for the discrete state estimate in the observer.
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