| 1. |
- Lindemann, Lars, et al.
(author)
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Funnel control for fully actuated systems under a fragment of signal temporal logic specifications
- 2021
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In: Nonlinear Analysis. - : Elsevier Ltd. - 1751-570X .- 1878-7460. ; 39
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Journal article (peer-reviewed)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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| 2. |
- Matsume, Hiroki, et al.
(author)
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Resilient self/event-triggered consensus based on ternary control
- 2021
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In: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 42
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Journal article (peer-reviewed)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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| 3. |
- Sharifi, Maryam, et al.
(author)
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Compositional construction of abstractions for infinite networks of discrete-time switched systems
- 2022
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In: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 44
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Journal article (peer-reviewed)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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| 4. |
- Yamalova, Diana, et al.
(author)
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Hybrid observer with finite-memory output error correction for linear systems under intrinsic impulsive feedback
- 2021
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In: Nonlinear Analysis. - : Elsevier BV. - 1751-570X .- 1878-7460. ; 41
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Journal article (peer-reviewed)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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| 5. |
- Bencherki, Fethi, et al.
(author)
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Realization of multi-input/multi-output switched linear systems from Markov parameters
- 2023
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In: Nonlinear Analysis: Hybrid Systems. - : Elsevier BV. - 1751-570X. ; 48
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Journal article (peer-reviewed)abstract
- This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the discrete states have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, stationary point set of a Hankel matrix with fixed dimensions built from the Markov parameters is examined. Splitting of this set into disjoint intervals and complements reveals linear time-invariant dynamics prevailing on these intervals. Clustering over a feature space permits recovery of the discrete states up to similarity transformations which is complete if a unimodality assumption holds and the discrete states satisfy a residence requirement. In the third stage, the switching sequence is estimated by three schemes. The first scheme is non-iterative in time. The second scheme is based on matching the estimated and the true Markov parameters of the SLS system over segments. The third scheme works also on the same principle, but it is a discrete optimization/hypothesis testing algorithm. The three schemes operate on different dwell time and model structure requirements, but the dwell time requirements are weaker than that needed to recover the discrete states. In the fourth stage, the discrete state estimates are brought to a common basis by a novel basis transformation which is necessary for predicting outputs to prescribed inputs. Robustness of the four-stage algorithm to amplitude bounded noise is studied and it is shown that small perturbations may only produce small deviations in the estimates vanishing as noise amplitude diminishes. Time complexities of the stages are also studied. A numerical example illustrates the derived results.
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