Impulsive zone model predictive control for rendezvous hovering phases

Louembet, Christophe; González, Alejandro H.; Gilz, Paulo Ricardo Arantes

doi:10.1109/cdc40024.2019.9030077

Cited by 3 publications

(2 citation statements)

References 28 publications

(40 reference statements)

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“…This situation is sufficient in many cases, such as the biomedical applications mentioned in Section 1 where the goal is just to maintain the system inside a safe zone called therapeutic window (see also the examples treated in Section 7). However a more predictable behavior could be mandatory in some other applications, such as [19], where a limit orbit is expected (see Figure 1, right). The following subsection is intended to cover those potentially interesting application cases where a more simple and periodic performance is desired.…”

Section: Stability Sufficient Conditionsmentioning

confidence: 99%

On stability of nonzero set-point for nonlinear impulsive control systems

D’Jorge

Anderson

Ferramosca

et al. 2022

Systems & Control Letters

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Section: Stability Sufficient Conditionsmentioning

confidence: 99%

On stability of nonzero set-point for nonlinear impulsive control systems

D’Jorge

Anderson

Ferramosca

et al. 2022

Systems & Control Letters

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“…Particularly, when the impulsive nature of the control actions (inputs) is the one that produces the discontinuity, we have an impulsively controlled system. Many control problems fall in the scope of impulsively controlled systems, as it is the case of drug scheduling in several disease treatments (by taking pills [40,41,37,34,27] or by applying injections [1,20]), or that of aircraft guidance [4,5,32]. The objective in this kind of control problem is to maintain the closed-loop system in a target region (defined by the problem itself) where the operation is safe.…”

Section: Introductionmentioning

confidence: 99%

Characterization and computation of control invariant sets within target regions for linear impulsive control systems

Sanchez,

Louembet,

Actis

et al. 2021

Preprint

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Linear impulsively controlled systems are suitable to describe a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they remain uncontrolled for certain periods of time. As a consequence, punctual equilibria characterizations outside the origin are no longer useful, and the whole concept of equilibrium and its natural extension, the controlled invariant sets, needs to be redefined. Also, an exact characterization of the admissible states, i.e., states such that their uncontrolled evolution between impulse times remain within a predefined set, is required. An approach to such tasks -based on the Markov-Lukasz theoremis presented, providing a tractable and non-conservative characterization, emerging from polynomial positivity that has application to systems with rational eigenvalues. This is in turn the basis for obtaining a tractable approximation to the maximal admissible invariant sets. In this work, it is also demonstrated that, in order for the problem to have a solution, an invariant set (and moreover, an equilibrium set) must be contained within the target zone. To assess the proposal, the so-obtained impulsive invariant set is explicitly used in the formulation of a set-based model predictive controller, with application to zone tracking. In this context, specific MPC theory needs to be considered, as the target is not necessarily stable in the sense of Lyapunov. A zone MPC formulation is proposed, which is able to i) track an invariant set such that the uncontrolled propagation fulfills the zone constraint at all times and ii) converge asymptotically to the set of periodic orbits completely contained within the target zone.

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