Sampled-data tracking under model predictive control and multi-rate planning

Elobaid, Mohamed; Mattioni, Mattia; Monaco, Salvatore; Normand‐Cyrot, D.

doi:10.1016/j.ifacol.2020.12.2043

Cited by 4 publications

(9 citation statements)

References 11 publications

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“…Theorem 3.1: The sampled-data model (11) of the unicycle kinematics (1) admits the time-varying pH form…”

Section: The Unicycle Model Under Samplingmentioning

confidence: 99%

“…Proof: Exploiting the representation (11), the proof consists in showing that ( 11) is equivalent to a discrete conservative pH dynamics (9) detailed as…”

Section: The Unicycle Model Under Samplingmentioning

confidence: 99%

“…Finite-time convergence in one step comes with a generally significant control effort that makes the implementation difficult in practice. Some of those issues have been partially solved in [11] embedding a Model Predictive Control (MPC) scheme. Other solutions involving sampled-data control basically rely upon emulation of the continuous-time (time-varying) control laws; i.e., through a direct implementation of the continuous-time control via sampled and hold devices without any further design [12], [13].…”

Section: Introductionmentioning

confidence: 99%

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Sampled-Data Steering of Unicycles via PBC

Mattioni

Moreschini

Monaco

et al. 2023

IEEE Control Syst. Lett.

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“…Theorem 3.1: The sampled-data model (11) of the unicycle kinematics (1) admits the time-varying pH form…”

Section: The Unicycle Model Under Samplingmentioning

confidence: 99%

“…Proof: Exploiting the representation (11), the proof consists in showing that ( 11) is equivalent to a discrete conservative pH dynamics (9) detailed as…”

Section: The Unicycle Model Under Samplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sampled-Data Steering of Unicycles via PBC

Mattioni

Moreschini

Monaco

et al. 2023

IEEE Control Syst. Lett.

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“…This is due to the fact that the references p𝑖 (•) provide bounded and admissible trajectories for the dynamics by construction of the multi-rate planner (19). This is specially true for 𝑅 small enough, when neglecting (22c) [41]. In this sense, the admissible references p𝑖 (𝑘) are specifically designed to ensure better performances while simplifying the optimization problem.…”

Section: B the Inner-loop Mpc Controllermentioning

confidence: 99%

“…Remark V. 2 The penalizing weighing matrices are fixed throughout the simulation scenarios as 𝑄 = 𝑑𝑖𝑎𝑔{10, 10, 10, 1, 1, 1}, 𝑅 = 0.1𝐼 3 . The small penalty on the control is chosen so that mimicking the cheap control setting one obtains, in nominal conditions, an almost dynamic inversion-like behaviour [41]. These values maybe widely different from, for example, the ones reported in [21].…”

Section: Remark V1mentioning

confidence: 99%

Station-keeping of $L_2$ halo orbits under sampled-data model predictive control

Elobaid¹,

Mattioni²,

Monaco³

et al. 2022

Preprint

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the digital nature of both actuation and sensing and possible limits on control, unavoidable in practice. In particular, we consider the case in which measures are available only at sporadic time instants whereas the control is piecewise constant over the sampling period (e.g. [25]). The approach we propose is based on the design of multi-rate (MR) strategies at the planning level providing a suitable reference governor for a model-predictive control (MPC) control scheme. The resulting control system enables to overcome the limits of small prediction horizons underlined in [21], when the controller is designed under usual MPC. As a matter of fact, such limits would bring to unfeasible controllers for small prediction horizons when the design makes use of a the sampled-data model, due to the cancellation of the possibly unstable zero-dynamics under sampling [26]. Also, the use of large prediction horizons, typically used as a stratagem in practice, might introduce large computational delays.This work is contextualized in this framework by proposing a new sampled-data MPC control scheme where the problem is simplified. This is achieved by generating a suitable reference trajectory based on a multi-rate planner which guarantees stability of the closed loop and feasibility of the optimization problem solved, at each step, by the MPC assuming cheap control. In particular, such a planner is designed starting from the nonlinear regulation-based controller proposed in [23] which yields, by construction, admissible and bounded trajectories which can be then fed to the MPC as reference to track. In this context, the contribution of this paper stands in the proposition of a new control scheme which employs at the low level an inherently robust nonlinear MPC fed by a references generated by a multi-rate sampled-data model of a control system designed making use of nonlinear regulation.The choice of the proposed control scheme is motivated by the observation that MPC and nonlinear regulation can be employed together to mitigate each the deficiencies of the other: nonlinear regulation appears to be the natural context for setting the problem since the references and perturbations are periodic although it lacks in robustness to unmodelled disturbances; MPC is becoming a standard tool for handling tracking applications, it is inherently robust to bounded perturbations [27] despite it requiring reference signals pre-processing to guarantee convergence and recursive feasibility.

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