skip to main content

Title: Self-triggered MPC with Performance Guarantee for Tracking Piecewise Constant Reference Signals
This paper considers a self-triggered MPC controller design strategy for tracking piecewise constant reference signals. The proposed triggering scheme is based on the relaxed dynamic programming inequality and the idea of reference governor; such a scheme computes both the updated control action and the next triggering time. The resulting self-triggered tracking MPC control law preserves stability and constraint satisfaction and also satisfies certain a priori chosen performance requirements without the need to impose stabilizing terminal conditions. An illustrative example shows the effectiveness of this self-triggered tracking MPC implementation.
; ;
Award ID(s):
Publication Date:
Journal Name:
Proceedings of European Control Conference, Doelen ICC Rotterdam, Netherlands, July 29-July 2, 2021
Page Range or eLocation-ID:
620 to 625
Sponsoring Org:
National Science Foundation
More Like this
  1. In this paper, we introduce a distributed secondary voltage and frequency control scheme for an islanded ac microgrid under event-triggered communication. An integral type event-triggered mechanism is proposed by which each distributed generator (DG) periodically checks its triggering condition and determines whether to update its control inputs and broadcast its states to neighboring DGs. In contrast to existing event-triggered strategies on secondary control of microgrids, the proposed event-triggered mechanism is able to handle the consensus problem in case of asynchronous communication. Under the proposed sampled-data based event-triggered mechanism, DGs do not need to be synchronized to a common clock and each individual DG checks its triggering condition periodically, relying on its own clock. Furthermore, the proposed method efficiently reduces communication rate. We provide sufficient conditions under which microgrid's frequency and a critical bus voltage asymptotically converge to the nominal frequency and voltage, respectively. Finally, effectiveness of our proposed method is verified by testing different scenarios on an islanded ac microgrid benchmark in the MATLAB/Simulink environment as well as a hardware-in-the-loop (HIL) platform, where the physical system is modeled in the Opal-RT and the cyber system is realized in Raspberry Pis.

    The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point processes continue to provide an important tool for analysing seismicity, given the epistemic uncertainty associated with physical models. In particular, the epidemic-type aftershock sequence (ETAS) model acts as a reference model for studying seismicity catalogues. The traditional ETAS model uses simple parametric definitions for the background rate of triggering-independent seismicity. This reduces the effectiveness of the basic ETAS model in modelling the temporally complex seismicity patterns seen in seismic swarms that are dominated by aseismic tectonic processes such as fluid injection rather than aftershock triggering. In order to robustly capture time-varying seismicity rates, we introduce a deep Gaussian process (GP) formulation for the background rate as an extension to ETAS. GPs are a robust non-parametric model for function spaces with covariance structure. By conditioning the length-scale structure of a GP with another GP, we have a deep-GP: a probabilistic, hierarchical model that automatically tunes its structure to match data constraints. We show how the deep-GP-ETAS model can be efficiently sampled by making use of a Metropolis-within-Gibbs scheme, taking advantage of the branching processmore »formulation of ETAS and a stochastic partial differential equation (SPDE) approximation for Matérn GPs. We illustrate our method using synthetic examples, and show that the deep-GP-ETAS model successfully captures multiscale temporal behaviour in the background forcing rate of seismicity. We then apply the results to two real-data catalogues: the Ridgecrest, CA 2019 July 5 Mw 7.1 event catalogue, showing that deep-GP-ETAS can successfully characterize a classical aftershock sequence; and the 2016–2019 Cahuilla, CA earthquake swarm, which shows two distinct phases of aseismic forcing concordant with a fluid injection-driven initial sequence, arrest of the fluid along a physical barrier and release following the largest Mw 4.4 event of the sequence.

    « less
  3. The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism.
  4. This paper is focused on the output tracking control problem of a wave equation with both matched and unmatched boundary uncertainties. An adaptive boundary feedback control scheme is proposed by utilizing radial basis function neural networks (RBF NNs) to deal with the effect of system uncertainties. Specifically, two RBF NN models are first developed to approximate the matched and unmatched system uncertain dynamics respectively. Based on this, an adaptive NN control scheme is derived, which consists of: (i) an adaptive boundary feedback controller embedded by the NN model approximating the matched uncertainty, for rendering stable and accurate tracking control; and (ii) a reference model embedded by the NN model approximating the unmatched uncertainty, for generating a prescribed reference trajectory. Rigorous analysis is performed using the Lyapunov theory and the C0-semigroup theory to prove that our proposed control scheme can guarantee closed-loop stability and wellposedness. Simulation study has been conducted to demonstrate effectiveness of the proposed approach.
  5. This paper presents four data-driven system models for a magnetically controlled swimmer. The models were derived directly from experimental data, and the accuracy of the models was experimentally demonstrated. Our previous study successfully implemented two non-model-based control algorithms for 3D path-following using PID and model reference adaptive controller (MRAC). This paper focuses on system identification using only experimental data and a model-based control strategy. Four system models were derived: (1) a physical estimation model, (2, 3) Sparse Identification of Nonlinear Dynamics (SINDY), linear system and nonlinear system, and (4) multilayer perceptron (MLP). All four system models were implemented as an estimator of a multi-step Kalman filter. The maximum required sensing interval was increased from 180 ms to 420 ms and the respective tracking error decreased from 9 mm to 4.6 mm. Finally, a Model Predictive Controller (MPC) implementing the linear SINDY model was tested for 3D path-following and shown to be computationally efficient and offers performances comparable to other control methods.