This paper deals with the output regulation problem of a linear time-invariant system in the presence of sporadically available measurement streams. A regulator with a continuous intersample injection term is proposed, where the intersample injection is provided by a linear dynamical system and the state of which is reset with the arrival of every new measurement updates. The resulting system is augmented with a timer triggering an instantaneous update of the new measurement and the overall system is then analyzed in a hybrid system framework. With the Lyapunov based stability analysis, we offer sufficient conditions to ensure the objectives of the output regulation problem are achieved under intermittency of the measurement streams. Then, from the solution to linear matrix inequalities, a numerically tractable regulator design procedure is presented. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are validated.
Model Reduction for Aperiodically Sampled Data Systems
Ecole Centrale de Lille（里尔中央理工学院）；Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL), UMR CNRS 9189（里尔信息、信号与自动化研究中心 (CRIStAL)）
Observer design for linear systems with aperiodic sampled-data measurements is addressed. To solve this problem, a novel hybrid observer is designed. The main peculiarity of the proposed observer consists of the use two output injection terms, one acting at the sampling instants and one providing an intersample injection. The error dynamics are augmented with a timer variable triggering the arrival of a new measurement and analyzed via hybrid system tools. Using Lyapunov theory, sufficient conditions for the convergence of the observer are provided. Relying on those conditions, an optimal LMI-…
This article is concerned with data-driven analysis of discrete-time systems under aperiodic sampling, and in particular with a data-driven estimation of the maximum sampling interval (MSI). The MSI is relevant for analysis of and controller design for cyber-physical, embedded and networked systems, since it gives a limit on the time span between sampling instants such that stability is guaranteed. We propose tools to compute the MSI for a given controller and to design a controller with a preferably large MSI, both directly from a finite-length, noise-corrupted state-input trajectory of the s…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic) sampling instants and the stability property of the continuous-time system when the maximum admissible sampling period converges to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the c…
In this article, we update the reference [14] in two aspects. First, we note that in order for the control law (12) in [14] to be equivalent to the control law (3) in [14], we need to assume that the samplings for all subsystems must be synchronous, i.e., we need to assume that $T_{i}=T$ for all $i=1,\cdots,N$. Second, we extend our results from periodic sampling to aperiodic sampling.
We investigate stability analysis and controller design of unknown continuous-time systems under state-feedback with aperiodic sampling, using only noisy data but no model knowledge. We first derive a novel data-dependent parametrization of all linear time-invariant continuous-time systems which are consistent with the measured data and the assumed noise bound. Based on this parametrization and by combining tools from robust control theory and the time-delay approach to sampled-data control, we compute lower bounds on the maximum sampling interval (MSI) for closed-loop stability under a given …
The paper deals with the design of an improved model predictive control scheme for achieving station-keeping in a quasi Halo orbit around the $L_2$ point in the Earth-Moon system. The improvement is obtained thanks to a multi-rate sampled-data trajectory planner that allows for simplifying the optimization problem of the model predictive controller while guaranteeing feasibility and convergence to the desired orbit. The multi-rate planner is designed based on a simplified model of the dynamics under a preliminary nonlinear regulation feedback. The proposed control scheme is shown to outperform…
We propose a delay-dependent sampled-data output-feedback LPV control technique to address the air-fuel ratio (AFR) regulation problem in spark ignition (SI) engines. AFR control and advanced fueling strategies are essential for maximizing fuel economy while minimizing harmful exhaust emissions. The fuel path of the SI engine, as well as the three-way catalyst (TWC) simplified dynamics, have been captured by a continuous-time linear parameter-varying (LPV) system with varying time delay, where the system dynamics rely on the engine speed, defined as the system's scheduling parameter. The inter…
Robust implementable output regulator design approaches are studied for general linear continuous-time \mbox{systems} with periodically sampled measurements, consisting of both the regulation errors and extra measurements that are generally non-vanishing in steady state. A digital regulator is first developed via the conventional emulation-based approach, rendering the regulation errors asymptotically bounded with a small sampling period. We then develop a hybrid design framework by incorporating a generalized hold device, which transforms the original problem into the problem of designing an …
