Learning Self-Triggered Controllers With Gaussian Processes

Abstract

This paper investigates the design of self-triggered controllers for networked control systems (NCSs), where the dynamics of the plant is unknown apriori. To deal with the unknown transition dynamics, we employ the Gaussian process (GP) regression in order to learn the dynamics of the plant. To design the self-triggered controller, we formulate an optimal control problem, such that the optimal pair of the inter-communication time step and control input can be determined based on the GP dynamics of the plant. Moreover, we provide an overall implementation algorithm that jointly learns the dynamics of the plant and the self-triggered controller based on a reinforcement learning framework. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.

Region-Based Self-Triggered Control for Perturbed and Uncertain Nonlinear Systems

“…Similarly to Delimpaltadakis and Mazo [13], we upper-bound the time evolution of the (homogenized) triggering functioñ φ(ξ(t; x), w(t)) along the trajectories of DI ( 19) with a function μ((x, w), t) in analytic form that satisfies (15). For this purpose, first we provide a lemma, similar to the comparison lemma [22] and to [13,Lemma V.2], which shows how to derive upper bounds with linear dynamics of functions evolving along flowpipes of DIs.…”

“…This has shifted the control community's research focus from periodic to aperiodic sampling techniques, which promish to reduce resource utilization (e.g., bandwidth, processing power, etc.). Arguably, event-based control is the aperiodic scheme that has attracted wider attention, with its two sub-branches being event-triggered control (ETC, e.g., [1]- [5]) and self-triggered control (STC, e.g., [4], [6]- [13]). For an introduction to the topic, the reader is referred to [14].…”

“…Finally, Tiberi and Johansson [11] design ETC and STC that guarantee uniform ultimate boundedness for perturbed uncertain systems, whereas Tolic et al [12] employ the small-gain approach to design STC that guarantees L p -stability. Alternative approaches relying on a stochastic framework and learning techniques have also been proposed, see, e.g., [15], [16]. In contrast to the robust approaches listed earlier, they can cope with potentially unbounded disturbances, but they relax the performance guarantees to probabilistic assurances.…”

Learning-based Event-triggered MPC with Gaussian processes and terminal constraints

“…The results of designing optimal control policies based on machine learning techniques can be broadly divided into two categories depending on whether models are taken into account when deriving the controllers; see model-free approaches [29,30,31,32] and model-based approaches [22,33,34,35,36,37,38,39,40,41,42,43,44,45]. In particular, our approach is related to the second category, since controllers are designed from the model estimated by the training data.…”

“…Optimal control frameworks that incorporate the GP regression were investigated in [42,43,22,34,40,41,44,45]. The authors in [42,43] formulated a chance-constrained MPC in terms of probabilistic reachable sets, and a sparse GP was introduced as an approximation technique to reduce the computational burden of solving the OCP.…”