A down-sampled controller to reduce network usage with guaranteed closed-loop performance

Abstract

A down-sampled controller to reduce network usage with guaranteed closed-loop performance.In: 53rd IEEE Conference on Abstract-We propose and evaluate a down-sampled controller which reduces the network usage while providing a guaranteed desired linear quadratic control performance. This method is based on fast and slow sampling intervals, as the closed-system benefits by being brought quickly to steady-state conditions while behaving satisfactorily when being actuated at a slow rate once at those conditions. This mechanism is shown to provide large savings with respect to network usage when compared to traditional periodic time-triggered control and other aperiodic controllers proposed in the literature.

Consistent Event-Triggered Control for Discrete-Time Linear Systems With Partial State Information

“…andȲ (i) ≤Ȳ (i + 1), i ∈ N 0 , by induction (which implies Y (i) ≤ Y (i + 1), i ∈ N): it holds for i = 0 due to (5) and assumingȲ (i) ≤Ȳ (i + 1) holds for a given i pre and postmultiplying this inequality by A and A T , respectively, adding W to both sides and using ( 18) we conclude that it holds for i + 1. The proof that g(i) ≤ g(j), if i < j follows then from the fact that g…”

“…Most of the statements follow from optimal control results [20]. Here we only prove the properties of g. We start by noticing that Y (1) ≥ 0 due to (5) and, if we letȲ (0) := Θ, Y (i) := Y (i) + Θ, for i ∈ N, we havē…”

“…While designing optimal event-triggered controllers in a given sense is typically hard [1]- [3], several researchers have proposed different strategies with stability guarantees and related closed-loop performance properties [4]- [10]; performance can be defined, for example, in terms of a quadratic cost [5]- [7], [9] and an 2 induced norm bound [9], [10]. In the present work, we follow [7], [8], where an ETC policy was proposed to guarantee two, so-called consistency, properties: (i) it achieves a better closed-loop performance than that of traditional periodic control for the same average transmission rate; and (ii) no transmissions are generated in the Fig.…”

“…absence of disturbances; performance in [7], [8] is measured by an average quadratic cost just as in traditional Linear Quadratic Gaussian control. Other works have proposed ETC strategies, relying on different ideas, that can achieve a better performance than that of periodic control for the same average transmission rate (first consistency property) [5]- [7], [9], [11], [12]. However, all these works consider that full state-feedback is available, and, to the best of our knowledge, only [11] has been extended to output-feedback, see [13], [14] and also [15].…”

Using Radial Basis Functions to Approximate the LQG-Optimal Event-Based Sampling Policy

“…However, each time we sample we incur a fixed cost ρ, and this is the trade-off our sampling policy should optimize. From (8) we see that the constant γ 0 can be disregarded in the objective 2, and we are now ready to formally define the optimal sampling problem: OSP ρ : Consider the closed-loop system in Fig. 2, with a Kalman-Bucy filter governed by (4) and an LQR controller based on a simulated plant according to (5).…”