Self-Triggered Model Predictive Control for Nonlinear Input-Affine Dynamical Systems via Adaptive Control Samples Selection

Abstract

Abstract-In this paper, we propose a self-triggered formulation of Model Predictive Control for continuous-time nonlinear input-affine networked control systems. Our control method specifies not only when to execute control tasks but also provides a way to discretize the optimal control trajectory into several control samples, so that the reduction of communication load will be obtained. Stability analysis under the sample-and-hold implementation is also given, which guarantees that the state converges to a terminal region where the system can be stabilized by a local state feedback controller. Some simulation examples validate our proposed framework.

Self‐triggered model predictive control for networked control systems based on first‐order hold

“…Based on the aforementioned setup, we further define the optimal input signal and the corresponding system state as It is worth noting that the conventional periodic/aperiodic continuous‐time MPCs generally utilize the idea to implement the input signal continuously during the consecutive triggering instants, ie, s ∈[ t k , t k +1 ), which, unfortunately, is not feasible when the MPC controller operates in a network environment like the one shown in Figure . The reason is that we need an infinite bandwidth to transmit the desired continuous‐time input signal u ∗( s ), s ∈ [ t k , t k +1 ) through the network . A feasible solution to this problem is to just send a few samples of and then implement these samples in the sample‐and‐hold manner.…”

“…To further illustrate the performance of the proposed results, we compare the proposed FOH‐based algorithm (Algorithm 2) with the ZOH‐based STMPC developed in the work of Hashimoto et al and focus on the communication rate. According to the self‐triggered mechanism, the communication rate is determined by ‖ x ( s ) − x ∗ ( s )‖ if the self‐triggered control input is utilized.…”

“…Proof Without losing generality, we only consider the case that the same samples of u ∗ ( s ) are selected for both methods. First for s ∈[ t k , t k +δ 1 ], denote s = t k +δ e ,δ e ∈[0,δ 1 ], and then, we have Furthermore, it is shown in the work of Hashimoto et al that if , then By calculating the difference between Υ 1 and Υ 2 , we have …”

“…We first apply the proposed approach to a nonholonomic robot system utilized in the ZOH‐based self‐triggered networked MPC; and the corresponding control target is to drive the robot to the desired position from its initial location. This system is nonlinear; the system equation of which is shown as follows: where the state vector is χ=[ x y θ] T and the input vector is u =[ v ω]; [ x , y ] and θ denotes the robot's location and orientation, respectively, whereas [ v ω] describes the robot's velocity.…”

“…In the stability analysis of nonlinear MPC, assumptions like Assumptions 2 and 3 are normally used. 22 Moreover, Ω(ϵ f ) and κ(x) in Assumption 2 can be easily calculated by the approaches developed in the work of Michalska and Mayne, 26 whereas the Lipschitz constants in Assumption 3 can be achieved by the methods in the works of Eqtami et al 18 and Hashimoto et al 19 Based on the aforementioned setup, we further define the optimal input signal and the corresponding system state as…”