Self-Triggered Model Predictive Control for Network Scheduling and Control

Abstract

Herein we present an algorithm for controlling LTI processes using an adaptive sampling interval where the controller at every sampling instant not only computes the new control command but also decides the time interval to the next sample. The approach relies on MPC where the cost function depends on the control performance as well as the cost for sampling. The paper presents a method for synthesizing such a predictive controller and gives explicit conditions for when it is stabilizing. Further it is shown that the optimization problem may be solved off-line and that the controller may be implemented as a lookup table of state feedback gains. The paper is concluded with a numerical example.

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

“…To ameliorate this communication burden, [9] proposes a packet-based predictive control scheme that combines a classical quadratic MPC cost function with ℓ 1 input regularization and sends the obtained sparse input sequences to the actuators. A STC approach for unconstrained discretetime linear systems that avoids bursts in communication and frequent updating of the actuators by sending only a single control value and keeping this constant until the next execution time is presented in [32]. The strategy in [32] solves a co-design problem of simultaneously designing the control law and the triggering condition and allows trading in control performance to obtain lower (communication and/or actuation) resource utilization.…”

“…A STC approach for unconstrained discretetime linear systems that avoids bursts in communication and frequent updating of the actuators by sending only a single control value and keeping this constant until the next execution time is presented in [32]. The strategy in [32] solves a co-design problem of simultaneously designing the control law and the triggering condition and allows trading in control performance to obtain lower (communication and/or actuation) resource utilization. In particular, [32] follows an ℓ 1 -like regularization to solve the codesign problem by augmenting the quadratic cost function related to control performance with a penalty related to sampling the system (and updating the control law).…”

“…The strategy in [32] solves a co-design problem of simultaneously designing the control law and the triggering condition and allows trading in control performance to obtain lower (communication and/or actuation) resource utilization. In particular, [32] follows an ℓ 1 -like regularization to solve the codesign problem by augmenting the quadratic cost function related to control performance with a penalty related to sampling the system (and updating the control law). Due to the additional penalties in [9,32], no performance guarantees are given in terms of the original MPC cost function.…”

“…In particular, [32] follows an ℓ 1 -like regularization to solve the codesign problem by augmenting the quadratic cost function related to control performance with a penalty related to sampling the system (and updating the control law). Due to the additional penalties in [9,32], no performance guarantees are given in terms of the original MPC cost function. In [33], a scheme with the same purpose as in [32] is considered, also for unconstrained discrete-time linear systems.…”

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

“…Optimal event-triggered control has been proposed in, e.g., [7], [9], [10] considering first-order linear systems and reset actuation inputs, while Lyapunov-based methods that guarantee stability of the closed-loop system have been proposed in several works, e.g., [11], [12], [13], [14], [15], [16]. More recently, model-predictive event-triggered control has been proposed in [17], [18]. A broad survey of eventtriggered control can be found in [19].…”