Event-driven optimization-based control of hybrid systems with integral continuous-time dynamics

Abstract

In this paper we introduce a class of continuous-time hybrid dynamical systems called integral continuous-time hybrid automata (icHA) for which we propose an event-driven optimization-based control strategy. Events include both external actions applied to the system and changes of continuous dynamics (mode switches). The icHA formalism subsumes a number of hybrid dynamical systems with practical interest, e.g., linear hybrid automata. Different cost functions, including minimum-time and minimum-effort criteria, and constraints are examined in the event-driven optimal control formulation. This is translated into a finite-dimensional mixed-integer optimization problem, in which the event instants and the corresponding values of the control input are the optimization variables. As a consequence, the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process. A receding horizon control scheme exploiting the event-based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite-time or asymptotic convergence of the closed-loop.

Event-driven model predictive control of timed hybrid Petri nets

“…Proposition Consider the event‐driven MPC scheme applied to a THPN where the cost function is the minimum‐time criterion , and where the terminal constraint is applied on the desired target marking . If the problem is feasible at time τ 0 with finite cost, then it is recursively feasible and the desired marking is reached in finite time, that is, for τ < ∞ . Proof The result follows from the convergence of the eMLD scheme proved in . Because at time τ 0 problem (19) is feasible with finite cost, due to terminal constraint and minimum‐time criterion, the command sequence μ * ( τ 0 ) brings the marking to the target in finite time J * ( τ 0 ).…”

“…In , the authors have proposed an event‐driven MLD model (eMLD), where χ ( k ) = [ x ( k ) ′ τ ( k )] ′ , , μ ( k ) = [ v ( k ) ′ u d ( k ) ′ q ( k )] ′ . In the eMLD , the counter k represents the number of events, the additional sta...…”

“…In the eMLD , the counter k represents the number of events, the additional state variable τ ( k ) is the total time elapsed when the k th event occurs, q ( k ) is the time between the k th and the ( k + 1)th events, and v ( k ) is the integral of the continuous control input between the k th and the ( k + 1)th events, where it is assumed piecewise constant, that is, v ( k ) = q ( k ) u c ( t ( k ) + ). As discussed in , in the eMLD system, an event occurs either when the value of δ changes, because of , or when the input μ is changed.…”

“…In [26], the authors have proposed an event-driven MLD model (eMLD), (4), the counter k represents the number of events, the additional state variable .k/ is the total time elapsed when the kth event occurs, q.k/ is the time between the kth and the .k C 1/th events, and v.k/ is the integral of the continuous control input between the kth and the .k…”

On fluidization of discrete event models: observation and control of continuous Petri nets

“…This produces a Mixed Integer Linear Programming Problem (MILP) whose objective function represents the pursued control goal, e.g., minimum-time, minimum-effort, minimum-displacement, etc, and whose solution contains the control actions that optimize the objective function (Di Cairano et al 2009). Let us exemplify the event-driven control through the net in Fig.…”