Tube-based distributed control of linear constrained systems

Abstract

In this paper we consider a linear system structured into physically coupled subsystems and propose an innovative distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Our method hinges on the availability of a decentralized stabilizing regulator for the unconstrained system and provides a two-layer controller for each subsystem. Upper controllers receive planned state trajectories from neighboring subsystems and exploit the notion of tubes [12] for achieving robustness of stability with respect to coupling. Lower controllers generate planned trajectories using Model Predictive Control (MPC) independently of the other subsystems. The proposed control scheme is arguably easier to design and apply than existing distributed controllers with similar features. A comparison of the proposed approach with existing centralized and distributed MPC regulators is conducted using an illustrative example.

Scalable monitoring of interconnected stochastic systems

“…where the parameters and their numerical values are defined in [21]. Since both ∆P refi and ∆P Li are assumed to be constant and known, for the sake of simplicity, we neglect them in our analysis.…”

“…The dynamics of each power generation area, equipped with primary control and linearized around the equilibrium value for all variables, is described by the following continuous time LTI model [21]: (16) where x i = (∆θ i , ∆ω i , ∆P mi , ∆P vi ) is the state, u i = ∆P refi is the control input of each area, and ∆P Li is the local power load. Note that the letter ∆ is used to denote the deviation from steady-state.…”

Distributed predictive control with minimization of mutual disturbances

“…We consider a modified version of the four-truck system from [15]. Each truck is modelled by the second-order dynamics The problem considered is controlling the trucks to equilibrium from initial states of…”

“…If the state and input constraint sets are large, then this naturally leads to large disturbance sets and, hence, more tightly constrained local optimal control problems, even for [14,15]. In this paper, we attempt to overcome this drawback by exploiting the fact that, often, subsystems do not use all of their state and input constraint sets and, hence, the mutual disturbance sets can be reduced by considering this.…”

“…To circumvent this, improved proposals have been made: in [14], tube-based controllers share reference trajectories and maintain true states and inputs in bounded neighbourhoods of these. In [15], the tube MPC concept is applied twice by each controller: once to maintain a planned perturbed state trajectory around a planned nominal trajectory, then again to maintain the true, perturbed state trajectory around the planned one.…”