Design of plug-and-play model predictive control: an approach based on linear programming

In this paper we consider a linear system represented by subsystems coupled through states and propose a distributed control scheme for guaranteeing asymptotic stability and satisfaction of constraints on system inputs and states. Our design procedure enables Plug-and-Play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the synthesis of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method, that is based on Model Predictive Control (MPC) advances the PnP design procedure proposed in (Riverso et al., 2013) in several directions. Notably, we show how critical steps in the design of a local controller can be solved through linear programming.

Plug-and-Play Model Predictive Control based on robust control invariant sets

Marcello Farina, Giancarlo Ferrari Trecate

In this paper we consider a linear system represented by a coupling graph between subsystems and propose a distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Most importantly, as in (Riverso et al, 2012) our design procedure enables plug-and-play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the design of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method hinges on local tube MPC controllers based on robust control invariant sets and it advances the PnP design procedure proposed in (Riverso et al, 2012) in several directions. Quite notably, using recent results in the computation of robust control invariant sets, we show how critical steps in the design of a local controller can be solved through linear programming. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.

2012

Plug-and-Play Model Predictive Control based on robust control invariant sets

Marcello Farina, Giancarlo Ferrari Trecate

We consider the problem of designing decentralized controllers for large-scale linear constrained systems composed by a number of interacting subsystems. As in (Riverso et al., 2013) (i) the design of local controllers requires limited transmission of information from other subsystems and (ii) the addition/removal of a subsystem triggers the design of local controllers for child subsystems only. These properties enable Plug-and-Play (PnP) operations, and we show how to perform them while preserving global stability of the origin and constraint satisfaction. We improve several aspects of the PnP design procedure proposed in (Riverso et al., 2013) and, using recent results in the computation of Robust Control Invariant (RCI) sets, we show that all critical steps in the design of a local controller can be solved through Linear Programming (LP). Finally, an application of the proposed design procedure to a large-scale mechanical system is presented.

2014

Predictive Control of Fast Unstable and Nonminimum-phase Nonlinear Systems

Dominique Bonvin, Kahina Guemghar, Philippe Müllhaupt

Predictive Control of Unstable Nonminimum-phase Systems K. Guemghar, B. Srinivasan, Ph. Mullhaupt, D. Bonvin ´ Institut d’Automatique, Ecole Polytechnique F´d´rale de Lausanne, ee CH-1015 Lausanne, Switzerland. Predictive control is a very eﬀective approach for tackling problems with constraints and nonlinear dynamics, especially when the analytical computation of the control law is diﬃcult. Standard predictive control involves predicting the system behavior over a prediction horizon and calculating the input that minimizes a criterion expressing the system behavior in the future. Only the ﬁrst part of the computed input is applied to the system, and this procedure is repeated with the advent of each new measurement. This methodology is widely used in the process industry where system dynamics are sufﬁciently slow to permit its implementation. In contrast, applications of predictive control to fast unstable dynamic systems are rather limited. Apart from computational considerations, a fundamental limitation arises from the accuracy of that prediction, which can be quite poor due to accumulation of numerical errors if the prediction horizon is large. In this paper, an upper bound on the prediction horizon based on the location of the unstable pole(s) of the linearized system will be provided. The problem becomes more acute when nonminimum-phase systems are considered. Nonminimum phase implies that the system starts in a direction opposite to its reference (inverse response). To control such systems, it is reasonable to predict the maneuvers, thus making predictive control a natural strategy. However, a large prediction horizon is required since it is necessary to look beyond the inverse response. In this context, a lower bound on the prediction horizon based on the location of the unstable zero(s) of the linearized system will be provided. The two bounds mentioned above may lead to the situation where there exist no value of the prediction horizon that can stabilize a given unstable nonmiminum-phase system. For such a case, a combination of tools from diﬀerential geometry and predictive control is proposed in this paper. The envisaged procedure has a cascade structure and is outlined below: 1. Using the input-output linearization technique, the nonlinear system is transformed into a linear subsystem and internal dynamics. However, since the original nonlinear system is nonminimum-phase, the internal dynamics are unstable. 2. The linear subsystem is made arbitrarily fast by using a stabilizing high-gain linear feedback (inner-loop). 3. A predictive control scheme is then used to stabilize the slow internal dynamics (outerloop) by manipulating the reference of the inner loop. The stability of the proposed procedure is analyzed using a singular perturbation approach. The results will be illustrated in simulation on a system consisting of an inverted pendulum on a cart. 1

2002

Predictive Control of Fast Unstable and Nonminimum-phase Nonlinear Systems

Dominique Bonvin, Kahina Guemghar, Philippe Müllhaupt

2002