D. Muñoz de la Peña

Lyapunov-Based Model Predictive Control of Nonlinear Systems Subject to Data Losses

In this work, we focus on model predictive control of nonlinear systems subject to data losses. The motivation for considering this problem is provided by wireless networked control systems and control of nonlinear systems under asynchronous measurement sampling. In order to regulate the state of the system towards an equilibrium point while minimizing a given performance index, we propose a Lyapunov-based model predictive controller which is designed taking data losses explicitly into account, both in the optimization problem formulation and in the controller implementation. The proposed controller allows for an explicit characterization of the stability region and guarantees that this region is an invariant set for the closed-loop system under data losses, if the maximum time in which the loop is open is shorter than a given constant that depends on the parameters of the system and the Lyapunov-based controller that is used to formulate the optimization problem. The theoretical results are demonstrated through a chemical process example.

Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control

This paper deals with the robustness of Model Predictive Controllers for constrained uncertain nonlinear systems. The uncertainty is assumed to be modeled by a state and input dependent signal and a disturbance signal. The framework used for the analysis of the robust stability of the systems controlled by MPC is the wellknown Input-to-State Stability. It is shown how this notion is suitable in spite of the presence of constraints on the system and of the possible discontinuity of the control law.

On Input-to-State Stability of Min-max Nonlinear Model Predictive Control

In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and other disturbance inputs. The min–max model predictive control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for robust stability of the resulting closed-loop system using the input-to-state stability (ISS) framework. First, we show that only input-to-state practical stability can be ensured in general for closed-loop min–max MPC systems; and we provide explicit bounds on the evolution of the closed-loop system state. Then, we derive new conditions for guaranteeing ISS of min–max MPC closed-loop systems, using a dual-mode approach. An example illustrates the presented theory.

Model Predictive Control techniques for Hybrid Systems

Abstract This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.

A distributed MPC scheme with low communication requirements

In this work, we consider the problem of controlling two linear systems coupled through the inputs. We propose a novel distributed model predictive control method based on game theory in which two different agents communicate in order to find a cooperative solution to the centralized control problem. We assume that each agent only has partial information of the model and the state of the system. The class of systems considered arises naturally in multi-input multi-output processes in which a transfer function model is obtained using standard identification techniques. The performance and the robustness of the proposed control scheme with respect to data losses in the communications are illustrated by extensive simulations.

MPC for tracking periodic reference signals

This paper is devoted to the design of a predictive controller for constrained linear systems to track periodic references. The only assumption on the dynamics of the reference is that it is periodic and its period is known. It is also assumed that the reference signal is a priori known by the controller. Inspired in the hierarchical control scheme based on the trajectory planification, the ideas of the MPC for tracking [Limon et al., 2008] are extended to this case. The proposed predictive controller has the future sequence of inputs and an artificial reference as decision variables. The cost function is divided into two terms: one penalizes the tracking error with the artificial reference and other penalizes the deviation of the artificial reference to the reference to be tracked. Stability is ensured thanks to the addition of two constraints: a terminal constraint on the predicted trajectory and a constraint that enforces the artificial reference to be periodic. It is proved that the proposed controller is recursively feasible and the controlled system satisfies the hard constraints, is asymptotically stable and converges to the best possible reachable trajectory. The properties of the proposed controller are illustrated in an example.

Distributed MPC: a supply chain case study

This work focuses on the application of distributed model predictive control to find the optimal decision variables to maximize profit in supply chains. A reduced version of the MIT beer game made of only two elements is taken as an application example. Three controllers, i.e., a standard centralized model predictive controller, an distributed non-cooperative model predictive controller and a recently proposed distributed scheme based on a cooperative game are applied to maximize profit. The properties of these controllers are compared extensively under different simulation scenarios.

Explicit solution of min–max MPC with additive uncertainties and quadratic criterion

Abstract Min–max model predictive control (MMMPC) is one of the strategies proposed to control plants subject to bounded uncertainties. This technique is very difficult to implement in real time because of the computation time required. Recently, the piecewise affine nature of this control law has been proved for unconstrained linear systems with quadratic performance criterion. However, no algorithm to compute the explicit form of the control law was given. This paper shows how to obtain this explicit form by means of a constructive algorithm. An approximation to MMMPC in the presence of constraints is presented based on this algorithm.

Brief paper: Min-max MPC using a tractable QP problem

Min-Max MPC (MMMPC) controllers [5] suffer from a great computational burden that is often circumvented by using upper bounds of the worst possible case of a performance index. These upper bounds are usually computed by means of linear matrix inequalities (LMI) techniques. In this paper a more efficient approach is shown. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min-max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min-max problem and the resulting control is shown to have guaranteed stability. Simulation examples are given in the paper.

Distributed MPC based on a cooperative game

In this work, we focus on the problem of stabilization of two constrained linear systems coupled through the inputs by two different agents which communicate in order to take a decision assuming that each agent only has partial information of the model and the state of the system. We extend previous results on distributed model predictive control and provide sufficient conditions that guarantee practical stability of the closed-loop system as well as an optimization based procedure to design the controller so that these conditions are satisfied. The theoretical results and the design procedure are illustrated through a simulation example.