David Muñoz de la Peña

Distributed model predictive control: A tutorial review and future research directions

Abstract In this paper, we provide a tutorial review of recent results in the design of distributed model predictive control systems. Our goal is to not only conceptually review the results in this area but also to provide enough algorithmic details so that the advantages and disadvantages of the various approaches can become quite clear. In this sense, our hope is that this paper would complement a series of recent review papers and catalyze future research in this rapidly evolving area. We conclude discussing our viewpoint on future research directions in this area.

Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements

In this work, we design distributed Lyapunov-based model predictive controllers for nonlinear systems that coordinate their actions and take asynchronous measurements and delays explicitly into account. Sufficient conditions under which the proposed distributed control designs guarantee that the state of the closed-loop system is ultimately bounded in a region that contains the origin are provided. The theoretical results are demonstrated through a chemical process example.

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.

Robust explicit MPC based on approximate multi-parametric convex programming

Many robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set

Constrained min-max predictive control: modifications of the objective function leading to polynomial complexity

In this note, an efficient way of implementing a constrained min-max predictive controller is presented. The new approach modifies the objective function in such a way that the resulting min-max problem can be solved in polynomial time. Different modifications are proposed. The main contribution of the note is to provide a robust constrained min-max predictive controller that can be implemented in real time. The new controller stabilizes the uncertain system.

Iterative Distributed Model Predictive Control of Nonlinear Systems: Handling Asynchronous, Delayed Measurements

In this work, we focus on iterative distributed model predictive control (DMPC) of large-scale nonlinear systems subject to asynchronous, delayed state feedback. The motivation for studying this control problem is the presence of asynchronous, delayed measurement samplings in chemical processes and the potential use of networked sensors and actuators in industrial process control applications to improve closed-loop performance. Under the assumption that there exist upper bounds on the time interval between two successive state measurements and on the maximum measurement delay, we design an iterative DMPC scheme for nonlinear systems via Lyapunov-based control techniques. Sufficient conditions under which the proposed distributed MPC design guarantees that the state of the closed-loop system is ultimately bounded in a region that contains the origin are provided. The theoretical results are illustrated through a catalytic alkylation of benzene process example.

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

In this work, we focus on control of nonlinear systems subject to data losses. 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.

Stability of nonlinear asynchronous systems

In this work, we focus on a class of nonlinear asynchronous systems defined by two different modes of operation, one stable and the other one unstable. The switching between the two modes of operation is driven by external asynchronous events. It is assumed that on any time interval of a given length, the maximum time in which the system evolves in the unstable mode is bounded. This property is given in the form of a rate constraint. Under this assumption, we study the behavior of this class of systems and provide existential results of conditions on this rate constraint under which various types of stability of the origin of the nonlinear asynchronous system can be assured.

Output feedback control of nonlinear systems subject to sensor data losses

In this work, we focus on output feedback control of nonlinear systems subject to sensor data losses. We initially construct an output feedback controller based on a combination of a Lyapunov-based controller with a high-gain observer. We then study the stability and robustness properties of the closed- loop system in the presence of sensor data losses. We state a set of sufficient conditions under which the closed-loop system is guaranteed to be practically stable. The theoretical results are demonstrated using a chemical process example.

A Decomposition Algorithm for Feedback Min–Max Model Predictive Control

An algorithm for solving feedback min-max model predictive control for discrete time uncertain linear systems with constraints is presented in the paper. The algorithm solves the corresponding multi-stage min-max linear optimization problem. It is based on applying recursively a decomposition technique to solve the min-max problem via a sequence of low complexity linear programs. It is proved that the algorithm converges to the optimal solution in finite time. Simulation results are provided to compare the proposed algorithm with other approaches.