State-Space Interpretation of Model Predictive Control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC)

Single-layer economic model predictive control for periodic operation

In this paper we consider periodic optimal operation of constrained periodic linear systems. We propose an economic model predictive controller based on a single layer that unites dynamic real time optimization and control. The proposed controller guarantees closed-loop convergence to the optimal periodic trajectory that minimizes the average operation cost for a given economic criterion. A priori calculation of the optimal trajectory is not required and if the economic cost function is changed, recursive feasibility and convergence to the new periodic optimal trajectory is guaranteed. The results are demonstrated with two simulation examples, a four tank system, and a simplified model of a section of Barcelona's water distribution network.Peer ReviewedPostprint (author’s final draft

An Implementable and Stabilizing Model Predictive Control Strategy for Inverted Pendulum-Like Behaved Systems

In control theory, the inverted pendulum is a class of dynamic systems widely used as a benchmarking for evaluating several control strategies. Such a system is characterized by an underactuated behavior. It is also nonlinear and presents open-loop unstable and integrating modes. These dynamic features make the control more difficult, mainly when the controller synthesis seeks to include constraints and the guarantee of stability of the closed-loop system. This chapter presents a stabilizing model predictive control (MPC) strategy for inverted pendulum-like behaved systems. It has an offset-free control law based on an only optimization problem (one-layer control formulation), and the Lyapunov stability of the closed-loop system is achieved by adopting an infinite prediction horizon. The controller feasibility is also assured by imposing a suitable set of slacked terminal constraints associated with the unstable and integrating states of the system. The effectiveness of the implementable and stabilizing MPC controller is experimentally demonstrated in a commercial-didactic rotary inverted pendulum prototype, considering both cases of stabilization of the pendulum in the upright position and the output tracking of the rotary arm angle

A robust multi-model predictive controller for distributed parameter systems

12 páginas, 6 figurasIn this work a robust nonlinear model predictive controller for nonlinear convection–diffusion-reaction systems is presented. The controller makes use of a collection of reduced order approximations of the plant (models) reconstructed on-line by projection methods on proper orthogonal decomposition (POD) basis functions. The model selection and model update step is based on a sufficient condition that determines the maximum allowable process-model mismatch to guarantee stable control performance despite process uncertainty and disturbances. Proofs on the existence of a sequence of feasible approximations and control stability are given. Since plant approximations are built on-line based on actual measurements, the proposed controller can be interpreted as a multi-model nonlinear predictive control (MMPC). The performance of the MMPC strategy is illustrated by simulation experiments on a problem that involves reactant concentration control of a tubular reactor with recycle.This work has been also partially founded by the Spanish Ministry of Science and Innovation (SMART-QC, AGL2008-05267-C03-01), the FP7 CAFE project (KBBE-2007-1-212754), the Project PTDC/EQU-ESI/73458/2006 from the Portuguese Foundation for Science and Technology and PI grant 07/IN.1/I1838 by Science Foundation Ireland. Also, the authors acknowledge financial support received by a collaborative grant GRICES-CSIC.Peer reviewe

An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements

This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network System