This paper provides an overview of commercially available model predictive control (MPC) technology, both linear and nonlinear, based primarily on data provided by MPC vendors. A brief history of industrial MPC technology is presented first, followed by results of our vendor survey of MPC control and identification technology. A general MPC control algorithm is presented, and approaches taken by each vendor for the different aspects of the calculation are described. Identification technology is reviewed to determine similarities and differences between the various approaches. MPC applications performed by each vendor are summarized by application area. The final section presents a vision of the next generation of MPC technology, with an emphasis on potential business and research opportunities.

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a statefeedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions...

. This paper provides an overview of nonlinear model predictive control (NMPC) applications in industry, focusing primarily on recent applications reported by NMPC vendors. A brief summary of NMPC theory is presented to highlight issues pertinent to NMPC applications. Five industrial NMPC implementations are then discussed with reference to modeling, control, optimization, and implementation issues. Results from several industrial applications are presented to illustrate the benefits possible with NMPC technology. A discussion of future needs in NMPC theory and practice is provided to conclude the paper. 1. Introduction The term Model Predictive Control (MPC) describes a class of computer control algorithms that control the future behavior of a plant through the use of an explicit process model. At each control interval the MPC algorithm computes an open-loop sequence of manipulated variable adjustments in order to optimize future plant behavior. The first input in the optima...

We present a structured interior-point method for the e cient solution of the optimal control problem in model predictive control (MPC). The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discrete-time Riccati recursion to solve the linear equations e ciently at each iteration of the interior-point method, and show that this recursion is numerically stable. We demonstrate the e ectiveness of the approach by applying it to three process control problems. 1

Predictive Control is one of the most powerful techniques in process control, but its application in non-linear processes is challenging. This is basically because the optimization method commonly used limits the kind of functions which can be minimized. The aim of this work is to show how the combination of Genetic Algorithms (GA) and Generalized Predictive Control (GPC), what we call GAGPC, can be applied to nonlinear process control. This paper also shows GAGPC performance when controlling non-linear processes with model uncertanties. Success in this area will open the door to using GAGPC for a better control of industrial processes.

We show that a sufficient condition for the robust stability of constrained linear model predictive control is for the plant to be open-loop stable, for zero to be a feasible solution of the associated quadratic programme and for the input weighting be sufficiently high. The result can be applied equally to state feedback and output feedback controllers with arbitrary prediction horizon. If integral action is included a further condition on the steady state modelling error is required for stability. We illustrate the results with two forms of integral action commonly used with model predictive control. 1

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This paper addresses the existence and implementation of the infinite horizon controller for the case of active steady-state constraints. The case of active steady-state constraints is important because, in many practical applications, controllers are required to operate at the boundary of the feasible region (for instance, in order to maximize global economic objectives). For this case, the usual finite horizon parameterizations with terminal cost cannot be applied since the origin lies on the boundary of the feasible region, and only suboptimal solutions are available. We propose here an iterative algorithm that generates an upper bound and a lower bound finite horizon approximation to the optimal solution. We show convergence of these boundary approximations to the optimal solution as the horizon increases is shown. The di#erence between the upper and lower bound solutions is used to bound the di#erence between the approximating solution and the optimal one. The algorithm provides a solution that is guaranteed to be within a user specified tolerance of the optimal solution. A numerical example with comparison between optimal and suboptimal controllers is presented. Index terms -- Model Predictive Control, Steady-state constraints, Optimal Control # author to whom correspondence should be addressed 1 1

Abstract — The difficulties imposed by actuator limitations in a range of active vibration and noise control problems are well recognized. This paper proposes and examines a new approach of employing Model Predictive Control (MPC). MPC permits limitations on allowable control action to be explicitly included in the computation of an optimal control action. Such techniques have been widely and successfully applied in many other areas. However, due to the relatively high computational requirements of MPC, existing applications have been limited to systems with slow dynamics. This paper illustrates that MPC can be implemented on inexpensive hardware at high sampling rates using traditional online quadratic programming methods for nontrivial models and with significant control performance dividends.

Most standard model predictive control (MPC) implementations partition the plant into several units and apply MPC individually to these units. It is known that such a completely decentralized control strategy may result in unacceptable control performance, especially if the units interact strongly. Completely centralized control of large, networked systems is viewed by most practitioners as impractical and unrealistic. In this dissertation, a new framework for distributed, linear MPC with guaranteed closed-loop stability and performance properties is presented. A modeling framework that quantifies the interactions among subsystems is em-ployed. One may think that modeling the interactions between subsystems and exchanging trajectory information among MPCs (communication) is sufficient to improve controller per-ormance. We show that this idea is incorrect and may not provide even closed-loop stability. A cooperative distributed MPC framework, in which the objective functions of the local MPCs are modified to achieve systemwide control objectives is proposed. This approach allows practitioners to tackle large, interacting systems by building on local MPC systems already in place. The iterations generated by the proposed distributed MPC algorithm are systemwide feasible, and the controller based on any intermediate termination of the algorithm is closed-loop sta-