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.

More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for nonlinear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty "rigorously" an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, nonlinear state estimation, and batch system control. Many practical problems like control objective prior...

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...

Control based on on-line optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for con-strained systems. The main limitation of MPC is, however, its on-line computational complexity. For discrete-time linear time-invariant systems with con-straints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law associated with MPC, and show that it is piecewise lin-ear and continuous. The controller inherits all the sta-bility and performance properties of MPC, but the on-line computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling ap-plications which cannot be covered satisfactorily with anti-windup schemes.

Issues of feasibility and stability are considered for a finite horizon formulation of receding horizon control for linear systems under mixed linear state and control constraints. We prove that given any compact set of initial conditions that is feasible for the infinite horizon problem, there exists a finite horizon length above which a receding horizon policy will provide both feasibility and stability, even when no end or stability constraint is imposed. Finally, computations for determining a sufficient horizon length are carried out on a simple open-loop stable example under control saturation constraints.

The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper. 1 Introduction The objective of this paper is to review some major trends in model predictive control (MPC) research with emphasis on recent developments in North America. We will focus on the spirit rather than the details, i.e. we do not attempt to provide a complete list of all the relevant papers published during the last few years. 1 We will try to contrast the motivations driving the research in the different camps. There is...

A BMI-based approach to an on-line computationally efficient robust nonlinear MPC is proposed. Theoretical results and a simple example accompany the proposed method. 1 Introduction Model predictive control (MPC) has been an active research area for close to two decades. The research has been driven by numerous successful applications of the technology [1], and during the last years a sound theoretical foundation has been established; [2], [3], and [4]. The issue of robust stability of MPC based control systems, however, is largely unsolved, at least for nonlinear MPC. Some results are available though. Works on robust MPC for linear systems include: [5] on constrained stable systems; [6] on unconstrained systems; [7] and [8] on constrained systems. Works on robust analysis of nonlinear MPC include: [9] and [10] on constrained continuous-time systems, and [11] on unconstrained discrete-time systems. Finally, works on robust synthesis, i.e. an uncertainty model is explicitly used when...

This paper addresses the identification and control of nonlinear systems by means of Fuzzy Hammerstein (FH) models, which consist of a static fuzzy model connected in series with a linear dynamic model. For the identification of nonlinear dynamic systems with the proposed FH models, two methods are proposed. The first one is an alternating optimization algorithm that iteratively refines the estimate of the linear dynamics and the parameters of the static fuzzy model. The second method estimates the parameters of the nonlinear static model and of the linear dynamic model simultaneously by using a constrained recursive least-squares algorithm. The obtained FH model is incorporated in a model-based predictive control scheme and a new constraint-handling method is presented. A simulated water-heater process is used as an illustrative example. A comparison with an affine neural network and a linear model is given. Simulation results show that the proposed FH modeling approach is useful for modular parsimonious modeling and model-based control of nonlinear systems.

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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