**2. Model Predictive Control**

Model predictive control is a form of control scheme in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state. Then the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. This is the main difference from conventional control which uses a pre-computed control law.

#### **2.1. Characteristics of MPC**

MPC is by now a mature technology. It is fair to mention that it is the standard approach for implementing constrained, multivariable control in the process industries today. Further‐ more, MPC can handle control problems where off-line computation of a control law is diffi‐ cult or impossible.

Specifically, an important characteristic of this type of control is its ability to cope with hard constraints on controls and states. Nearly every application imposes constraints. For in‐ stance, actuators are naturally limited in the force (or equivalent) they can apply, safety lim‐ its states such as temperature, pressure and velocity, and efficiency, which often dictates steady-state operation close to the boundary of the set of permissible states. In this regard, MPC is one of few methods having applied utility, and this fact makes it an important tool for the control engineer, particularly in the process industries where plants being controlled are sufficiently slow to permit its implementation.

In addition, another important characteristic of MPC is its ability to handle control problems where off-line computation of a control law is difficult or impossible. Examples where MPC may be advantageously employed include unconstrained nonlinear plants, for which online computation of a control law usually requires the plant dynamics to possess a special structure, and time-varying plants.

A fairly complete discussion of several design techniques based on MPC and their relative merits and demerits can be found in the review article by [4].

#### **2.2. Essence of MPC**

dictive control (RMPC) techniques have been developed in recent decades. We review dif‐ ferent RMPC methods which are employed widely and mention the advantages and disadvantages of these methods. The basic idea of each method and some method applica‐

Most MPC strategies consider hard constraints, and a number of RMPC techniques exist to handle uncertainty. However model and measurement uncertainties are often stochastic, and therefore RMPC can be conservative since it ignores information on the probabilistic distribution of the uncertainty. It is possible to adopt a stochastic uncertainty description (in‐ stead of a set-based description) and develop a stochastic MPC (SMPC) algorithm. Some of

In recent years, there has been much interest in networked control systems (NCSs), that is, control systems close via possibly shared communication links with delay/bandwidth con‐ straints. The main advantages of NCSs are low cost, simple installation and maintenance, and potentially high reliability. However, the use of the network will lead to intermittent losses or delays of the communicated information. These losses will tend to deteriorate the performance and may even cause the system to become unstable. MPC framework is partic‐ ularly appropriate for controlling systems subject to data losses because the actuator can profit from the predicted evolution of the system. In section 7, results from our recent re‐ search are summarized. We propose a new networked control scheme, which can overcome

At the beginning of research on NCSs, more attention was paid on single plant through net‐ work. Recently, fruitful research results on multi-plant, especially, on multi-agent net‐ worked control systems have been obtained. MPC lends itself as a natural control framework to deal with the design of coordinated, distributed control systems because it can account for the action of other actuators while computing the control action of a given set of actuators in real-time. In section 8, a number of distributed control architectures for inter‐ connected systems are reviewed. Attention is focused on the design approaches based on

Model predictive control is a form of control scheme in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state. Then the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant. This is the main difference from conventional control which uses a pre-computed control law.

MPC is by now a mature technology. It is fair to mention that it is the standard approach for implementing constrained, multivariable control in the process industries today. Further‐

tions are stated as well.

78 Advances in Discrete Time Systems

the recent advances in this area are reviewed.

the effects caused by the network delay.

model predictive control.

**2.1. Characteristics of MPC**

**2. Model Predictive Control**

As mentioned in the excellent review article [2], MPC is not a new method of control design. Rather, it essentially solves standard optimal control problems which is required to have a finite horizon in contrast to the infinite horizon usually employed in *H*2and *H∞*linear opti‐ mal control. Where it differs from other controllers is that it solves the optimal control prob‐ lem on-line for the current state of the plant, rather than providing the optimal control for all states, that is determining a feedback policy on-line.

The on-line solution is to solve an open-loop optimal control problem where the initial state is the current state of the system being controlled which is just a mathematical programming problem. However, determining the feedback solution, requires solution of Hamilton-Jaco‐ bi-Bellman (Dynamic Programming) differential or difference equation, a vastly more diffi‐ cult task (except in those cases, such as *H*2and *H*∞linear optimal control, where the value function can be finitely parameterized). From this point of view, MPC differs from other control methods merely in its implementation. The requirement that the open-loop optimal control problem be solvable in a reasonable time (compared with plant dynamics) necessi‐ tates, however, the use of a finite horizon and this raises interesting problems.
