| Model Predictive Control (MPC) also known as Moving Horizon Control (M HC) or Receding Horizon Control (RHC) is a popular new control method in the later of 70'. It appeared due to two factors. One factor is the development of computer and the other is the requirement of shift from complicated industrial control to advanced optimal control. In the contrast with other control methods, the advantage of MPC are as follows: MPC needn't accurate model, creating model is convenient and the depiction of process may be got from simple experiment.; MPC does not use least model; using moving horizon optimal policy, not optimization for a time, can make up for uncertainty caused by model mismatch, disturbance and so on. So the dynamic process is good; MPC is easily expanded into the system with constrained control, not least model, long delay and non-linear process. To the most important, MPC can deal with constrained and multi-variables system.MPC appears in variable forms, but its essence is made of three properties: predictive model, moving horizon optimization and feedback revise. All kinds of predictive arithmetic are nearly same: At every instant, MPC requires the on-line solution of an optimization problem to compute optimal control inputs over a fixed number of future time instants, known as the "time horizon". Although more than one control move is generally calculated, only the first one is implemented. At the next sampling time, the optimization problem is reformulated and solved with new measurements obtained from the system. The on-line optimization can be reduced to either a linear program or a quadratic program. With the development of MPC theory, it is used in wider and wider areas. It involves in chemical process control in the petrochemical, paper industries and gas pipeline control, aviation, metallurgy, military affairs and so on. At the same time, both the control technology and control measure are improved.The theory on the robustness of MPC is mature, among which the MPC theory based is shortcut for robust stability of constrained system. There are two reasons for saying so. On the one hand, control provides perfect theoretic foundation for the analyse and design of robustness. On the other hand, MPC is a efficient way to deal with the constraints of system, because MPC expressly describes constraints in the open-loop optimization and satisfies dynamic performance by moving horizon. Unfortunately, most literature on this didn't discuss the performance of the system. Document [28,44] discussed control of the constrained system, in the form of LMI and multi-objection control. They also showed the moving horizon control arithmetic by combing MPC and control. There are two reasons why LMI optimization is relevant to MPC. Firstly, LMI-based optimization problems can be solved in polynomial-time, often in times comparable to that required for the evaluation of an analytical solution for a similar problem. Thus, LMI optimization can be implemented on-line. Secondly, it is possible to recast much of existing robust control theory in the framework of LMIs. The implication is that we can devise an MPC scheme where at each time instant; an LMI optimization problem (as opposed to a conventional linear or quadratic programs) is solved, which incorporates input and output constraints. The main advantage of moving horizon control arithmetic is its capability of automatically relaxing or tightening the performance specification in order to obey hard control constraints while achieving the best possible performance in a suitable class of LMI-generated control gains.Traditional control does not consider the constraints of system, but the constraints of inputs and state exit in a common control system. On the base of control, control of constrained system is formed. It solves the problem of constraints just as MPC does, by transforming the constraints of the input or state into the constraints of optimized parameters, taking the performance of as optimized objection and resolving the...
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