Predictive control for linear constrained systems : linear control performance and constrained control strategy

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Model predictive control (MPC) has become a standard control strategy for constrained multivariable systems. The essential part of the MPC strategy is that the optimal control problem is solved on line over a finite-horizon and the first value of the resulting control signals is applied. In the general MPC systems, it is observed that a linear appropriate control works in the unconstrained region around the equilibrium point and the auxiliary compensation is additionally applied in case when some of the system constraints turn to be active. Motivated by this observation, this research project clarifies the following feature on the predictive control: 1) performance limitation of linear predictive control systems, and 2) derive a model predictive control, which enables to elaborate the performance in the linear control regions. For H2 or LQ control problems, a control strategy, which clarifies the linear control performance with account of the compensation in the constrained regions, is obtained. The results are summarized as follows.1) For unconstrained linear systems, the H-infinity and H2 preview control problems are solved. Furthermore it is shown that analytic solution for H-infinity preview and delayed control problem is obtained based on the framework of finite-dimensional operations.2) LQ control problem for continuous-time linear systems is solved. It is clarified that the control consists of linear LQ control and additional auxiliary signals, which make up the linear LQ control in case when the constraints work.The control laws obtained by 1), 2) are applied to an inverted pendulum system and the strength and limitation are further discussed.