Discrete-time MPC Using Laguerre Functions
In essence, the core technique in the design of discrete-time MPC is based on optimizing the future control trajectory, that is the difference of the control signal, Δu(k). By assuming a finite control horizon N c , the difference of the control signal Δu(k) for k = 0, 1, 2, ..., N c −1 is captured by the control vector Δu while the rest of the Δu(k) for k = N c , N c +1, ..., N p is assumed to be zero. In the examples encountered before, there were cases where the neglected trajectory Δu(k) was not zero, however, it was small in its magnitude. The idea in this chapter is to generalize the design procedure by introducing a set of discrete orthonormal basis functions into the design. For the present, let us focus on the basic ideas by treating it as a generalization of the basic approach. This generalization will help us in reformulating the predictive control problem and simplifying the solutions, in addition to tuning the predictive control system. Furthermore, a long control horizon can be realized without using a large number of parameters. Several MATLAB tutorials are presented in this chapter for the design of discrete-time predictive control systems, with or without constraints.
KeywordsModel Predictive Control Active Constraint Prediction Horizon Sampling Instant Control Trajectory
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