By Wook Hyun Kwon, Soo Hee Han
Easy-to-follow studying constitution makes absorption of complicated fabric as pain-free as attainable Introduces whole theories for balance and price monotonicity for limited and non-linear platforms in addition to for linear platforms In co-ordination with MATLAB® documents on hand from springeronline.com, workouts and examples supply the coed extra perform within the predictive keep watch over and filtering options awarded
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Extra info for Receding Horizon Control: Model Predictive Control for State Models (Advanced Textbooks in Control and Signal Processing)
31). 40). Depending on Qf , Ki,if may be nonsingular (positive deﬁnite) or singular (positive semideﬁnite). This property will be important for stability and the inversion of the matrix Ki,if in coming sections. 43) is given in the following theorem. 2. 50) r with boundary condition wif ,if = xrT if Qf xif . Proof. 1. Thus, we derive the optimal cost using dynamic programming, where the optimal control and the optimal cost are obtained simultaneously. Let J ∗ (xi+1 ) denote the optimal cost associated with the initial state xi+1 and the interval [i + 1, if ].
27). In the case of controllable systems, Gi0 ,if is guaranteed to be nonsingular if if − i0 is more than or equal to the controllability index nc . 79) It is noted that the open-loop control is deﬁned for all i ∈ [i0 , if − 1]. 80) It is noted that the closed-loop control can be deﬁned only on i that is less than or equal if −nc . After the time if −nc , the open-loop control can be used, if necessary. 3, the regions of the closed- and open-loop control are shown respectively. The above solutions can also be obtained with the formal procedure using the minimum principle, but it is given in a closed form from this procedure.
22) is satisﬁed and the matrix ∂2H ∗ ∗ ∗ (x , u , p , i) ∂u2i i i i+1 is positive deﬁnite, then this is suﬃcient to guarantee that u∗i makes Ja a local minimum. 22) and ∂ 2 H/∂u2i > 0 are necessary and suﬃcient for H(x∗i , u∗i , p∗i+1 , i) to be a global minimum. 9) is equal to zero. 13) is not necessary, which is replaced with xif = xrif . 24) i=i0 where xi ∈ n is the state, ui ∈ m is the input and wi ∈ l is the disturbance. e. ui ∈ U and wi ∈ W. Here, the ﬁxed terminal state is not dealt with because the minimax problem in this case does not make sense.
Receding Horizon Control: Model Predictive Control for State Models (Advanced Textbooks in Control and Signal Processing) by Wook Hyun Kwon, Soo Hee Han