Receding Horizon Control: Model Predictive Control for State by Wook Hyun Kwon, Soo Hee Han
By Wook Hyun Kwon, Soo Hee Han
Easy-to-follow studying constitution makes absorption of complex fabric as pain-free as attainable Introduces whole theories for balance and value monotonicity for restricted and non-linear platforms in addition to for linear structures In co-ordination with MATLAB® records on hand from springeronline.com, routines and examples supply the scholar extra perform within the predictive keep watch over and filtering strategies offered
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Extra resources for Receding Horizon Control: Model Predictive Control for State Models (Advanced Textbooks in Control and Signal Processing)
142) respectively. The derivation for hi,if is left as an exercise. 149) is nonnegative. To conclude, the solution of the HTC problem can be reduced to ﬁnding Mi,if and gi,if for i = i0 , · · · , if − 1. 141). 143). e. 150) look like an LQ solution. 147). 151) It is noted that Mi,if is obtained from Ki,if of the LQ control by replacing BR−1 B T by Π. 156) with Here, Qf must be nonsingular. 157) which is required for the existence of the saddle-point. 136) may not be satisﬁed. That is why the terminal equality constraint for case of the RH H∞ control does not make sense.
167). We are now in a position to ﬁnd out the mean of p(xi |Yi ). 168) to zero. 175) Pi+1|i can be obtained recursively from the error dynamic equations. 176) where x ˜i|i = x ˆi|i − xi and x ˜i|i−1 = x ˆi|i−1 − xi . 178) 52 2 Optimal Controls on Finite and Inﬁnite Horizons: A Review The initial values x ˆi0 |i0 −1 and Pi0 |i0 −1 are given by E[xi0 ] and E[(ˆ xi0 − xi0 − xi0 )T ], which are a priori knowledge. 180) with the given initial condition Pi0 . 179) is used instead of Pi|i−1 . Throughout this book, we use the predicted form x ˆi|i−1 instead of ﬁltered ˆi|i−1 will be denoted by x ˆi if necessary.
50). e. 62) Now, we have only to ﬁnd the boundary value of gi,if and wi,if . J ∗ (xif ) should be equal to the performance criterion for the ﬁnal state. Thus, wif ,if and gif ,if r r should be chosen as wif ,if = xrT if Qf xif and gif ,if = −Qf xif so that we have J ∗ (xif ) = xTif Kif ,if xif + 2xTif gif ,if + wif ,if r = xTif Qf xif − 2xTif Qf xrif + xrT if Qf xif = (xif − xrif )T Qf (xif − xrif ) This completes the proof. 2 will be utilized only for zero reference signals in subsequent sections.