By Basil Kouvaritakis, Mark Cannon
For the 1st time, a textbook that brings jointly classical predictive keep an eye on with remedy of updated powerful and stochastic techniques.
Model Predictive keep an eye on describes the advance of tractable algorithms for doubtful, stochastic, restricted platforms. the place to begin is classical predictive keep watch over and the right formula of functionality pursuits and constraints to supply promises of closed-loop balance and function. relocating directly to powerful predictive keep watch over, the textual content explains how related promises should be received for instances within which the version describing the procedure dynamics is topic to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are thought of and the state-of-the-art in computationally tractable equipment in accordance with uncertainty tubes offered for platforms with additive version uncertainty. ultimately, the tube framework can also be utilized to version predictive keep an eye on difficulties related to demanding or probabilistic constraints for the circumstances of multiplicative and stochastic version uncertainty. The ebook provides:
- extensive use of illustrative examples;
- sample difficulties; and
- discussion of novel keep watch over purposes reminiscent of source allocation for sustainable improvement and turbine-blade keep an eye on for maximized energy catch with concurrently decreased danger of turbulence-induced damage.
Graduate scholars pursuing classes in version predictive keep watch over or extra quite often in complicated or approach keep watch over and senior undergraduates short of a really good remedy will locate Model Predictive regulate an valuable advisor to the cutting-edge during this very important topic. For the teacher it offers an authoritative source for the development of courses.
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Extra info for Model Predictive Control: Classical, Robust and Stochastic
As in Sect. 9 requires that there exists a symmetric matrix H such that Pz , Ac and Cc satisfy ⎡ ⎣ Pz − ⎤ H F + G K GCc ⎦ (F + G K )T Pz T (GCc ) T Pz 0 0, eiT H ei ≤ 1, i = 1, . . n C . 11 again apply. Using Ez as the constraint set in the online optimization in place of Z reduces the region of attraction of the MPC law. However, to compensate for this effect it is possible to design the prediction system parameters Ac and Cc so as to maximize the projection of Ez onto the x-subspace. 59b). 9 Optimized Prediction Dynamics 49 the case considered in Sect.
This uses an input–output model to express the vector of output predictions as an affine function of the vector of predicted inputs ⎤ ⎤ ⎡ y1|k Δu 0|k ⎥ ⎥ ⎢ ⎢ f .. yk = ⎣ ... ⎦ = C G Δuk + yk , Δuk = ⎣ ⎦ . y N |k Δu Nu −1|k ⎡ Here Nu denotes an input prediction horizon which is chosen to be less than or equal to the prediction horizon N . The matrix C G is the block striped (Toeplitz) lower 52 2 MPC with No Model Uncertainty triangular matrix comprising the coefficients of the system step response, C G Δuk f denotes the predicted forced response at time k, and yk denotes the free response at time k due to non-zero initial conditions.
27b). The stage cost (namely the part of the cost incurred at each prediction time step) has the general form x 2 Q + u 2 R = x 2 Q + Kx + c = z 2 , Qˆ 2 R = x T (Q + K T R K )x + c T E T R Ec Q + K T RK K T RE . 1, W is the (positive-definite) solution of the Lyapunov equation W = T W ˆ + Q. 34) The special structure of and Qˆ in this Lyapunov equation implies that its solution also has a specific structure, as we describe next. 27b) can be written as ⎡ J (xk , ck ) = xkT Wx xk + ckT Wc ck B T Wx B + R 0 ··· 0 TW B + R ··· ⎢ 0 B 0 x ⎢ Wc = ⎢ ..