Page - 31 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2.4. ACC Controller Here, the new matrices are defined as F=        C Ae C A2e C A3e ... C A Np e        and (2.37) Φ=        C b 0 0 · ·· 0 C Aeb C b 0 · ·· 0 C A2eb C Aeb C b · ·· 0 ... ... ... ... ... C A Np−1 e b C A Np−2 e b C A Np−3 e b · ·· C ANp−Nce b        . (2.38) The cost function is defined as Jk= (Ydes,k−Yk)T(Ydes,k−Yk)+∆UTk R ∆Uk, (2.39) where the vector containing the desired output reads Ydes,k= [ I(m×m) I(m×m) · ·· ]T ydes,k. (2.40) The size of the identity matrix I is (m×m), wherem is the number of outputs of the system (i.e. the number of rows ofy). The matrixRweights the right part of eq. (2.39), which contains the change of the control variable to the left part, which describes the error of the output. Entering eq. (2.36) in the cost function of eq. (2.39), the optimal solution can be found by minimizing J. Therefore, the necessary condition is that the first derivative of J with respect to ∆Uk equals 0. Solving this equation, the optimal control variable reads ∆Uk= ( ΦTΦ+R )−1 ΦT(Ydes,k−F ek) . (2.41) Performing this optimization by solving eq. (2.41) is fast compared to a numerical opti- mization. The first component of ∆Uk is passed to the lower level controller. As already mentioned above, the MPC is able to include constraints, such as limiting the desired acceleration to a minimum and a maximum, amin ≤ uk ≤ amax. This limitation results in a system of 2Nc inequalities because they have to be a function of thecomponentsof∆Uk. Thisoptimizationproblem,whichcannotbesolvedanalytically, increases the computation time. 2.4.3.3. Fuzzy Control The main advantage of the Fuzzy Controller is that it can be designed without exact knowledge of the plant, [Ada09a]. As a first step, linguistic labels are assigned to fuzzy 31