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Tham khảo tài liệu 'evolutionary robotics part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 152 Frontiers in Evolutionary Robotics b 50 2 0 c p o -50_ _ . _ _ 0 2 4 6 8 10 No Online adaptation of a k sec 50 0 c p o -50_ _ . _ _ 0 2 4 6 8 10 Online adaptation of a k sec Figure 6. Control signal without the adaptation of the search space a control signal with the adaptation of the search space b sec Figure 7. Online adaptation of gain a k 6.2 The computational delay problem The implementation of a MBPC procedure implies the online optimization of the cost index J at every sampling period Ts. In most of theoretical and simulation studies concerning the MBPC the problems related to the computational delay that is the CPU time Tc required for the numerical optimization of index 1 are seldom taken into account. In the ideal situation Tc 0 the optimal control signal applied in the m-th sampling interval depends directly on the current state x kTs at the same instant. Under this hypothesis the optimal control law is defined by the following function fs úk f fs x kTs u kTs t t mTs m i Ts 19 Although this hypothesis can be reasonable in some particular cases the computational delay is a major issue when nonlinear systems are considered because the solution of a nonlinear dynamic optimization problem with constraints is often computationally intensive. In fact in many cases the computation time Tc required by the optimization Real-Time Evolutionary Algorithms for Constrained Predictive Control 153 procedure could be much longer than the sampling interval Ts making this control strategy not implementable in real-time. Without loss of generality we assume that the computing time is a multiple of the sampling time Tc H Ts 20 where H is an integer. The repetition of the optimization process in each sampling instant is related to the desire of inserting robustness in the MBPC by updating the feedback information at the beginning of each sampling interval Ts before the new optimization is started. Generally the mismatches between system and model cause the prediction .