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This paper proposes a Genetic Programming based algorithm that can be used to design optimal controllers. The proposed algorithm will be named a Multiple Basis Function Genetic Programming (MBFGP). Herein, the main ideas concerning the initial population, the tree structure, genetic operations, and other proposed non-genetic operations are discussed in details. An optimization algorithm called numeric constant mutation is embedded to strengthen the search for the optimal solutions. The results of solving the optimal control for linear as well as nonlinear systems show the feasibility and effectiveness of the proposed MBFGP as compared to the optimal solutions which are based on numerical methods. Furthermore, this algorithm enriches the set of suboptimal state feedback controllers to include controllers that have product time-state terms.
The mathematical model of hydraulic drive unit of quadruped robot was built in this paper. According to the coupling characteristics between position control system and force control system, the decoupling control strategy was realized based on diagonal matrix method in AMESim?. The results of simulation show that using diagonal matrix method can achieve the decoupling control effectively and it can achieve the decoupling control more effectively with the method of not offset pole-zero in the S coordinate. This research can provide theoretical basis for the application of test system of hydraulic drive unit.