Research On Several Control Optimization Problems Based On Harmony Search Algorithm

With the scales and complexities of modern control systems are increasing,the control index of the system becomes more and more needed.Many control problems with nonlinear,non-convex and NP-hard constraints can be transformed into optimization problems.A number of significant research results are obtained by taking full advantages of Harmony search for the optimization problems in the control engineering.However,due to the inherent of the Harmony Search algorithm and the control problems various features,there are still many problems to be solved.The main contents are outlined as follows:(1)An adaptive global harmony search(AGHS)algorithm for the problem of premature convergence in NGHS algorithm has been proposed in this dissertation.First of all,the diversity of harmony memory is characterized by the norm of differential vector,and the adaptive factor is given based on the diversity of harmony memory which reflects the changes of the harmony memory.Then,a novel position updating strategy is employed in the algorithm with the adaptive factor such that the algorithm generates the new harmony dynamically with the guidance of the diversity of harmony memory,which can avoid the algorithm trapped in local optimal and improves the ability of exploration of the solution space.In this case,the optimal performance of the algorithm has been improved.In addition,the mutation operator of the NGHS algorithm has been ruled out thus the less experience parameters needed,which can improve the applicability of the algorithm.Finally,the simulation is carried out using the optimization algorithm of AGHS and other state-of-the-art HS variants that were reported in the recent literature.The simulation results demonstrate the AGHS algorithm has higher convergence precision and convergence rate.(2)Exact robust pole assignment has been studied in this dissertation and the AGHS algorithm has been proposed to resolve the related optimization problem.First,robust pole assignment for linear system by state feedback has been considered when the state variables are measurable fully.Then,the problem of observer design using estimation of output variables based on robust pole assignment is discussed in detail if the state variables are not measurable.The AGHS algorithm is proposed to resolve the nonlinear optimization problems,in contrast to the classic methods,the information on the gradient and differentiability of the nonlinear function is not needed and the shortage of convex conversion process in condition number optimization has been overcame,and has better global convergence.In addition,it is easy to implement arbitrary pole placement for the linear system using the stochastic optimization approach based on AGHS algorithm,and the closed-loop system show better robustness with the optimization controller.(3)Based on AGHS algorithm,exact robust pole assignment idea has been extended to robust pole assignment in a specified circular region and the problem of optimization design for state observer.For the circular region,the optimal robustness and region robust stability of the closed-loop system has been discussed in detail,and the robust measure index is given,respectively,for the objective.Based on geometric principles,the position information of poles in the circular region is depicted and the rules of dynamic selection of poles from the circular region are determined.This ensures the algorithm select poles dynamically from the circular region.In order to get a set of poles and feedback controller which allow the system to have a maximum allowable perturbation or uncertainty,the upper bound of perturbation or uncertainty is optimized by the AGHS algorithm for the poles in the circular region.On the other hand,the shortage of the approach based on Riccati equation is overcame by the proposed method.In contrast to most existing methods,an optimization method using AGHS algorithm for the dynamic selection of poles,makes the closed-loop system show better robustness.The simulation results demonstrate the effectiveness of the proposed approach.(4)The problems of robust pole assignment in a specified union region and H?control are concerned based on AGHS algorithm.The union region consists of a single circular region or a set of disjoint circular regions.The exact robust pole assignment idea is extended further for this problem.For the poles within the disjoint regions,a sufficient condition for the robust measure index is derived and it ensures the poles of the closed-loop system to remain within the specified union region when the perturbation or uncertainty appears.A new optimation scheme for state feedback controller and H? controller design based on AGHS algorithm is proposed,respectively.For the robust measure index,a set of dynamic poles and the corresponding state feedback controller can be achieved by global dynamic optimization based on AGHS algorithm.In this way,not only the difficult of describing disjoint region for the Riccati equation method has been overcame,but also avoids the problem of high conservative using multiple LMI constraints for disjoint regions.The simulation results illustrate the effectiveness and superiority of the proposed method.(5)Fast control optimization for switched linear systems has been addressed using AGHS algorithm.AGHS algorithm is presented to address the global optimization problem for the fast control performance index in periodic switching law designing,without imposing restrictions on the number of switching,switching time,and the convex combination coefficients.Thus,the NP-hard problem for the combination has been resolved,and the fast control objective can be achieved for the switched linear system which consists of stable subsystems or unstable subsystems,respectively.Under the premise of quadratic stability,the switching law designing becomes relatively simple based on stochastic optimization approach.Finally,the simulation results demonstrate the effectiveness and merits of the proposed method.