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<p>This paper considers optimal feedback control of probability path-constrained nonlinear dynamical systems (PPCNDSs). To begin with, optimal feedback control of PPCNDSs is rewritten and approximated by a deterministic constrained parameter optimization problem (POP) by utilizing an adaptive sample technique. Following that, a dual-performance index optimization-based matrix adaptation evolutionary algorithm (DPIO-MAEA) is proposed for the resulting deterministic constrained POP based on equivalent and auxiliary performance indexes (EAPIs), a matrix adaptation evolutionary algorithm and an adaptive weight parameter regulation strategy. Compared with existing algorithms, the constraint-handling scheme in DPIO-MAEA is simpler because it only need to minimize EAPIs without requiring the gradient information and any specific constraint-handling schemes. This indicates that the performance of DPIO-MAEA can be effectively improved. Further, convergence results for DPIO-MAEA is established and it is theoretically demonstrated that utilizing auxiliary performance indexes can effectively reduce the possibility of premature convergence. Finally, numerical results on twenty-four test functions from IEEE CEC 2017 and a hang glider optimal flight problem shows that compared with other meta-heuristics, DPIO-MAEA can obtain a better solution with smaller standard deviation and less computational cost.</p>

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Dual-performance index optimization-based matrix adaptation evolutionary algorithm for optimal feedback control of probability path-constrained nonlinear dynamical systems

  • 期刊论文

  • 发表日期：

    2025年5月25日

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  • Xiang Wu,
  • Xiaolan Yuan,
  • Haozheng Meng,
  • Qunxian Zheng,
  • Xiaojiao Zhang

摘要

This paper considers optimal feedback control of probability path-constrained nonlinear dynamical systems (PPCNDSs). To begin with, optimal feedback control of PPCNDSs is rewritten and approximated by a deterministic constrained parameter optimization problem (POP) by utilizing an adaptive sample technique. Following that, a dual-performance index optimization-based matrix adaptation evolutionary algorithm (DPIO-MAEA) is proposed for the resulting deterministic constrained POP based on equivalent and auxiliary performance indexes (EAPIs), a matrix adaptation evolutionary algorithm and an adaptive weight parameter regulation strategy. Compared with existing algorithms, the constraint-handling scheme in DPIO-MAEA is simpler because it only need to minimize EAPIs without requiring the gradient information and any specific constraint-handling schemes. This indicates that the performance of DPIO-MAEA can be effectively improved. Further, convergence results for DPIO-MAEA is established and it is theoretically demonstrated that utilizing auxiliary performance indexes can effectively reduce the possibility of premature convergence. Finally, numerical results on twenty-four test functions from IEEE CEC 2017 and a hang glider optimal flight problem shows that compared with other meta-heuristics, DPIO-MAEA can obtain a better solution with smaller standard deviation and less computational cost.