计及执行器饱和的拟哈密顿系统的非线性随机最优控制
摘要
本论文主要研究了计及执行器饱和的拟Hamilton系统以响应最小为目标的非线性随机最优控制。对于执行器饱和的多自由度拟不可积与完全可积Hamilton系统,先运用随机平均法得到部分平均的It(?)随机微分方程,然后对该方程运用随机动态规划原理建立动态规划方程,最后求解动态规划方程确定最优有界控制力。对执行器饱和的部分观测的非线性系统,用一部分控制力使系统满足Charalambous和Elliott定理的条件,从而将该部分可观测系统的控制问题转化成有限维的完全可观测线性系统的控制问题,再运用随机平均法与动态规划原理确定最优有界控制力。对于滞迟系统,采用Bouc-Wen模型,先将滞迟力分解为等效的非线性弹性力与非线性阻尼力两部分,用分解后的非滞迟非线性系统代替原来的滞迟系统,然后再运用随机平均法与动态规划原理确定滞迟系统的最优有界控制力。对上述各种情形,通过求解Fokker-Planck-Kolmogorov方程得到了控制前后系统响应的概率与统计量。研究结果表明,本文提出的控制策略具有较高的控制效果和控制效率。
The stochastic optimal control for minimizing the response of quasi Hamiltonian systems with actuator saturation is investigated. For multi-degree-of-freedom quasi non-integrable and integrable Hamiltonian systems with actuator saturation, the partially averaged It(o|^) stochastic differential equations are first obtained by using the stochastic averaging method, then the dynamical equation is established by using the stochastic dynamical programming principle, and finally the optimal bounded control law is obtained by solving the dynamical equation. In the case of partially observable nonlinear systems with actuator saturation, the partially observable control problem is first converted into completely observable control problem of linear system of finite dimension by using Charalambous and Elliott theorem. The optimal control law is then obtained by using stochastic averaging method and stochastic dynamical principle. For hysteretic system with actuator saturation, the hysteretic force is represented by using Bouc-Wen model and split into nonlinear elastic restoring force and nonlinear damping force. Then, the original hysteretic system is replaced by a equivalent nonlinear non-hysteretic system. Finally, the optimal control law for hysteretic systems is obtained by using stochastic averaging method and stochastic dynamical principle. For each case, the probability and statistics of the response of uncontrolled and controlled systems are obtained via solving the Fokker-Planck-Kolmogorov equation. Theoretical results are configured by using the results from Monte Carlo simulation and both the two results show that the proposed optimal control strategies are very effective and efficient.
The stochastic optimal control for minimizing the response of quasi Hamiltonian systems with actuator saturation is investigated. For multi-degree-of-freedom quasi non-integrable and integrable Hamiltonian systems with actuator saturation, the partially averaged It(o|^) stochastic differential equations are first obtained by using the stochastic averaging method, then the dynamical equation is established by using the stochastic dynamical programming principle, and finally the optimal bounded control law is obtained by solving the dynamical equation. In the case of partially observable nonlinear systems with actuator saturation, the partially observable control problem is first converted into completely observable control problem of linear system of finite dimension by using Charalambous and Elliott theorem. The optimal control law is then obtained by using stochastic averaging method and stochastic dynamical principle. For hysteretic system with actuator saturation, the hysteretic force is represented by using Bouc-Wen model and split into nonlinear elastic restoring force and nonlinear damping force. Then, the original hysteretic system is replaced by a equivalent nonlinear non-hysteretic system. Finally, the optimal control law for hysteretic systems is obtained by using stochastic averaging method and stochastic dynamical principle. For each case, the probability and statistics of the response of uncontrolled and controlled systems are obtained via solving the Fokker-Planck-Kolmogorov equation. Theoretical results are configured by using the results from Monte Carlo simulation and both the two results show that the proposed optimal control strategies are very effective and efficient.
引文
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