控制与决策
控製與決策
공제여결책
CONTROL AND DECISION
2013年
1期
49-54
,共6页
Markov 跳跃非线性系统%风险灵敏度控制%积分反推
Markov 跳躍非線性繫統%風險靈敏度控製%積分反推
Markov 도약비선성계통%풍험령민도공제%적분반추
Markovian jump nonlinear systems%risk-sensitive control%integrator backstepping
在无限时区风险灵敏度指标下,研究了一类具有严格反馈形式的 Markov 跳跃非线性系统的控制器设计问题.首先,将此问题的可解性转化为一类 HJB 方程的可解性;然后根据此方程,构造性地给出一个与模态无关的控制器,此控制器可保证闭环系统是依概率有界的,且风险灵敏度指标不大于任意给定的正常数,特别地,当噪声项在原点处消逝时,能够确保风险灵敏度指标为零;最后,通过仿真例子验证了理论结果的正确性.
在無限時區風險靈敏度指標下,研究瞭一類具有嚴格反饋形式的 Markov 跳躍非線性繫統的控製器設計問題.首先,將此問題的可解性轉化為一類 HJB 方程的可解性;然後根據此方程,構造性地給齣一箇與模態無關的控製器,此控製器可保證閉環繫統是依概率有界的,且風險靈敏度指標不大于任意給定的正常數,特彆地,噹譟聲項在原點處消逝時,能夠確保風險靈敏度指標為零;最後,通過倣真例子驗證瞭理論結果的正確性.
재무한시구풍험령민도지표하,연구료일류구유엄격반궤형식적 Markov 도약비선성계통적공제기설계문제.수선,장차문제적가해성전화위일류 HJB 방정적가해성;연후근거차방정,구조성지급출일개여모태무관적공제기,차공제기가보증폐배계통시의개솔유계적,차풍험령민도지표불대우임의급정적정상수,특별지,당조성항재원점처소서시,능구학보풍험령민도지표위령;최후,통과방진례자험증료이론결과적정학성.
The controller design for a class of strict-feedback nonlinear stochastic systems with Markovian jump under a risk-sensitive cost function criterion is studied. Firstly, this problem is solvable if a class of HJB equation is solvable. Then, a constructive control law, which is independent of the regime, is designed based on this HJB equation, which guarantees any desired positive level of long-term average cost for a given risk-sensitivity parameter and achieve boundedness in probability for the closed-loop system. As a special case, when the vector fields for the disturbance vanish at the origin, the control law can actually guarantee a zero long-term average cost for the closed-loop system. Finally, an example is given to illustrate the correctness of the main results.
