状态右端受限的滞后控制系统的最优控制*
The Optimal Control of Delay Control Systems with Restricted State Right Endpoint
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摘要: 本文对非线性滞后控制系统x(t)=f[x(t),x(t-1),u(t),t] t∈[t0,t1] x(t)=φ(t) t∈[t0,t1]就其状态右端x(t1)在 φk=[x(t1)]=0(k=1,2,…,l)的限制条件下,给出最大值原理.作为特例,还将给出在部分状态变量右端完全固定的情况下的最大值原理.最后举例说明主要结果的应用.Abstract: In this paper, for the delay control system:x(t)=f[x(t),x(t-1),u(t),t] t∈[t0,t1] x(t)=φ(t) t∈[t0,t1] with State right endpoint restricled by condition φk=[x(t1)]=0(k=1,2,…,l) a maximum principle is given. And as a specificexample. this paper gives a maximumprinciple under the condition that partial states right endpoints be completely fixed.Finally, this paper gives an example to explain the application of the main result ofthis paper. All the results are suitable for the control systems with multidelay as well.
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Key words:
- delay control system /
- restricted state right endpoint /
- maximum principle
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[1] 谢绪恺,《现代控制理论基础》,辽宁人民出版社,沈阳(1981). [2] 王照林,《现代控制理论基础》,国防工业出版社,北京(1981). [3] D,H,Chyung and E,Brucelee,Linear optimal systems with time delays,J.Siam Control,4(3)(1966),548-575. [4] 刘永清、唐功友,《大型动力系统的理论与应用》(卷3),华南理工大学出版社,广州(1992).
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