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26 March 1983, Volume 3 Issue 1 Previous Issue    Next Issue

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TWO OPTIMAL CONTROL PROBLEM OF LINEAR DISCRETE-TIME SYSTEM Wang Yaoyuan Acta mathematica scientia,Series A. 1983, 3 (1):  87-98.  Abstract ( 78 )   RICH HTML PDF (553KB) ( 15 )   Save In[1] the optimal stochastic control problem of linear discrete-time system is discussed when the state noise has no delay.In[2] the optimal stochastic control problem is discussed when the state noise has a delay and the noise is independent of the measurement noise.The paper composes of two parts.In §1 the stochastic control problem is discussed when the system contains non-stochastic input (the system with the state noise for which mean value is not zero can be transformed into this case) and the state noise is mutually dependent on the measurement noise In §2 the filter and the optimal stochastic control problem is discussed with the Moor-Penrose inverse when the state noise and the measurement noise are one-step correlated.In this paper the optimal control law is given which coincides with the separation principle. Related Articles | Metrics

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CONTINUOUS-TIME STOCHASTIC APPROXIMATION UNDER MEASUREMENT ERROR BEING PROCESS OF DEPENDENT INCREMENT Chen Hanfu Acta mathematica scientia,Series A. 1983, 3 (1):  99-112.  Abstract ( 62 )   RICH HTML PDF (676KB) ( 60 )   Save If the accurate value of a function h(·) is available at any point then there are many numerical methods recursively estimating the root of the regression equation h(·)=0.But the measurement is usually disturbed by random errors.In this case how can the root of h(·) be found out? This is just the problem investigated by stochastic approximation. Related Articles | Metrics

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THE GENERALIZED SINE-GORDEN EQUATIONS AND THEIR GEOMETRIC ASPECTS Chen Zuxi, Qian Chunlin Acta mathematica scientia,Series A. 1983, 3 (1):  113-119.  Abstract ( 55 )   RICH HTML PDF (321KB) ( 22 )   Save The work on "Lie group and KDV equations" has been done in[1].From the structure equations of certain Lie Group,a class of evolution equations of Sine-Gorden type may be achieved.In this paper from a new viewpoint introduced in[2],we will derive a class of evolution equations of Sine-Gorden type.Furthermore we have given geometric interoretations for our evolution equations of Sine-Gorden type.The evolution equations of Sine-Gorden type which have been got in[3]are a special class of our paper. Related Articles | Metrics