(復雜系統(tǒng)的性能評價與優(yōu)化課件資料）lqg_pb

1、( (復雜系統(tǒng)的性能復雜系統(tǒng)的性能評價與優(yōu)化課件評價與優(yōu)化課件資料）資料）lqg_pblqg_pb6DP Approach (cont.)SetWe haveLetandThen 111u NiBNiNi M NiNx Ni 00iNuiNxJiN iNAiNiNMiNiNST1 iNxiNSiNxiNxJTi210N 111111iNSiNiNiNSiNiNBiNiNSiNSiNMTT7DP Approach (cont.)By induction, we have the optimal solution to bewhereand with boundary conditionwith

2、111Tu iBii M iNx i iAiiMiiST1 NANSN 11111111iSiiiSiiBiiSiSiMTT0,.,1 Ni8Static Statesubject to state transitionwith initial conditionwhereand is noise ixix1 00 x ixiz NixxizJ0221minN9Static State (cont.)Set Thus, 00Nixiz0 xJ NiizNx011N10Static State (cont.)New Estimate = Old Estimate + Confidence Fac

3、tor Correction Term 1111111izijziiiixij 1111iziixii Term CorrectionFactor Confidence111ixiziixN11Dynamic Statesubject to state transition with disturbance (i)where and is noise iixix1 NiNiixixizixJ0210222121021min ixizN12Dynamic State (cont.)Cost-to-goSetwhereWe haveN 220000021021min0 xzxxJx 0000 xJ

4、 002100210 xzxzx 0410200zxJ 00 x13Dynamic System (cont.)Cost-to-goSubstitute 0411121021min01121021min122210022101zxzxJxzxJxx 010 xx 04111210121min1222101zxzxxxJxN14Dynamic System (cont.)SetLet Then, we have 0101xJ 012102011xzxxzx 01xx 112111xzxxN15Dynamic System (cont.)Cost-to-goSubstitute 12121min0

5、1220ixJixiziixJiixi 1 ixixi 121121min01220ixJixizixixixJiixiN16Dynamic System (cont.)SetLet and Then, we have 00ixJi 121121ixizixixizix 1ixix ixizixix21 00 xN17With Controlsubject to state transitionwith disturbance (i)where and is noise iwiuixix1N ixiz NiNiixixizixJ0210222121021min18With Control (c

6、ont.)Cost-to-goSetWe haveN 220000021021min0 xzxxJx 0000 xJ 0210zx 0410200zxJ19With Control (cont.)Cost-to-goSubstitute 0411121021min01121021min122210022101zxzxJxzxJxx 0010uxx 041112100121min1222101zxzuxxxJxN20With Control(cont.)SetLet Then, we have 0101xJ 001210020011uxzuxuxzx 001uxx 112111xzxxN21Wi

7、th Control(cont.)Cost-to-goSubstitute 12121min01220ixJixiziixJiixi 11iuixixi 1211121min01220ixJixiziuixixixJiixiN22With Control(cont.)SetLet andThen, we have 00ixJi 112111211iuixiziuixiuixizix 11iuixix ixizixix21N 00 x23Linear Feedback ControlThe predicted statewith initial statebased on the estimat

8、or112111ixHizixix 11iuixix 00 xxN24Linear Feedback Control (cont.)Optimal control based on the estimated state:whereandwith boundary conditionwithN ixiSNiMiiBiuT111 iAiiMiiST1 NANS0,.,1 Ni 11111111iSiiiSiiBiiSiSiMTT25ApplicationsApollo program: control of the space craft.Airplane controllers: autopilot.Neighboring Optimal Control for Non-Linear SystemsChemical process controllerGuidance and controlN26References: Bryson, Jr., A. E. and Y.-C. Ho, Applied O