By Peter S. Maybeck
This quantity builds upon the rules set in Volumes 1 and a couple of. bankruptcy thirteen introduces the fundamental thoughts of stochastic keep watch over and dynamic programming because the basic technique of synthesizing optimum stochastic regulate legislation.
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Extra info for Stochastic models, estimation and control. Volume 3
Looking at the vehicle head-on as in Fig. 12, if the vehicle generates a larger amount of lift force, we maintain the desired amount of vertical force by rolling the vehicle by the appropriate roll angle 4, thereby generating a horizontal component of lift available for lateral maneuvering. Thus, the total lift is determined by vehicle and trajectory characteristics, and its vertical component and thus 141 by down-range distance to the landing site: these are not at our disposal to change. Lateral control then entails deciding when to switch from ( 141)to ( - 141)or vice versa.
DYNAMIC PROGRAMMING AND STOCHASTIC CONTROL One statement of this principle is “Whatever any initial states and decision [or control law] are, all remaining decisions must constitute an optimal policy with regard to the state which results from the first decision” . 5 To appreciate the fundamental concept of the “optimality principle” and dynamic programming, consider a scalar-state, scalar-control problem lasting two sample periods, assuming that perfect knowledge of the current state x(t,) is available.
If we could accomplish this for the range of possible values of Zj, we could specify the function u*[-,rj] which, when given any particular history of measurements Zj, could be evaluated to yield the optimum r-vector of controls to apply to the system. e.. a function that accepts an argument Zj from mj-dimensional Euclidean space and an argument t j from a time set T , to yield an r-dimensional control vector. It is this function that we seek as a solution to the stochastic optimal control problem.
Stochastic models, estimation and control. Volume 3 by Peter S. Maybeck