D.D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automat. Contr., AC-14 (1969) 9-14.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and risk sensitive control. Here denotes the derivative of and denotes the transpose of while are bounded and measurable matrix functions on , EEFU8 8# 0 and is a linear map that arises from the presence of state dependent and or jump noise in the C state equation; see [1] 2] 9] 13] 14] [12]. Equation (1) plays a central role in these problems because the existence of its solution in an interval determines the solutions to these problems in M horizon . It is well known that the solution to (1) may blow up at some point ; that is, MT ab T T # ababsatisfies the equation (1) ....

D.D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automat. Contr., Vol. AC-14 (1969) 9-14.

....(1) with . C oe For a derivation, see [3] 5] 7] 27] or Theorem 1 below. The inclusion of the term is important for C application of (1) to stochastic control problems with Markovian jumping noises and differential game problems with noises depending on both of state and control; see [23] and [16] for example. Although the term may be considered as a part of , we will keep them separated for generality. GTGT Cab Readers who are interested in the equation associated with problem (3) may assume that . C oe Riccati equations (differential, difference and algebraic) appear in ....

D.D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automat. Contr., Vol. AC-14 (1969) 9-14.

....aircraft control systems, large flexible structures for space stations (such as antenna, solar arrays) etc. Several authors have analyzed different aspects of such a class and some successful applications have, in part, spurred a considerable interest on it (see, e.g. 3] 5] 8] 12] 13] [17] [19] 22] and the references therein) In particular with regard to the filtering problem, minimum variance filtering schemes for discrete time systems have been studied in, for instance, 3] 4] 18] and [22] To the best of the authors s knowledge, to date the problem of H1 filtering for ....

D.D. Sworder, "Feedback control for a class of linear systems with jump parameters," IEEE Trans. Automat. Control , Vol. AC-14, pp. 9-14, 1969.

....of the two. Systems of this form arise in various applications and system formulations, such as power systems [1] target tracking [2] and fault tolerant control system [3, 2] Control of hybrid systems where the modal variable is modeled as a random process has been studied by many authors. In [4] a theory for linear hybrid systems with a Markovian jump parameter (modal variable) is developed and it is shown that an optimal state feedback control law in the case of a quadratic cost functional is given by a system of coupled Riccati equations. In [2] the theory for jump linear systems with ....

D.D. Sworder, "Feedback Control of a Class of Linear Systems with Jump Parameters," IEEE Transactions on Automatic Control 14 (1969), pp. 9-14.

....a certain version of a gradient concept and, from this, the linear approximation to nonholomorfic functionals. With such a tool in hand, weareallowed to conveniently specify the above infinitesimal generator. There is nowadays an extensive theory surrounding MJLS. An initial trickle of papers ([26], 28] soon grew to a considerable amount (see, e.g. 2] 3] 5] 7] 14] 16] 17] 19] 20] 23] 26] 28] and references therein) with a sober eyetowards applications, as befits a maturing field (see, e.g. 4] 18] 22] 23] 26] and references therein) Potential ....

....such a tool in hand, weareallowed to conveniently specify the above infinitesimal generator. There is nowadays an extensive theory surrounding MJLS. An initial trickle of papers ( 26] 28] soon grew to a considerable amount (see, e.g. 2] 3] 5] 7] 14] 16] 17] 19] 20] 23] [26], 28] and references therein) with a sober eyetowards applications, as befits a maturing field (see, e.g. 4] 18] 22] 23] 26] and references therein) Potential applications include, inter alia, safety critical and high integrity systems (e.g. aircraft, chemical plants, nuclear power ....

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Sworder, D.D., Feedbackcontrol for a class of linear systems with jump parameters, IEEE Trans. Automat. Control AC-14 (1969), 9-14.

....are stochastic controlled processes that evolve according to a deterministic dynamic except at some stochastic time where a stochastic jump of the state variable occurs. For three decades, PDCS have been the object of considerable investigation in Control Theory (see for example [9] 10] 19] [20] and [21] They ooeer a wide variety of applications for the modeling of industrial and economic processes; we can quote, amongst other things, manufacturing (see e.g. 5] 2] and [14] optimal exploration and consumption of renewable and non renewable resources [12] permanent health insurance ....

D. D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Transactions on Automatic Control, 14 (1969), pp. 914.

....by given transition probability rates. Such stochastic models, referred to as jump linear systems in the following, have been studied extensively since the work of Krasovskii and Lidskii [13] Most contributions deal with the optimal control problem, see for instance the work of Sworder [21, 22] , Wonham [24] Mariton and Bertrand [16, 15] Caines and Chen [5] Ji and Chizeck [11, 12] Rishel and Harris [20] Hopkins [10] In general, the optimal control problem is reduced to finding a solution to a set of nonstandard, coupled Internet: elghaoui ensta.fr y Internet: ....

....1:3 1:7 0 0 0 3 7 7 5 ; Pi 0 = 2 4 Gamma2:24 1:792 0:448 3:36 Gamma5:04 1:68 2:24 1:96 Gamma4:2 3 5 : First, we consider the stabilization problem for the nominal transition probability matrix Pi 0 , using a mode dependent control law. We have used the JLQ approach of Refs. [21, 24, 12] (all ponderations matrices are taken equal to the identity) We have solved a set of coupled Riccati equations, using the method of Ref. 2] implemented with the software of Refs. 23, 6] This provides the following stabilizing, mode dependent control law K 1 = Theta Gamma3:9706 ....

D. D. Sworder. Feedback control of a class of linear systems with jump parameters. IEEE Trans. Aut. Control, 14(1):9--14, February 1969.

....by given transition probability rates. Such stochastic models, referred to as jump linear systems in the following, have been studied extensively since the work of Krasovskii and Lidskii [10] Most contributions deal with the optimal control problem, see for instance the work of Sworder [18, 19], Wonham [21] Mariton and Bertrand [13, 12] Caines and Chen [4] Ji and Chizeck [8, 9] Rishel and Harris [17] Hopkins [7] In general, the optimal control problem is reduced to finding a solution to a set of coupled Riccati equations. Several algorithms have been devised for solving this kind ....

D. D. Sworder. Feedback control of a class of linear systems with jump parameters. IEEE Trans. Aut. Control, 14(1):9--14, February 1969.

....are stochastic controlled processes that evolve according to a deterministic dynamic except at some stochastic time where a stochastic jump of the state variable occurs. For three decades, PDCS have been the object of considerable investigation in Control Theory (see for example [9] 10] 19] [20] and [21] They offer a wide variety of applications for the modeling of industrial and economic processes; we can quote, amongst other things, manufacturing (see e.g. 5] 2] and [14] optimal exploration and consumption of renewable and non renewable resources [12] permanent health insurance ....

D. D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Transactions on Automatic Control, 14 (1969), pp. 9--14.

....Studies, Universit e de Gen eve, 102 boulevard Carl Vogt, 1211 Gen eve 4, Switzerland. 1 Introduction Piecewise deterministic control systems (PDCS) offer an interesting paradigm for the modeling of many industrial and economic processes. The theory developed by Wonham [26] or Sworder [24] for linear quadratic systems, Davis [7] Rishel [19, 20] and Vermes [25] for more general cases, has established the foundations of a dynamic programming (DP) approach for the solution of this class of problems. There are two possible types of DP equations that can be associated with a PDCS: i) ....

D.D. Sworder. Feedback control of a class of linear systems with jump parameters. IEEE, Trans. Aut. Control, AC-14(1):9--14, 1969.

....will be understood to be predictable versions of the associated right continuous, random processes (e.g. # i is actually the inner product e # i # t in (2) # is the Hadamard product ( x # y) i = x i y i ) 2 error. For such systems a quadratic optimal control can be easily determined [Swo69]: u t = X i K i # i x t (3) where the gains K i ; i # S satisfy a set of ordinary di#erential equations. Equation (3) is a type of gain scheduling in which the controller parameters are calculated at a number of operating conditions using some suitable design method. The controller is ....

D.D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automatic Control 14 (1969), no. 1, 9--14. 16

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D.D. Sworder, Feedback control of a class of linear systems with jump parameters, IEEE Trans. Automat. Contr., AC-14 (1969) 9-14.

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SWORDER,D.D.(1969): "Feedback control of a class of linear systems with jump parameters." IEEE Transactions on Automatic Control, 14:1, pp. 9--14.

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Sworder, D.D., "Feedback Control of a Class of Linear Systems with Jump Parameters ", IEEE, Trans. Aut. Control, Vol. AC-14, No 1, pp.9-14, 1969.

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