W. E. Schmitendorf and B. R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Contr. Optim., vol. 18, no. 4, pp. 327--345, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....see that local null controllability in the sense of Definition 1 is implied by the apparently weaker condition obtained by letting T depend on x 0 rather than on the neighbourhood V . There is a basic criterion for local null controllability of system (5) which is due to Barmish and Schmitendorf [2, 15]. To state it, we introduce the adjoint homogeneous system (t) y (y 2 R ) 6) where A is the transpose of the matrix A. The Barmish Schmitendorf criterion then goes as follows. Theorem 1 The control system (5) is locally null controllable if and only if there exists a positive number ....

W.E. Schmitendorf and B.R. Barmish, Null controllability of linear systems with constrained controls, SIAM J. Control & Optim., 18 (1980), 327--345.

....paper [28] by E. B. Lee. The necessity conditions for the continuous time case are ussually credited as first appearing in the text by E.B. Lee and L. Markus ( 29] although it was only proved in its full generality in the single input case. The papers of Brammer [5] and Schmitendorf and Barmish [42] removed the assumptions, and the paper by Sontag [44] gave an algebraic approach for both continuous time and discrete time systems. An important component of these works is the extension to more general constraint sets; such a level of generality is not of concern to the problems studied in this ....

W.E. Schmitendorf and B.R. Barmish. Null controllability of linear systems with constrained controls. SIAM J. Control and Optimization, 18(4):327--345, 1980.

....Wing [6, 7, 8] where the K step controllable set is described by its vertices. Later in 1970, Lin [22] introduced the so called facial representation of C(K) which characterizes it in terms of its boundary hyperplanes (faces) From that time on, it became convenient in related control literature [2, 9, 11, 13, 17, 19, 21, 26, 29, 32, 14, 15] to describe C(K) by its vertices or by facial representation which is usually computed via a combination of the Fourier Moltzkin projection algorithm and linear programming techniques used for the elimination of inactive inequalities. As K is increasing the complexity of the controllable set is ....

W. E. Schmitendorf and B. R. Barmish, Null Controllability of Linear Systems with Constrained Control, SIAM Journal of Control and Optimization, 18, pp. 327-345, 1980.

....theory in the past [5] 6] However, their frameworks are different from that of this work. Moreover, unlike the present work, 5] 6] do not provide algorithms for synthesis of controllers. In addition, systems with saturating actuators have been studied in numerous publications (e.g. see [7] [15] but the problem of designing controllers that minimize a quadratic performance index remains open. The present work is intended to contribute to this end. The outline of this paper is as follows: Section 2 gives the problem formulation. Section 3 presents a brief review of the stochastic ....

W. E. Schmitendorf and B. R. Barmish, "Null controllability of linear systems with constrained controls, " SIAM J. Contr. Optim., vol. 18, no. 4, pp. 327--345, 1980.

....On the other hand, it was shown in [16] that a linear system subject to input saturation can be globally asymptotically stabilized by nonlinear feedback if and only if the system in the absence of saturation is asymptotically null controllable with bounded controls. This condition, as shown in [14,15], is equivalent to the system being stabilizable in the usual linear sense and having open loop poles in the closed left half plane. A nested feedback design technology for designing nonlinear globally asymptotically stabilizing feedback laws was proposed in [19] for a chain of integrators of ....

W.E. Schmitendorf and B.R. Barmish. Null controllability of linear systems with constrained controls. SIAM J. Control and Optimization, 18:327--345, 1980.

....of the possible polynomially unstable modes,using bounded inputs. This more general statement was proved for continuous time scalar (m=1) systems in [2] which also gives a proof in the (continuous) case with m 1 but with extra assumptions on A. These assumptions were dropped in [1] see also [5]) One goal of this note is to show that this result can be obtained as a Research supported in part by US Air Force Grant AFOSR 80 0196 2 simple consequence of some general facts (to be developed below) in the module theoretic theory of linear systems together with a rather interesting ....

W.E.Schmitendorf and B.R.Barmish, "Null controllability of linear systems with constrained controls", SIAM J. Control and Opt. 18(1980): 327-345.

....A1. All the eigenvalues of A are located on the closed left half s plane; A2. The pair (A; B) is stabilizable; A3. The pair (A; C) is detectable. Remark 2.1. We should point out that assumptions A1 and A2 are equivalent to the notion of asymptotic null controllability that was introduced in [8] and [9] Before stating the problem at hand, we have the following definitions. Definition 2.1. Semi global exponential stabilization via linear static state feedback) The system (2.1) 2.2) is semi globally exponentially stabilizable by linear static state feedback if for any a priori given ....

W.E. Schmitendorf and B.R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Control and Optimization, vol. 18, pp. 327-345, 1980.

....On the other hand, it was shown in [18] that a linear system subject to input saturation can be globally asymptotically stabilized by nonlinear feedback if and only if the system in the absence of saturation is asymptotically null controllable with bounded controls. This condition, as shown in [16,17], is equivalent to the system being stabilizable in the usual linear sense and having open loop poles in the closed left half plane. A nested feedback design technology for designing nonlinear globally asymptotically stabilizing feedback laws was proposed in [21] for a chain of integrators of ....

W.E. Schmitendorf and B.R. Barmish. Null controllability of linear systems with constrained controls. SIAM J. Control and Optimization, 18:327--345, 1980.

....min j=1; n Gamma w ij h j (x j ) 8 x j 2 R Delta ; max j=1; n Gamma w ij h j (x j ) 8 x j 2 R Delta ; i = 1; n Psi . If V does not contain the origin, then the additive networks in Equation (12) do not satisfy any of the global controllability theorems discussed in Schmitendorf and Barmish (1980). For example, this would occur if w ij 0 and h i (x i ) 1 1 e GammaG i x i . 4 Simulation Results Now an example is presented in which the parameters of the additive network in Equation (12) are learned, using the training rule in Equations (7) and (8) The trajectories used for training ....

Schmitendorf, W., & Barmish, B. (1980). Null controllability of linear systems with constrained controls. SIAM Journal of Control and Optimization, 18 (4), 327--345.

....significant results have emerged. The main focus have been on global and semiglobal stabilization of linear systems, and in particular null controllable systems. Null controllable systems have, in addition to the usual stabilizability property, eigenvalues with non positive real part, see e.g. [7]. In general, null controllable systems are not globally stabilizable by bounded linear control laws. This fact was pointed out in [2] However, in [10] it was shown that an integrator chain of length n can be globally stabilized by bounded input using nonlinear controllers. This result was later ....

W. E. Schmitendorf and B. R. Barmish. Null Controllability of Linear Systems with Constrained Controls. SIAM Journal on control and optimization, 18:327--345, 1980.

....of the associated linear system x = Ax Bu subject to constraints on control values; one needs that this system be asymptotically null controllable using arbitrarily small controls. The theory of controllability of linear systems with bounded controls is well studied; see for instance [3], 5] and references there, for the above characterization. Note that there may be nontrivial Jordan blocks in A corresponding to critical eigenvalues, so the system x = Ax may be unstable; this makes the problem more interesting. We only look at global problems; local stabilization can always ....

Schmitendorf, W.E. and B.R. Barmish, "Null controllability of linear systems with constrained controls, " SIAM J. Control and Opt. 18(1980): 327345.

.... part, and (b) all eigenvalues of the uncontrollable part of Sigma have strictly negative real parts (that is, the pair (A; B) is stabilizable in the ordinary sense) The theory of controllability of linear systems with bounded controls is a well studied topic; see e.g. the fundamental paper [5], as well as the different, more This research was supported in part by US Air Force Grants 91 0343 and 91 0346 and by NSF Grants DMS 8902994 and DMS92 02554. algebraic approach discussed in [8] Note that under Conditions (a) and (b) there may very well be nontrivial Jordan blocks ....

Schmitendorf, W.E. and B.R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Control and Opt. 18(1980): 327-345.

.... with positive real part, and (ii) the pair (A; B) is stabilizable in the ordinary sense (i.e. all the uncontrollable modes of 6 have strictly negative real parts) The theory of controllability of linear systems with bounded controls is a well studied topic; see e.g. the fundamental paper [6], as well as the different, more algebraic approach discussed in [9] Notice that under Condition (ANCBC ) there may very well be nontrivial Jordan blocks corresponding to critical eigenvalues, so the system x = Ax need not be asymptotically stable or even Lyapunov stable. This is what makes the ....

Schmitendorf, W.E. and B.R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Control and Opt. 18(1980): 327-345.

No context found.

W. E. Schmitendorf and B. R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Contr. Optim., vol. 18, no. 4, pp. 327--345, 1980.

No context found.

W.E. Schmitendorf and B.R. Barmish, Null controllability of linear systems with constrained controls, SIAM J. Control and Optimization, vol. 18, pp. 327-345, 1980.

No context found.

W.E. Schmitendorf and B.R. Barmish, Null controllability of linear systems with constrained controls, SIAM J. Control and Optimization, vol. 18, 1980, pp. 327-345.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC