Sontag E.D. and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3414--3416, 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are nowwelladdressed for linear systems that are not exponentially unstable. For example, it is well known [2, 8] that such systems are globally null controllable with bounded controls as long as they are controllable in the usual linear system sense. In regard to stabilizability, it is shown in [9] that a linear system subject to actuator saturation can be globally asymptotically stabilized by smooth feedback if and only if the system is asymptotically null controllable with bounded controls (ANCBC) which, as shown # #### ######### ## #### ## ### ## ### ## ##### ######## ##### ....

E.D. Sontag and H.J. Sussmann, \Nonlinear output feedback design for linear systems with saturating controls," ##### #### #### ##### ######## ### ######## pp. 3414-3416, 1990.

....to obtain global stabilization. For systems with poles on the Research supported by the Army Research Office under grant DAAH 04 95 1 0588 1 closed left half plane, under the additional assumption of null controllability, one can obtain either global results using nonlinear control laws ([5, 6]) or semi global results using linear feedback ( 7] Similar results for discrete time systems can be found in [8, 9] Semi global output regulation for linear, null controllable systems can be found in [10] and is also considered in [6] Most of the previous results hold for linear systems. ....

Sontag E.D. and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3414--3416, 1990.

....of integrators with more than two states, one must use nonlinear feedback in order to obtain global stabilization. For systems with poles on the closed left half plane, under the additional assumption of null controllability, one can obtain either global results using nonlinear control laws ([10, 11]) or semi global results using linear feedback ( 12] Similar results for discrete time systems can be found in [13, 14] In our opinion, the problem of output tracking in the presence of control constraints has not been heavily addressed in sufficient detail. Semi global output regulation for ....

....without necessarily using linear feedback laws after we have feedback linearized the open loop system. The problem of stabilizing linear systems with saturation has received great deal of attention in recent years. Solutions involving linear feedback [14, 12] as well as nonlinear feedback [11, 10, 13] have been developed. We illustrate some of the issues involved in this endeavor. Consider the following system, x = Gammax 3 u (31) juj M The above system is globally asymptotically stable with u = 0. But, the methodology of the last section suggests that we should use, u = x 3 v ....

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Sontag E.D. and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3414--3416, 1990.

....such a class of systems, probably due to a wide recognition of the inherent limitation on the actuator. Most of the results in this study pertain to the issues related to global and semi global internal stabilization of such a class of systems. In regard to global stabilization, it was shown in [9] that a linear system subject to input saturation can be globally asymptotically stabilized if and only if the system in the absence of saturation is asymptotically null controllable 1 . Moreover, it was also shown (see [1,11] that, in general, global asymptotic stabilization of linear systems ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proceedings of the 29th IEEE Conference on Decision and Control, pp. 3414-3416, 1990.

....last few years there has been a surge of interest in the study of linear systems subject to input saturation due to a wide recognition of the inherent constraints on the control input. Although most of the results in this study pertain to the problem of global stabilization (see, for example, 2] [10], 11] 13] 12] and semi global stabilization (see, for example, 3] 4] 5] 6] 15] 7] some attempts have also been made in the solution of output regulation problems. Roughly speaking, this problem is one of controlling a linear system subject to input saturation in order to have ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....Recently there has been a surge of interest in the study of linear systems subject to input saturation due to a wide recognition of the inherent constraints on the control actuator. Although most of the results in this study pertain to the problem of global stabilization (see, for example, 2] [12], 14] 16] 15] and semi global stabilization (see, for example, 6] 7] 8] 9] 18] 11] some attempts have also been made in the solution of output regulation problems for continuous time systems. Roughly speaking, this problem is one of controlling a linear system subject to input ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....last few years there has been a surge of interest in the study of linear systems subject to input saturation due to a wide recognition of the inherent constraints on the control input. Although most of the results in this study pertain to the problem of global stabilization (see, for example, 2] [10], 11] 13] 12] and semi global stabilization (see, for example, 3] 4] 5] 6] 15] 7] some attempts have also been made in the solution of output regulation problems. Roughly speaking, this problem is one of controlling a linear system subject to input saturation in order to have ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....to the problem of global and semi global stabilization. In regard to global stabilization, it was shown in [4,17] that, in general, global asymptotic stabilization of linear systems subject to input saturation cannot be achieved using linear feedback laws. 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 ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....inputs, but may be insufficient in extreme cases. A more detailed treatment of feedback linearization in the presence of constraints may be found in [15] The problem of stabilization of linear and nonlinear systems in the presence of actuator saturations has also been extensively studied in [16, 17]; the stabilization approaches are inapplicable to trajectory tracking, however. The analysis of [15] also addresses the issue of tracking. 3.3.5 Regulation Layer Once a feasible dynamic trajectory has been determined, the Regulation Layer is asked to track it. Assuming that the aircraft dynamic ....

E. Sontag and H. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," in Proceedings of the 29th IEEE Conference on Decision and Control, pp. 3414--3416, 1990.

....linear system which is subject to input saturation . This problem has a rich history (see, for example, 2] and much of the literature of the 1950 s and 1960 s on the absolute stability was motivated by this problem (see, for example, 1] 6] 7] A recent result due to Songtag and Sussmann ([10]) shows that only linear stabilizable systems having no open loop eigenvalues with positive real parts can be globally asymptotically stabilized by a bounded control. Another interesting aspect of this problem was shown by Fuller ( 4] and more recently by Sussmann and Yang ( 12] They showed ....

....recently by Sussmann and Yang ( 12] They showed that for a system of a chain of integrators of length n where n 3 and which is subject to input saturation , there does not exist a linear control law that globally asymptotically stabilizes the given system. The implication of the results of [10], 4] and [12] is straightforward and can be concluded as follows: Given a linear system which is subject to input saturation , the global stabilization can be solved if and only if all the eigenvalues of the given system are in the closed left half plane, and, even then, in general one must use ....

E.D. Sontag ans H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....to the problem of global and semi global stabilization. In regard to global stabilization, it was shown in [4,19] that, in general, global asymptotic stabilization of linear systems subject to input saturation cannot be achieved using linear feedback laws. 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 ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....inputs, but may be insufficient in extreme cases. A more detailed treatment of feedback linearization in the presence of constraints may be found in [15] The problem of stabilization of linear and nonlinear systems in the presence of actuator saturations has also been extensively studied in [16, 17]; the stabilization approaches are inapplicable to trajectory tracking, however. The analysis of [15] also addresses the issue of tracking. 5 Comparison to the PATH architecture 5.1 Similarities to the PATH AHS architecture The ATMS control architecture proposed here may be compared with the ....

E. Sontag and H. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," in Proceedings of the 29th IEEE Conference on Decision and Control, pp. 3414--3416, 1990.

....Recently there has been a surge of interest in the study of linear systems subject to input saturation due to a wide recognition of the inherent constraints on the control actuator. Although most of the results in this study pertain to the problem of global stabilization (see, for example, [2,14,15,17,16]) and semi global stabilization (see, for example, 4,6,7,9,8,13,19,11] some attempts have also been made in the solution of output regulation problems for continuous time systems. Roughly speaking, this problem is one of controlling a linear system subject to input saturation in order to have ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

....systems subject to input saturation, probably due to a wide recognition of the inherent constraints on the control input. Most of the results in this study pertain to the problem of global and semi global stabilization. A crucial result on the subject of stabilization of such systems appeared in [13] where it was established that linear systems with saturating input can be globally asymptotically stabilized if and only if the system in the absence of saturation is asymptotically null controllable 1 . Another crucial result related to the stabilization problem is that, in general, linear ....

E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990. 32

....Linear systems with actuator saturation constitute one of the most important classes of nonlinear systems encountered in practice. Surprisingly, until recently few general theoretical results were available regarding global feedback design problems for them. One such general result was given in [14], which showed that global state space stabilization for such systems is possible under the assumptions 3 This research was supported in part by US Air Force Grant AFOSR 91 0346. E mail addresses: fwliu,chitour,sontagg math.rutgers.edu that all the eigenvalues of A are in the closed left hand ....

....best possible, since they are also necessary. The controller consists of an observer followed by a smooth static nonlinearity. For more recent work, see [20] which showed based upon techniques introduced in [16] for a particular case how to simplify the controller that had been proposed in [14]. See also [8] for closely related work showing that such systems can be semiglobally (that is, on compacts) stabilized by means of linear feedback. In this paper, we are interested in studying not merely closed loop state space stability, but also stability with respect to measurement and ....

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Sontag, E.D., and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990, pp. 3414-3416.

....or, alternatively, if desired, of a parallel form involving such saturations. The results in this paper are in no way surprising or unexpected, since they are closely analogous to similar results presented by the authors, and by A. Teel, for continuous time systems, in the sequence of papers [6], 9] 7] and [8] Although the organization of the current work is tightly patterned after that of [8] and many of the arguments but not all are, conceptually, straightforward generalizations of the corresponding arguments in that continuous time paper, it seems appropriate to present ....

Sontag, E.D., and Sussmann, H.J., Nonlinear output feedback design for linear systems with saturating controls. Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 3414-3416.

....an F 8 aircraft, and tests the obtained controller on the original nonlinear model. This paper represents the first detailed derivation of a controller using the techniques in question, and the results are very encouraging. Keywords: Aircraft control, saturated controllers 1. Introduction In [5], 6] 12] and [8] the authors and Sussmann considered linear time invariant continuous time systems of the type x = Ax Boe(u) where as usual A 2 IR n2n and B 2 IR n2m , for some integers n, the dimension of the system, and m, the number of inputs. The function oe is supposed to be a ....

....part by US Air Force Grant AFOSR 91 0343 even marginally stable. Moreover, Fuller had already shown long ago in [2] see [7] for a related result) that the naive technique consisting of just using a linear controller will in general lead to oscillations and even instability. In the first paper, [5], we presented a fairly abstract existence theorem. Motivated by this, Teel introduced a constructive approach to the problem, in the particular case of single input multiple integrators. He proposed a feedback law u = k(x) which consisted of certain linear combinations of the basic linear ....

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E.D. Sontag, and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. IEEE Conf. Decision and Control , Honolulu, IEEE Publications, 1990, pp. 3414-3416.

....Lemma 3.1, by a X c u 2 i 4 = a c 4 kuk 2 : It follows that this derivative is negative when x is large enough, for essentially bounded u, and it is negative for u j 0. By standard arguments (see e.g. 4] this provides the BIBS conclusion. 3. 1 Linear Systems With Saturation In [10], we studied the particular case of systems of the type x = Ax B oe(u) 12) where A and B are n Theta n and n Theta m matrices respectively; that is, linear systems with saturating controls. We assume now also that oe is strictly increasing and bounded. Such a system is said to be ....

....a system is said to be asymptotically null controllable if every state can be driven asymptotically to zero using some (measurable) control; equivalently, it must hold that the pair (A; B) is stabilizable in the ordinary sense, and all eigenvalues of A have nonpositive real part. We proved in [10]: Theorem 4 For the system (12) there is a smooth feedback so that (3) is globally asymptotically stable if and only if (12) is asymptotically null controllable. In other words, subject only to the obvious necessary condition, there are smooth feedback stabilizers. From here, one can obtain ....

[Article contains additional citation context not shown here]

Sontag, E.D. and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990.

No context found.

Sontag E.D. and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3414--3416, 1990.

No context found.

Sontag E.D. and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 3414--3416, 1990.

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E.D. Sontag and H. J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proceedings of the 29 on Decision and Control, pages 3414--3416, 1990.

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E.D. Sontag and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 3414-3416, 1990.

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E.D. Sontag ans H.J. Sussmann, Nonlinear output feedback design for linear systems with saturating controls, Proc. 29th IEEE Conf. Decision and Control, pp. 34143416, 1990.

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E.D. Sontag ans H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. 29th IEEE Conf. Decision and Control, pp. 34143416, 1990.

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E.D. Sontag ans H.J. Sussmann, Nonlinear output feedback design for linear systems with saturating controls, Proc. 29th IEEE Conf. Decision and Control, 1990, pp. 3414-3416.

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