H. Sussman, E. Sontag and Y. Yang, A general result on the stabilization of Linear Systems using bounded controls. IEEE Trans. Automat. Contr., pp. 2411-2425, Dec. 1994. 12  Home/Search   Document Details and Download   Summary   Related Articles   Check

....stabilise integrator chains of arbitrary length. The proof is made in an inductive fashion, and the strategy consists of stabilising the state block by block by the means of a linear subcontroller, with each block of consisting of one or two states. Later work by Sussman, Sontag and Yang in [46, 47] extended this construction to include generic saturation functions. At present, we are primarily concerned with the analysis problem, and so these results will be summarised in a simplified theorem which will now be given. The important point at present is that it is possible to globally ....

....(i.e. all the eigenvalues of A are non positive) there exists a state feedback of the form: u(x) a 1 x oe(a 2 x oe(a 3 x : with the function description terminating after a finite number of terms) which globally stabilises the plant. Proof: See the papers [50] 46] [47] for details. 2 For large systems with many saturation and similar nonlinearities (i.e. relays, hysteresis elements) present, the determination of whether a system is state space stable is quite a difficult problem. In [37] and related publications) N.B.O.L. Pettit and P.E. Wellstead describe a ....

H.J. Sussman, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. In Proc. IEEE Conf. Dec. and Cont., pages 1802--1807, 1993.

....are velocity independent. Reporting (5) in (2) the real control is: ffi = arctan( K d tanOE K p x)l cos 3 OE) 7) Unfortunately, this control law did not prevent from actuator saturation. We have therefore saturated m 3 (and thus ffi) using a sigmoid. The stability is then preserved [11]. The new expression of the control law becomes: ffi(x; OE) arctan i K l cos 3 OE 1 Gammae Gamma (K d tan OE Kp x) 1 e Gamma (K d tan OE Kp x) j (8) This control law can be saturated to any arbitrary value ffi max by tuning K. HEADING ESTIMATION. The main problem we had to face ....

H. Sussmann, E. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, 39(12):2411--2425, January 1994.

....trajectories are velocity independent. Reporting (6) in (3) the real control is : ffi = arctan( K d tanOE K p x)L cos 3 OE) 8) Unfortunately, this control law did not prevent from actuator saturation. We have therefore saturated w 3 (and thus ffi) using a sigmoid. The stability is preserved [9]. The new expression of the control law is: ffi(x; OE) arctan i K L cos 3 OE 1 Gammae Gammak(K d tan OE Kp x) 1 e Gammak(K d tan OE Kp x) j (9) This control law can be saturated to any arbitrary ffi max by tuning K. 4. FIRST RESULTS. 4.1 Real time implementation of the control law ....

H. Sussmann, E. Sontag, and Y. Yang. "A general result on the stabilization of linear systems using bounded controls". IEEE Transactions on Automatic Control, 39(12):2411--2425, January 1994.

....disk and that each component of u is magnitude bounded (ju i j ffl) For discrete systems, Sontag (1984) proved the existence of a feedback controller which globally asymptotically stabilizes this system. However, the construction of a stabilizing controller is difficult (Sontag and Yang 1991, Sussmann, Sontag and Yang 1992). For example, Teel (1992) showed that for a system with more than two integrators the stabilizing controller has to be nonlinear. It turns out to be quite easy to prove that MPC globally asymptotically stabilizes such a system (Balakrishnan, Zheng and Morari 1993) Moreover, the tuning parameters ....

Sussmann, H. J., Sontag, E. D. and Yang, Y. (1992). A general result on the stabilization of linear systems using bounded controls, Technical Report Report SYCON-91-XX, Rutgers University.

.... Specifically, the addressed problem is the suboptimal determination of a command (reference) signal and of a feedback controller that minimize the worst case settling time subject to given overshoot and undershoot constraints and to an amplitude limit for the plant control actuator (see e.g. [4] for the problem of stabilizing a linear system using bounded controls) The general idea behind the provided solution for this problem is the combined synthesis of the controller and of the command signal using a dynamic inversion methodology. Previous work on this theme 1 Partial support for ....

H. J. Sussmann, E. D. Sontag, Y. Yang, "A general result on the stabilization of linear systems using bounded controls", IEEE Trans. on Aut. Cont., Vol. 39, pp. 2411-22425, 1994.

.... (su#ciently large) state constraints region and by applying the tech niques suggested in [5] 8] 22] We finally remind that for systems with no state constraints and with no eigenvalues outside the closed unit disk a completely di#erent approach can be used for global stabilization [25] or semi global stabilization [26] 27] In this case those approaches can be successfully applied to the solution of the tracking problem with an arbitrarily large initial condition set. ....

Sussmann H.J., Sontag E.D., and Yang Y.D. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Contr., Vol.39, No.12, pp.2411--2425, 1994.

....the recent textbook [8] or the overview paper [1] and the references therein. A quite general and unified description of the so called Anti Windup schemes is given for instance in [2] Analysis of constraint systems in terms of stability, controllability and feasibility is of interest as well [7, 9, 10, 11]. To solve the constraint control problem in a linear 1 Work supported by the german DFG (1996 1999 WAPprogram: topic Synthese optimaler Regler unter der Berucksichtigung von Beschrankungen und Robustheitsforderungen ) which is gratefully acknowledged. framework, one implicitly has to ....

H. J. Sussmann, E. D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. on Automatic Control, 39(12):2411--2425, Dec. 1994.

.... of semi stable LTI systems, i.e. continuous time systems with all poles in the closed left half of the complex plane and discrete time systems with all poles in the closed unit disk, it was shown that nonlinear controllers could be designed to make the closed loop system globally stable, e.g. see [19]# it was shown that saturated linear controllers could be designed to make any prescribed bounded set attractivee.g. see [12,13, 1 This work is supported by the ResearchGrants Council of Hong Kong and the Natural Sciences and Engineering Research Council of Canada. 14,17] The input constrained ....

H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls", IEEE Trans. Automat. Contr. AC-39, pp. 2411-2425, 1994.

....being stabilizable in the usual linear sense and having open loop poles in the closed left half plane. A nested feedback design technique for designing nonlinear globally asymptotically stabilizing feedbacklaws was proposed in [11] for achain of integrators and was fully generalized in [10]. The notion of semi global asymptotic stabilization on the null controllable region for linear systems subject to actuator saturation was introduced in [5] The semi global framework for stabilization requires feedbacklaws that yield a closed loop system which has an asymptotically stable ....

H.J. Sussmann, E.D. Sontag, and Y. Yang, \A general result on the stabilization of linear systems using bounded controls", #### ###### ######## ###### Vol. 39, pp. 2411-2425, 1994.

....The problem of LQ tracking and regulation under constraints is the topic of the present paper and a solution based on the predictive control methodology is described. The class of linear plants that are globally stabilizable in the presence of input constraints (ANCBI systems) was characterized in [4]. It was also shown that linear controllers cannot stabilize such plants whenever their dimension is greater than two. While positional actuator saturation has been addressed in the recent literature, see [6, 7, 8, 9] few design techniques are currently available to deal with actuator rate ....

H. J. Sussmann, E. D. Sontag and Y. Yang, "A general result on the stabilization of linear systems using bounded control", IEEE Trans. Aut. Control., Vol. 39, pp. 2411-2424, 1994.

....share a common perspective and similar utilities. In this case, 4. 8) reduces to a simpler form M = Phi U 1:M ; B 1:M ; Theta; F ; PA ; PR ; PBjC ; PC ; b Psi : It is frequently desirable to consider the set of decisions acceptable to coalition K under a constraint condition i(uK ) c [8, 13, 65]. Define the set C = fuK : i(uK ) cg, for some constraining function i : K 7 L , c 2 L . Then (4.3) changes to restrict attention to only those sets G in the oe algebra that are subsets of C S j = arg sup GK2BK :GK aeC Theta P j A (GK ) Gamma b P j R (GK ) ....

H. J. Sussamnn, E. D. Sontag, and Y. Yang. A General Result on the Stabilization of Linear Systems Using Bounded Controls. IEEE Transactions on Automatic Control, 39(12):2411--2425, 1994.

....the overall system is proved to fulfill the constraints and have desirable performance stability properties. 1 Introduction In recent years there have been substantial theoretical advancements in the field of feedback control of dynamic systems with input and or state related constraints [1, 2] . Amongst the various approaches, the developments of this note are more akin to the predictive control methodology [3] 4] Predictive control, wherein the receding horizon control philosophy is used, selects the control action by possibly taking into account the future evolution of the ....

H.J. Sussmann, E.D. Sontag and Y. Yang, "A general result on the stabilization of linear systems using bounded controls", IEEE T. A. C., Vol. 39, pp. 2411-2424, 1994. 11

....problem of automatic control. In spite of this, the problem has been given exhaustive and constructive systematic answers, mainly during the last decade. From one side it has been characterized the class of dynamical linear systems which can be controlled to zero with arbitrarily small controls (Sussmann et al. 1994): the so called ANCBI systems. They coincide with the class of stabilizable linear systems with open loop eigenvalues in the closed unit disk. They encompass stable systems with integrator chains of arbitrary complexity and are representative of a great deal of industrial processes. From a ....

....deal of industrial processes. From a different side, linear control structures were shown to only provide semi global stabilization of input saturated ANCBI systems (Lin, 1995) Non linear state feedback schemes for input saturated ANCBI plants were discussed in (Susmmann and Yang, 1991) and (Sussmann et al. 1994). All of such schemes amount to low gain control strategies which feature conservative behaviour and poor regulation performance. In an attempt to provide enhanced regulation 1 performance capabilities and global stabilization, gain scheduling variants were proposed in (Alvarez Ram irez and ....

H. J. Sussmann, E. D. Sontag and Y. Yang, "A general result on the stabilization of linear systems using bounded control", IEEE Trans. Aut. Control., Vol. 39, pp. 2411-2424, 1994.

....an input disturbance of a fixed energy) However, for the currently exploited stabilization algorithms, such bounds are generally not known. 2 Recently, a series of results has been obtained on stabilization of marginally unstable and exponentially unstable linear systems using bounded controls [14, 5, 7, 15, 4, 13, 12, 8, 3]. The results are based on the use of small feedback gains, which rises questions about the efficiency of the control action (the control is allowed to stay far below the saturation level for large intervals of time) Performance characteristics of the transition process in the closed loop system, ....

....characteristics of the transition process in the closed loop system, such as the induced gains, would be good indicators of efficiency. Currently, only the asymptotic magnitude gain bounds [11] and the controll error L p induced gain bounds [15] are available for the algorithms [14] [5]. This paper is based on a new method of designing a stabilizing output feedback, originating from ideas similar to those employed in [4, 12] The resulting controller is characterized by an efficient use of the actuator capacity ( agressive control, which, if necessary, can stay at the ....

E. Sontag H. Sussmann and Y. Yang. A general result on the stabilization of linear systems using bounded controls. 32nd CDC, pages 1802--1807, 1993.

....constraints has been a significant topic of automatic control since its origin. Despite the efforts and the various approaches, only in the beginning of the nineties the class of dynamical linear systems which can be controlled to zero with arbitrarily small controls has been characterized, (Sussmann et al. 1994) . These are the so called ANCBI (AsymptoticallyNull Controllable with Bounded Inputs) systems. While positional actuator saturation has been addressed in the recent literature, e.g. see (Zheng and Morari, 1994) and (Alvarez Ramirez and Suarez, 1996) few design techniques are currently ....

H. J. Sussmann, E. D. Sontag and Y. Yang, "A general result on the stabilization of linear systems using bounded control", IEEE Trans. Aut. Control., Vol. 39, pp. 2411-2424, 1994.

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H. Sussmann, E.D. Sontag, and Y. Yang, A general result on the stabilization of linear systems using bounded controls, IEEE Trans. Automat. Control, 39 (1994), pp. 2411-2425.

....to ISS related theory and applications. 7 Additional References Textbooks and research monographs which make use of ISS and related concepts include [13,24,37,38,32,60] After the definition in [63] and the basic characterizations in [69] the main results on ISS are given in [73] See also [8,78] for early uses of asymptotic gain notions. Practical ISS is equivalent to ISS with respect to compact attractors, see [71] Several authors have pointed out that time varying system versions of ISS are central to the analysis of asymptotic tracking problems, see e.g. 87] In [10] one can ....

Sussmann, H.J., E.D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Autom. Control 39(1994): 2411-2425.

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H. Sussman, E. Sontag and Y. Yang, A general result on the stabilization of Linear Systems using bounded controls. IEEE Trans. Automat. Contr., pp. 2411-2425, Dec. 1994. 12

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Sussman, H., Sontag, E., and Yang, Y., A general result on the stabilization of Linear Systems using bounded controls,, IEEE Trans. Automat. Contr. 24112425 (1994).

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Hector J. Sussmann, Eduardo D. Sontag, and Yudi Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, 39(12), dec 1994.

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H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Automat. Contr., vol. 39, no. 12, pp. 2411--2425, 1994.

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H. J. Sussmann, E. D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control, pages 2411--2425, December 1994.

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H. J. Sussmann, E. D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Auto. Control, 39:2411-- 2425, 1994.

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H. J. Sussmann, E. D. Sontag and Y. Yang, A General Result on the Stabilization of Linear Systems Using Bounded Controls, IEEE Transaction on Automatic Control, AC-39, pp. 2411-2425, 1994.

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H. J. Sussmann, E. D. Sontag, and Y. Yang, "A general result on the stabilization of linear systems using bounded controls," IEEE Trans. Automat. Contr., vol. 39, no. 12, pp. 2411--2425, 1994.

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