J. Doyle, K. Glover, P. Khargonekar, and B. Francis, "State-space solutions to standard H and H control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831--846, Aug. 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....frequency domain, the induced norm is still well defined for linear time varying systems also, although the term H1 norm has become a commonly used misnomer for the induced norm of such systems. After the state space solutions of Glover and Doyle [28] and Doyle, Glover, Khargonekar and Francis [22] were derived, connections were made to a number of other research areas, in particular that of risk sensitive control as developed by Whittle [78] Further connections were made to dynamic game theory by Basar and Bernhard [7] and Limebeer et al. 50] In both these areas, solutions are ....

....does not require knowledge of all future sampling operations. Chapter 5: Riccati differential inequalities In this chapter we present a solution of the continuous time infinite horizon linear time varying H1 synthesis problem, using the separation theory of Doyle, Glover, Khargonekar and Francis [22]. We extend the results of Khargonekar, Ravi and Nagpal [43] to replace the Riccati differential equations with Riccati differential inequalities, and remove a particular stability assumption on the solutions to these inequalities. We then obtain similar results using game theoretic techniques, by ....

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J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Transactions on Automatic Control, 34(8):831--847, August 1989.

....to the development of ODD s, much effort has been spent to solve the multivariable robustness analysis and synthesis where different classes of uncertainties have been considered. Unstructured uncertainties (full block complex perturbation uncertainties) can be used in the H framework, see [DGKF89] In general, a less conservative controller is achieved if the control problem is formulated in the framework which considers structured uncertainties. Common to both approaches is the description of model uncertainties as transfer functions, which are norm bounded but otherwise unknown. ....

....on the complementary sensitivity or on the control signal. For simplicity, only the sensitivity weight is specified in this paper and as the results show later, a satisfactory controller is obtained. 5 mixed synthesis All the existing algorithms for synthesis are based on H synthesis, see e.g. DGKF89] In the following only parametric uncertainties where perturbations are restricted to be real are used in order to allow a more accurate and consequently less conservative representation of the CD mechanism s dynamics. A synthesis procedure based on the parametric uncertainty model proposed in ....

J. Doyle, K. Glover, P. Khargonekar, and B.A. Francis. State-space solutions to standard H 2 and H control problems. IEEE Transactions on Automatic Control, AC-34:831--847, 1989.

....system is quadratically shable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties. It is shown that such a problem is equivalent to a scaled HE control problem. The last decade has witnessed significant advances in the H control theory; see [5] 8] 13] 15] and the references therein. It is a well known fact that H control is closely associated with many robustness problems such as scnsitivity minimization [20] and stabilization of uncertain systems [8] 9] 12] However, when there is parameter uncertainty in plant modelings, no ....

....shable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties. It is shown that such a problem is equivalent to a scaled HE control problem. The last decade has witnessed significant advances in the H control theory; see [5] 8] 13] 15] and the references therein. It is a well known fact that H control is closely associated with many robustness problems such as scnsitivity minimization [20] and stabilization of uncertain systems [8] 9] 12] However, when there is parameter uncertainty in plant modelings, no robust behavior ....

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J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, "State-space solutions to the standard H 2 and H control prob- 1256 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 37, NO. 8, AUGUST 1992.

....(v, 0) and P = there exists c such that (v, c) We will assume that the plant P full is given in input state output representation. Our results on the general problem set up will lead to a solution for the state space case, analogous to those on the standard H# problem obtained in [1]. This double Riccati equation solution and its variations have been the subject of very intensive research, see e.g. 5, 14] and generalizations in [10, 11] 6, 7] 3, 4] and [2] Assume the plant P full is given in input state output representation by x = Ax Bu Gd y = Cx Dd f = ....

.... is also su#cient for the existence of an internally stabilizing, strictly disturbance attenuating feedback controller and formulas for such controllers can be given analogous to those obtained for the non strict problem in [17] We note that our conditions are equivalent to those obtained in [1]. In fact, by pre and postmultiplying (4) and (5) by (K ) 1 and (K ) 1 , respectively, we find that P : K ) 1 and Q : K N ) 1 satisfy the mixed sign algebraic Riccati equations P PA PGG (PB H P J H) H H = 0, AQ QA QH HQ (QC ) ....

[Article contains additional citation context not shown here]

J.C. Doyle, K. Glover, P. Khargonekar and B.A. Francis, State space solutions to standard H 2 and H# control problems, IEEE Transactions on Automatic Control, volume 34, pages 831-847, 1989.

....flight conditions, say the dynamic pressure [11] The gain scheduling is aimed to keep some feature of the closed loop system (e.g. natural frequency of the dominant poles) approximately constant throughout the flight envelope. Another approach may invoke H methods to design a collection of full [5] or reduced [12, 14] order controllers, a controller with a fixed structure being designed for each operation point in the flight envelope grid. The resulting set of controllers is then transformed into a gain scheduled single controller by simply obtaining a least squares fit of its parameters ....

Doyle J. K., Glover K. , Khargonekar P. and Francis B., State space solutions to standard H 2 and H Control Problems. IEEE Trans. on Automat. Contr., Vol. AC-34, pp. 831-846, (1989).

....are known to exist, or are likely to be found. One example is determining stability of a linear system in which several parameters vary over given ranges [3, 4] One of the most famous contributions of robust control theory is the development of ( central ) H1 controller synthesis (see, e.g. [7]) This synthesis procedure is no more complicated than LQG synthesis, but yields controllers that can be more robust to plant variations than LQG controllers. The type of plant variations such H1 controllers can tolerate has a very specialized form, and not one that can be said to accurately ....

J. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Trans. Aut. Control, 34(8):831--847, August 1989.

....corresponding operator norms. In particular, if the system is linear, then the condition (2) can be written in the form kI H yu (p)F (p)k H1 1; 3) where H yu (p) is the transfer function of the object, F (p) is the transfer function of the learning operator. Here the operator norm is H1 norm [3, 4, 5] and the functional norm is L 2 norm. As it was said before, the learning control can be applied in the case, when the operator of the system is not known precisely. Namely, suppose that H yu (p) H yu (p) H yu (p) where H yu is the known part and H yu is the unknown perturbation. Then ....

J.C. Doyle, K.G. Glover, P.P. Khargonekar, and B.A. Francis, \State-Space Solutions to Standard H 2 and H1 Control Problems", IEEE Trans. Auto. Control, AC-34, 1989, pp. 831-847.

....on the camera inclination angle. Oscillations and instability occur even for a weak variation of ff ( Sigma2 ffi ) Due to these problems, we have decided to investigate a robust control approach. 3. 2 Robust control We chose the approach developed in H1 space at the beginning of the eighties [18, 10, 5, 6, 4], concerning controller design with plant uncertainties modelled as unstructured additive perturbations in the frequency domain. 3.2.1 Generality on H1 control The servoing scheme is presented in the Figure 5 . C(p) y y D y D F (p) 0 0 F (p) Figure 5: Servoing scheme in H1 ....

J. Doyle, K. Glover, P. Khargonekar, and B. Francis. State space solutions to standard H 2 and H1 control problems. IEEE Transactions on Automatic Control, 34(8), 1989.

.... problem were based on an input output setting and involved analytic functions (Nevanlinna Pick interpolation) or operator theoretic functions [5, 92] The state space characterization of all solutions to the H 1 control problem for linear time invariant systems has been obtained by Doyle et al. [23]. It is based on the solution of two coupled Riccati equations, with a constraint expressed in terms of a spectral radius. The class of all controllers are built around the socalled central controller and parametrized by a free parameter Q . However, as pointed out in [30] and [53] a major de ....

....Riccati equations, with a constraint expressed in terms of a spectral radius. The class of all controllers are built around the socalled central controller and parametrized by a free parameter Q . However, as pointed out in [30] and [53] a major de ciency of the controller design approach in [23] is that Q is dicult to choose in practice. Moreover, the results in [23] can only be applicable to regular systems. The main feature of solving the Riccati equations requires the tuning of a symmetric positive de nite matrix, which makes the Riccati equation approach of [23] dicult to use. To ....

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J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Trans. Automat. Control, 34:831{ 847, 1989.

....plant behavior is given in input state output representation, and the weighting func2 tional is a constant two variable polynomial matrix. In this case, our general results of part I lead to solvability conditions in terms of algebraic Riccati equations and inequalities, as studied before in [1], 4] 7] 12] 13] 14] 15] 3] 18] 16] 17] 5] 6] 9] 10] In section 6 of the paper, we address the important issue of feedback implementability. We nd conditions under which a controller that renders a system dissipative, can implemented as a feedback controller The proofs ....

....we apply the results of part I to the special case that the plant is given in input state output representation. We shall see that our results and proofs concerning the general problem set up lead to a solution for the state space case, analogous to those on the standard H1 problem obtained in [1]. This double Riccati equation solution and its variations have been the subject of very intensive research, see e.g. 7, 18] and generalizations in [12, 13] 16, 17] 9, 10] 5, 6] and [3] Whereas most of the existing literature deals with the problem of nding an internally stabilizing ....

[Article contains additional citation context not shown here]

J.C. Doyle, K. Glover, P. Khargonekar and B.A. Francis, State space solutions to standard H 2 and H1 control problems, IEEE Transactions on Automatic Control, volume 34, pages 831-847, 1989.

....of the Institute for Mathematics and Computing Science, P.O. Box 800, 9700 AV Groningen, The Netherlands, email: J.C.Willems math.rug.nl, H.L.Trentelman math.rug.nl. 1 clever coupling condition between the solutions of algebraic Riccati equations that rst appeared in the classic paper [2]. Our solvability conditions also require the dissipativeness of the hidden behavior and of the orthogonal complement of the plant behavior. These conditions feature prominently also in [4, 5, 6] We will cast the development completely in the language of behaviors and the associated quadratic ....

....storage functions Q N and Q P , and coupling the dissipativeness of N and P . This condition is analogous to (but a representation free generalization of) the remarkable condition coupling solutions of 10 algebraic Riccati equations that rst appeared in the instant classic paper [2]. Our main result, theorem 5, is stated merely as an existence result. Since storage functions are in an essential way non unique, the theorem leaves unanswered which storage functions yield likely candidates for satisfaction of (1) Next, we state a result that avoids this drawback, but, in order ....

J.C. Doyle, K. Glover, P. Khargonekar and B.A. Francis, State space solutions to standard H 2 and H1 control problems, IEEE Transactions on Automatic Control, volume 34, pages 831-847, 1989.

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J. Doyle, K. Glover, P. Khargonekar, and B. Francis, "State-space solutions to standard H and H control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831--846, Aug. 1989.

No context found.

J.C. Doyle, K. Glover, P. Khargonekar, and B. Francis. State-Space Solutions to Standard H 2 and H# Control Problems. IEEE Trans. Automat. Control, 34:831--847, August 1989.

No context found.

J. Doyle, K. Glover, P. Khargonekar, and B. Francis, "State-space solutions to standard H and H control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831--847, Aug. 1989.

No context found.

J. Doyle, K. Glover, P. Khargonekar, and B. Francis, State-space solutions to standard H 2 and H1 control problems, IEEE Trans. Automat. Control, AC-34 (1989), pp. 831--847.

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J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, State-Space Solutions to Standard H 2 and H# Control Problems, IEEE Trans. Automat. Contr. AC-34 (1989), no. 8, 831--847.

No context found.

J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, "State space solutions to standard H and H control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831--847, Aug. 1989.

No context found.

J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, "State space solutions to standard H and H control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831--847, Aug. 1989.

No context found.

J.C. Doyle, K. Glover, P. Khargonekar, and B.A. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Transactions on Automatic Control, 34(8):831--47, 1989.

No context found.

J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, "State-space solutions to standard H 2 and H# control problems'. IEEE Trans. Aut. Contr, AC-34, pp. 831-847, 1989.

No context found.

J. C. Doyle, K. Glover, P. Khargonekar, and B. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Trans. Auto. Cont., 34(8):831--847, Aug 1989.

No context found.

J. Doyle, K. Glover, P. Khargonekar, and B.A. Francis. State-space solutions to standard H 2 and H control problems. IEEE Transactions on Automatic Control, AC-34:831--847, 1989.

No context found.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solutions to standard H 2 and H1 control problems. IEEE Transactions on Automatic Control, 34(8):831--847, 1989.

No context found.

J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, State-space solutions to standard H 2 and H1 control problems, IEEE Trans. on Automat. Control 34 (1989) 831--847.

No context found.

J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis, State-Space Solutions to Standard H 2 and H1 Control Problems, IEEE Trans. Aut. Control, AC--34 (8) (1989) 831---847.

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