Robust H2/H∞-state estimation for discrete-time systems with error variance constraints

Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results

A Computational Method For Optimal L-q Regulation With Simultaneous Disturbance Decoupling

The disturbance decoupling problem with stability (DDPS) and simultaneous infinite-time horizon optimal L-Q regulation, for continuous time-invariant linear systems, is formulated as a parameter optimization problem in L-Q regulators subject to control constraints imposed by the solution of DDPS. For computational solution of DDPS an efficient numerical procedure is proposed which gives the solution directly in the form of constraints on some parameters of the state-feedback matrix. For computational solution of the optimization problem a specialized hybrid descent method is proposed composed by a sequence of steps of modified Newton, Newton's and Quasi-Newton methods, suitable for problems with severe control structural constraints. © 1994.311155160Anderson, Moore, (1989) Optimal Control: Linear Quadratic Methods, , Prentice-Hall International Editions, Prentice-Hall Inc, Englewood Cliffs, NJBeseler, Chow, Minto, A feedback decent method for solving constrained LQG control problems (1992) Proc. 1992 American Control Conf., pp. 1044-1048. , Chicago, ILDórea, Milani, A computational method for optimal L-Q regulation with simultaneous disturbance decoupling (1993) Proc. 1993 American Control Conf., pp. 2669-2672. , San Francisco, CAGeromel, Bernussou, Optimal decentralized control of dynamic systems (1982) Automatica, 18, pp. 545-557Golub, Van Loan, (1989) Matrix Computations, , Johns Hopkins University Press, BaltimoreKwakernaak, Sivan, (1972) Linear Optimal Control Systems, , Wiley-Interscience, John Wiley & Sons, New YorkLinnemann, A condensed form for disturbance decoupling with simultaneous pole placement using state feedback (1987) Proc. 10th IFAC World Congress, Munich, 9, pp. 92-97Luenberger, (1984) Linear and Non-Linear Programming, , Addison-Wesley Publishing Company, Redwood CityMäkilä, Toivonen, Computational methods for parametric L-Q problemsâ A survey (1987) IEEE Transactions on Automatic Control, 32, pp. 658-671Martinez, Quasi-Newton methods with factorization scaling for solving sparse non-linear systems of equations (1987) Computing, 38, pp. 133-141Milani, On the computation of the optimal constant output feedback gains for large-scale linear time-invariant systems subjected to control structure constraints (1979) Proc. 9th IFIP Conf. Optimiz. Technique, 22, pp. 332-341. , Warsaw, Lecture Notes in Control and Information Sciences, Springer, BerlinMoore, Laub, Computation of Supremal (AB)-invariant and controllability subspaces (1979) IEEE Transactions on Automatic Control, 23, pp. 783-792Paraskevopoulos, Koumboulis, Tzierakis, Disturbance rejection of left-invertible systems (1992) Automatica, 28, pp. 427-430Toivonen, Mäkilä, Newton's method for solving parametric linear quadratic control problems (1987) Int. J. Control, 46, pp. 897-911Van Dooren, The generalized eigenstructure problem in linear system theory (1981) IEEE Transactions on Automatic Control, 26, pp. 111-129Wonham, (1979) Linear Multivariable Control. A Geometric Approach, , Springer, New Yor

Rejection Of Perturbations For Static Feedback At The Outset In Linear Systems [rejeição De Perturbações Por Realimentação Estática De Saída Em Sistemas Lineares]

This work addresses the Disturbance Decoupling Problem in linear systems via static output feedback. Necessary and sufficient conditions for solvability in two important families of systems are established. The problem is solvable if and only if a given subspace verifies an invariance property. The set of output feedback matrices which solve the problem is then parameterized through a suitable change of the coordinate basis of the state, input and output spaces. A numerical example illustrates the proposed approach.14118Basile, G., Marro, G., Self-bounded controlled invariant subspaces: A straightforward approach to constrained controllability (1982) J. Optimiz. Theory Appl., 38, pp. 71-81Basile, G., Marro, G., (1992) Controlled and Conditioned Invariants in Linear System Theory, , Prentice-HallChen, B.M., Solvability conditions for disturbance decoupling problems with static measurement feedback (1997) Int. J. Contr., 68, pp. 51-60Dórea, C.E.T., Milani, B.E.A., A computational method for optimal L-Q regulation with simultaneous disturbance decoupling (1995) Automatica, 31 (1), pp. 155-160Dórea, C.E.T., Milani, B.E.A., Disturbance decoupling in a class of linear systems (1997) IEEE Trans. Automat. Contr., 42 (10), pp. 1427-1431Hamano, F., Furuta, K., Localization of disturbances and output decomposition in decentralized linear multivariable systems (1975) Int. J. Contr., 22, pp. 551-562Schumacher, J.M., Compensator synthesis using (C.A.B)-pairs (1980) IEEE Trans. Automat. Contr., 25 (6), pp. 1133-1138Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback - A survey (1997) Automatica, 33 (2), pp. 125-137Van Dooren, P., The generalized eigenstructure problem in linear system theory (1981) IEEE Trans. Automat. Contr., 26, pp. 111-129Willems, J.C., Commault, C., Disturbance decoupling by measurement feedback with stability or pole placement (1981) SIAM J. Contr. Optimiz., 19 (4), pp. 491-504Wonham, W.M., (1985) Linear Multivariable Control - A Geometric Approach, , Springer-Verlag, New Yor