Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the ε-optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45246/1/10957_2005_Article_BF02275352.pd

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Méthodes de décomposition-coordination et analyse de stabilité appliquées aux systèmes interconnectés

Méthodes de décomposition-coordination -- Formulation du problème -- Problème global et conditions d'optimalité -- Méthodes de décomposition-coordination -- Méthode admissible-coordination par le modèle -- Méthode non-admissible -- coordination par le critère découpage -- Méthode mixte -- Méthode de prédiction des intéractions de Takahara -- Méthode de prédiction et opérateurs d'intéractions -- Analyse de la stabilité : systèmes interconnectes -- Formulation du problème -- les hypothèses -- Fonction de Lyapunov -- Inégalité différentielle -- Systèmes de comparaison -- Un exemple : système linéaire

Optimal Decentralized Control Of Dynamic Systems

In this paper, several aspects of decentralized control theory applied to dynamic systems are studied. First of all, some classical definitions about matricial functions and new results on gradient calculations are presented. In the following we generalize to matricial problems the method of gradient projection of Rosen. Finally, some aspects of stability, initialization and initial condition independence are studied in detail, and two numerical examples are considered in order to emphasize the advantages of the given procedure: the decentralized Kalman filter and the optimal power-frequency control. © 1982.185545557BaySpec,COPSESA,et al.,FiberCore,FiberSensing,OZ OpticsAnderson, Moore, (1971) Linear Optimal Control, , Prentice-Hall, Englewood CliffsAoki, On feedback stabilizability of decentralized dynamic systems (1972) Automatica, 8, p. 163Athans, The matrix minimum principle (1968) Inf. & Control, 11, p. 592Athans, The role and the use of the stochastic linear-quadratic-guassian problem in control system design (1971) IEEE Transactions on Automatic Control, 16 AC, p. 529Athans, Falb, (1966) Optimal Control, , McGraw-Hill, New YorkBaptistella, An iterative method for economic stabilization policies under decentralized control and conflicting objectives (1974) Note Interne, ASC 79-1-50, , LAAS, Toulouse, FranceBernussou, Geromel, An easy to find gradient matrix of composite matricial functions (1981) IEEE Transactions on Automatic Control, 26 AC, p. 538Cohen, Commande par contre reaction, sons contrainte de structure du gain d'un systéme stochastique lineaire (1975) Resolution par une methode de gradient, , Rairo, ParisChong, Athans, On the stochastic control of linear systems with different information sets (1971) IEEE Transactions on Automatic Control, 16 AC, p. 423Davison, Rau, Palmay, The optimal output feedback control of a synchronous machine (1971) IEEE Transactions on Power Apparatus and Systems, 90 PAS, p. 2123Davison, The decentralized stabilization and control of a class of unknown non-linear time-varying systems (1974) Automatica, 10, p. 309Elgerd, (1973) Electric Energy Systems Theory: An Introduction TATA, , THM edition, McGraw-HillElgerd, Fosha, Jr., Optimum megawatt-frequency control of multiarea electric energy systems (1970) IEEE Transactions on Power Apparatus and Systems, 89 PAS, p. 556Fosha, Jr., Elgerd, The megawatt-frequency control problem a new approach via optimal control theory (1970) IEEE Transactions on Power Apparatus and Systems, 89 PAS, p. 563Geromel, Sur un probléme d'optimisation paramétrique de l'equation matricielle de Lyapunov (1978) C. r. Acad. Sci. Paris, 286, p. 843Geromel, Contribution à l'etude des systémes dynamiques interconnectes: aspects de decentralisation (1979) Thése de Doctorat d'Etat, Toulouse, FranceGeromel, Bernussou, Stability of two-level control schemes subjected to structural perturbations (1979) Int. J. Control, 29, p. 313Geromel, Bernussou, An algorithm for optimal decentralized regulation of linear quadratic interconnected systems (1979) Automatica, 14, p. 489Hoskins, Meek, Walton, The numerical solution of A'Q + QA = â C (1977) IEEE Transactions on Automatic Control, 15 AC, p. 882Johnson, Athans, On the design of optimal constrained dynamic compensators for linear constant systems (1970) IEEE Transactions on Automatic Control, 15 AC, p. 658Julien, (1980) Thése de Docteur Ingenieur, , LAAS, Toulouse, FranceKalman, Betram, Control Systems analysis and design via the â second methodâ of Lyapunov I continuous time systems (1960) Journal of Basic Engineering, p. 371Kleimnan, On the linear regulator problem and the matrix riccati equation (1966) MA ESL-R-271, , M.I.T. Electronic systems Laboratory, CambridgeKleimnan, Athans, The design of suboptimal linear time-varying systems (1968) IEEE Transactions on Automatic Control, 13 AC, p. 150Kosut, Suboptimal control of linear time-invariant systems subjected to control structure constraints (1970) IEEE Transactions on Automatic Control, 15 AC, p. 557Kwakernaak, Sivan, (1972) Linear Optimal Control Systems, , John Wiley, New YorkLasdon, (1970) Optimization Theory for Large Systems, , Macmillan, London, Macmillan Series in Operation ResearchLevine, Athans, On the determination of the optimal constant output feedback gains for linear multivariable systems (1970) IEEE Transactions on Automatic Control, 15 AC, p. 44Rosen, The gradient projection method for nonlinear programming Iâ Linear constraints (1960) Journal of the Society for Industrial and Applied Mathematics, 8, p. 181Sanders, Tacker, Linton, A new class of decentralized filters interconnected systems (1974) IEEE Transactions on Automatic Control, 19 AC, p. 259Sezer, Huseyin, Stabilization of linear time-invariant interconnected systems using local state feedback (1978) IEEE Systems, Man, & Cybern., 8 SMC, p. 751Siljak, (1978) Large Scale Dynamic Systems: Stability and Structure, , North-Holland, New YorkWonham, Linear Multivariable Control (1974) Lectures Notes in Economics and Mathematical Systems, 101. , Springe

Parametrical Optimization Approach For Decentralized Regulation Of Discrete Systems.

The problem of optimal decentralized control for an interconnected discrete system has been investigated. The approach used is called parametrical optimization which consists of defining a parameterized class of control and then using some nonlinear optimization algorithm in order to determine, in this case, an element which is, at least, locally optimum. Starting from a linear quadratic dynamic optimization problem, the parametric optimization problem is first defined and written in a matrix formulation. For that, a simple way to find the cost gradient matrix with respect to the feedback gain is derived.2312313

ON A CONVEX PARAMETER SPACE METHOD FOR LINEAR-CONTROL DESIGN OF UNCERTAIN SYSTEMS

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors' knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.29238140

On A Convex Parameter Space Method For Linear Control Design Of Uncertain Systems

This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a convex programming problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors' knowledge, this is one of the first numerical procedures able to handle and solve this interesting design problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.29238140

On Robust Output Feedback Control For Polytopic Systems

Robust dynamic output feedback design is an open problem, computationally speaking, since its determination asks for the solution of nonlinear matrix inequalities, namely bilinear ones. This is particularly the case, for polytopic uncertainty. Here a new sufficient condition is proposed by the use of bounds and scaling for completion of squares. The usefulness of the provided conditions stands in the fact that its solution can be performed using the Frank-Wolfe algorithm which runs in only one shot. The control design of an inverted pendulum with uncertain friction coefficients illustrates the theory. © 2005 IEEE.200550185023Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaDoyle, J.C., Stein, G., Multivarible feedback design - Concepts for a classical modern synthesis (1981) IEEE Trans. Automat. Contr, 26 (1), pp. 4-16Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A., State space solutions to standard H2 and H∞, control problems (1989) IEEE Trans. Automat. Contr, 34 (8), pp. 831-847Doyle, J.C., Zhou, K.M., Glover, K., Bodenheimer, B., Mixed H2 and H∞, performance objectives - optimal control (1994) IEEE Trans. Automat. Contr, 39 (8), pp. 1575-1587Gahinet, P., Apkarian, P., A linear matrix inequality approach to H∞ control (1994) Inter Jour of Robust and Nonlinear Contr, 4 (4), pp. 421-448Geromel, J.C., Palhares, A.G.B., Análise Linear de Sistemas Dinâmicos : Teoria, Ensaios Práticos e (2004) Exercícios (in Portuguese), Editora Edgard Blucher LTDA, , São Paulo, BrazilGeromel, J.C., Bernussou, J., de Oliveira, M.C., H-2-norm optimization with constrained dynamic output feedback controllers: Decentralized and reliable control (1999) IEEE Trans. Automat. Contr, 44 (7), pp. 1449-1454Zames, G., Feedback and optimal sensitivity - model reference transformations, multiplicative seminorms and approximate inverses (1981) IEEE Trans. Automat. Contr, 26 (2), pp. 301-320Zames, G., Francis, B.A., Feedback, minimax sensitivity and optimal robustness (1983) IEEE Trans. Automat. Contr, 28 (5), pp. 585-60

A Linear Programming Oriented Procedure For Quadratic Stabilization Of Uncertain Systems

This paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty. A constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain. Some experiments are presented. © 1989.1316572CAS; Ministry of Education of the People's Republic of China; CSF; Ministry of Education of the People's Republic of China; DFG; Ministry of Education of the People's Republic of China; FCT; Ministry of Education of the People's Republic of China; HGF; Ministry of Education of the People's Republic of China; HIP; Ministry of Education of the People's Republic of China; MEC; Ministry of Education of the People's Republic of China; NIH; Ministry of Education of the People's Republic of China; NSF; Ministry of Education of the People's Republic of China; NSFC; Ministry of Education of the People's Republic of China; RAS; Ministry of Education of the People's Republic of China; RFBR; Ministry of Education of the People's Republic of China; RPF; Ministry of Education of the People's Republic of China; SFI; Ministry of Education of the People's Republic of China; Ministry of Education of the People's Republic of China; LAS; Ministry of Education of the People's Republic of China; MOE; Ministry of Education of the People's Republic of China; STFC; Ministry of Education of the People's Republic of China; UM; Ministry of Education of the People's Republic of ChinaBarmish, Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) J. Optim. Theory Appl., 46 (4), pp. 399-408Horisberger, Belanger, Regulators for linear, time invariant plants with uncertain parameters (1976) IEEE Transactions on Automatic Control, 21 (5), pp. 705-708Khargonekar, Rotea, Stabilization of uncertain systems with norm bounded uncertainty using control Lyapunov functions (1976) Proceedings of the 27th Conference on Decision and Control, pp. A 503-A 507Leitman, Guaranteed ultimate boundedness for a class of uncertain linear dynamical systems (1978) IEEE Transactions on Automatic Control, 21 (6), pp. 1109-1110Peres, Bernussou, Geromel, Stabilisation de systèmes linéaires incertains par approche de programmation linéaire (1988) Internal Report LAAS du CNRS, No. 88205, , Toulouse, FrancePetersen, A stabilization algorithm for a class of uncertain linear systems (1987) System Control Lett., 8 (4), pp. 351-357Petersen, Hollot, A Riccati equation approach to the stabilization of uncertain linear systems (1986) Automatica, 22 (4), pp. 397-411Stalford, Robust control of uncertain systems in the absence of matching conditions: scalar input (1986) Proceedings of the 26th Conference on Decision and Control, pp. 1298-1307. , Los Angeles, CAThorp, Barmish, On guaranteed stability of uncertain linear systems via linear control (1981) J. Optim. Theory Appl., 35 (4), pp. 559-579Zhou, Khargonekar, Robust stabilization of linear systems with norm-bounded time-varying uncertainty (1988) Systems Control Lett., 10 (1), pp. 17-2