A Estabilidade Na Presenca De Uma Variedade Invariante e a Sua Aplicacao a Estabilicabilidade De Sistemas De Controle Não Lineares (original) (raw)
Advanced Topics in Robust Control. Volume 2. Invariants and Structured Singular Values
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On a class of controlled invariant sets
Proceedings of the American Control Conference
In this paper we introduce a new class of controlled invariant sets, called controllable invariant sets. Intuitively, a controllable invariant set has the property that from any "large enough" connected region of the set it is possible to reach any such other region of the set, regardless of disturbances. Disturbances are assumed to be bounded. The range of the control inputs is assumed to be given and is allowed to be bounded. The main result of the paper is a nonrecursive approach for the computation of controllable invariants. The other results of the paper deal with properties of the proposed method and of controllable invariance. The results of the paper assume hybrid system modes with linear discrete-time dynamics.
Invariants of Linear Control Systems with Analytic Matrices and the Linearizability Problem
Journal of Dynamical and Control Systems, 2021
The paper continues the authors' study of the linearizability problem for nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett. 134 (2019), 104572], conditions on mappability of a nonlinear control system to a preassigned linear system with analytic matrices were obtained. In the present paper we solve more general problem on linearizability conditions without indicating a target linear system. To this end, we give a description of invariants for linear non-autonomous singleinput controllable systems with analytic matrices, which allow classifying such systems up to transformations of coordinates. This study leads to one problem from the theory of linear ordinary differential equations with meromorphic coefficients. As a result, we obtain a criterion for mappability of nonlinear control systems to linear control systems with analytic matrices.
Control of constrained systems of controllability index two
IEEE Transactions on Automatic Control, 1980
Fig. 8. "Peg in a hole" expcriment. 20. 15 10 5 I. 0 1 2 3 . depth (cm) 4 9. Evolution of the vertical forces Fv and horizontal forccs FH measured during the insertion of the peg, accounting for the clarticities (dashed line) or not (solid line). Manufactwin8 @st., Nancy, France. June 25-26, 1979, pp. 137-147. P. Borrel. "Modile dc comportement dcs manipulateurs. Applications a l'analyse de leura pcrfom~ances et a leur commandc automatique," thesis. USTL, Montpellicr. France, Sept 1979. W. KhaU A. Liigcois, and A. Foumier, '%omman& dynamique de robots," RAIRO/S~SI. AMI. Contr., vol. 13, no. 2, pp. 189-201, June 1979. A. K. Bejczy, "Robot arm dynamic and control," Jet Propulsion Lab., NASA T-M-33-469. Fcb. 1974. M. H. RaibcTt and B. K. Horn, "Manipulator control using the configuration-space method" I d Robot, vol. 5, no. 2, 1978. A. Liegeois and E. Domhre, "Amelioration des performances d'un manipulateur muni de commandcs en force adaptativcs," IRIA, Final Rep. 78175, Rojct Spartacus, Aug. 1979. Addison-Wesley, 1977. pp. 171-178. S. M. Shinners, M&rn Control System. 7 7~0 1~ and Application. Rea-MA: Y. Tsypkin, Adqtation and k r n i n g in Automatic System. New York: Academic. W. Khal i l . "Contribution a la commandc automatique des manipulateun avec 1971. l'aide g u n modile mathematiquc des mecanismes," thesis, USTL. Montpcllier, France, Oct. 1978. R. Paul. "Modelling trajectory calculation and scrvoing of a computer controlled arm," Advanced Res. Projects Agency. Stanford Univ., Stanford, CA, 1973. Absbuler-Many natural and man-made system satisfy a stroog conbdl.bllityhypothesiswhichresultsfromanaturalpartitiondthestate space into "positioo" and " v e l * coordinntes. In pllrthh, plane linkagesystemrsdasbipedlocomotioomodelssatisfytheseco~~ whichcanbedtopositionnotonlytbepdesdtbesystem,butPlso(to Systems satisfying this hypothesis admit Unear sta&variaMe feedbocl, a substpntw extent) tbe correspooding eigenvectm. The resulting eigen-structurescanbededgnedtostaMUzeanddeutuplesystemsinsuchawry th.tspedfiedsubspPcesofthestate-spaceareinvariPotuodertbedylumicsoftheclosedloopsystem CompuCstiolls and s i m w n s for several types of coaotrained motioo prisins in biped locomotion problem are pr esent ed.
On the parametrization of all stabilizing controllers
Proceedings of the 44th IEEE Conference on Decision and Control, 2005
In the behavioral approach, the stabilization problem is to find, for a given plant behavior, a controller behavior such that the manifest controlled behavior is stable. In this paper we will establish, for a given plant behavior, a parametrization of all stabilizing controller behaviors.
Automatica, 1999
The properties of positively invariant sets are involved in many di!erent problems in control theory, such as constrained control, robustness analysis, synthesis and optimization. In this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems.
A novel unified approach to invariance in control
In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous or discrete dynamical system. In proving invariance of ellipsoids and Lorenz cones for discrete systems, instead of the traditional Lyapunov method, our novel proofs are based on the S-lemma, which enables us to extend invariance conditions to any set represented by a quadratic inequality. Such sets include nonconvex and unbounded sets. Finally, according to the framework of our novel method, sufficient and necessary conditions for continuous systems are derived from the sufficient and necessary conditions for the corresponding discrete systems that are obtained by Euler methods.
NOVASINERGIA REVISTA DIGITAL DE CIENCIA, INGENIERÍA Y TECNOLOGÍA, 2022
En este trabajo estudiamos la controlabilidad aproximada de un sistema de control con retardo no acotado, impulso no instantáneo y condiciones no locales. Estos resultados prueban una vez más que la controlabilidad de un sistema lineal se preserva si consideramos los impulsos, las condiciones no locales y los retardos como perturbaciones del mismo, lo cual es muy natural en los problemas de la vida real, nunca los puntos críticos de una ecuación diferencial corresponden exactamente el punto crítico del modelo que representa, lo mismo ocurre con los impulsos, el retardo y las condiciones no locales; son fenómenos intrínsecos al problema real, que muchas veces no son tomados en cuenta al momento de realizar la modelación matemática. Para lograr nuestro resultado, utilizaremos una técnica desarrollada por A. Bashirov et al., que no utiliza teoremas de punto fijo. Por otro lado, como el retardo es infinito, consideramos un espacio de fase que satisface la teoría axiomática propuesta por...
An invariant parameter in linear estimation and control
IEEE Transactions on Automatic Control, 1984
An invariant parameter for the joint observer-controller d e sign, the forward and backxud Kalman-Bucy (KB) filter, and the LQG control problem is obtained. Next the balancedness in balanced realizations is interpreted from the invariant parameter viewpoint. It is shown that in general a balanced realization does not lead to a balanced observer-controller design. Also the concept of continuous-time balanced stochastic realization is developed.