The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Michael R Caputo - One of the best experts on this subject based on the ideXlab platform.
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How to do comparative dynamics on the back of an envelope for open‐loop Nash equilibria in differential game theory
Optimal Control Applications and Methods, 2016Co-Authors: Michael R Caputo, Chen LingAbstract:Summary The primal-dual comparative statics method of Samuelson (1965) and Silberberg (1974) is extended to cover the class of non-autonomous, finite horizon differential games in which a locally differentiable open-loop Nash equilibrium exists. In doing so, not only is a one-line proof of an envelope theorem provided but also the heretofore unknown intrinrsic comparative dynamics of open-loop Nash equilibria are uncovered. The intrinsic comparative dynamics are shown to be contained in a symmetric and Negative Semidefinite matrix that is subject to constraint. The results are applied to a canonical differential game in capital theory, and the resulting comparative dynamics are given an economic interpretation. Copyright © 2016 John Wiley & Sons, Ltd.
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comparative statics of a monopolistic firm facing rate of return and command and control pollution constraints
Bulletin of Economic Research, 2014Co-Authors: Michael R Caputo, Dmitriy PopovAbstract:The intrinsic comparative statics properties of a general rate-of-return regulated, profitmaximizing model of a monopolist facing a command-and-control pollution constraint are derived. Recent advances in the theory of comparative statics are used to derive the basic comparative statics of the model, which are contained in an observable Negative Semidefinite matrix and possess the form of Slutsky-like expressions. We consider several command-and-control pollution constraints that are commonly implemented in practice, and conclude that the intrinsic comparative statics properties of the model are qualitatively invariant to the type of command-andcontrol pollution constraint imposed. We compare our results with those extant, and find that several basic results from the standard A-J model no longer hold in our model.
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COMPARATIVE STATICS OF A MONOPOLISTIC FIRM FACING RATE‐OF‐RETURN AND COMMAND‐AND‐CONTROL POLLUTION CONSTRAINTS
Bulletin of Economic Research, 2014Co-Authors: Michael R Caputo, Dmitriy PopovAbstract:The intrinsic comparative statics properties of a general rate-of-return regulated, profitmaximizing model of a monopolist facing a command-and-control pollution constraint are derived. Recent advances in the theory of comparative statics are used to derive the basic comparative statics of the model, which are contained in an observable Negative Semidefinite matrix and possess the form of Slutsky-like expressions. We consider several command-and-control pollution constraints that are commonly implemented in practice, and conclude that the intrinsic comparative statics properties of the model are qualitatively invariant to the type of command-andcontrol pollution constraint imposed. We compare our results with those extant, and find that several basic results from the standard A-J model no longer hold in our model.
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comparative statics of the generalized maximum entropy estimator of the general linear model
European Journal of Operational Research, 2008Co-Authors: Michael R Caputo, Quirino ParisAbstract:The generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation. Using a new development in the method of comparative statics, the sensitivity of the resulting coefficient and error estimates to the prior information is investigated. A Negative Semidefinite matrix reminiscent of the Slutsky-matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity, and an upper bound for the rank of the matrix is derived.
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An Atemporal Microeconomic Theory and an Empirical Test of Price-Induced Technical Progress
Journal of Productivity Analysis, 2005Co-Authors: Michael R Caputo, Quirino ParisAbstract:An exhaustive comparative statics analysis of a general price taking cost-minimizing model of the firm operating under the influence of price-induced technical progress is carried out from a dual vista. The resulting refutable implications are observable and thus amenable to empirical verification, and take on the form of a symmetric and Negative Semidefinite matrix. Using data from individual cotton gins in California’s San Joaquin Valley, we empirically test the complete set of implications of the price-induced technical progress theory using both classical and Bayesian statistical procedures. We find that the data are fully consistent with the atemporal, cost-minimizing, price-induced microeconomic theory of technical progress.
F. Mazenc - One of the best experts on this subject based on the ideXlab platform.
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Output feedback, attitude dynamics, robustness
2015 European Control Conference (ECC), 2015Co-Authors: F. Mazenc, Sungpil Yang, Maruthi R. AkellaAbstract:This paper considers stabilization of fully actuated rigid-body attitude dynamics in the absence of angular velocity measurements and presents new robustness results to bounded unknown external disturbance torques. In particular, it is assumed that only body orientation is measured in the form of a unit-quaternion signal. It is well known that the passivity properties of the dynamics allows design of velocity-free controllers using a first-order stable filter driven by measured states. When external disturbance torques are taken into account, however, the robustness properties of these passivity-based output feedback controllers cannot be readily analyzed because the Lyapunov-like function from which the controller is derived has a time-derivative that is only Negative Semidefinite, and therefore non-strict. This obstacle is circumvented through a new partial-strictification approach which ultimately allows the characterization of robustness properties for this closed-loop system.
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An explicit construction of strong Lyapunov functions for systems satisfying conditions of the La Salle theorem
2004 5th Asian Control Conference (IEEE Cat. No.04EX904), 2004Co-Authors: F. Mazenc, Dragan NesicAbstract:We present a construction of a (strong) Lyapunov function whose derivative is Negative definite along the solutions of the system using another (weak) Lyapunov function whose derivative along the solutions of the system is Negative Semidefinite. The construction can be carried out if a Lie algebraic condition that involves the (weak) Lyapunov function and the system vector field is satisfied. Our main result extends to general nonlinear systems the strong Lyapunov function construction presented in Fauboug, L., et al. (June 2000), which was valid only for homogeneous systems.
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An explicit construction of strong Lyapunov functions for systems satisfying conditions of The La
2004Co-Authors: Salle Theorem, F. MazencAbstract:We present a construction of a (strong) Lyapunov function whose derivative is Negative definite along the solutions of the system using another (weak) Lyapunov function whose derivative along the solutions of the system is Negative Semidefinite. The construction can be carried out if a Lie algebraic condition that involves the (weak) Lyapunov function and the system vector field is satisfied. Our main result extends to general nonlinear systems the strong Lyapunov function construction presented in 121 that \vas valid only for homogeneous systems.
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Strong Lyapunov functions for systems satisfying the conditions of La salle
IEEE Transactions on Automatic Control, 2004Co-Authors: F. Mazenc, Dragan NesicAbstract:We present a construction of a (strong) Lyapunov function whose derivative is Negative definite along the solutions of the system using another (weak) Lyapunov function whose derivative along the solutions of the system is Negative Semidefinite. The construction can be carried out if a Lie algebraic condition that involves the (weak) Lyapunov function and the system vector field is satisfied. Our main result extends to general nonlinear systems the strong Lyapunov function construction presented in a previous paper that was valid only for homogeneous systems.
Quirino Paris - One of the best experts on this subject based on the ideXlab platform.
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comparative statics of the generalized maximum entropy estimator of the general linear model
European Journal of Operational Research, 2008Co-Authors: Michael R Caputo, Quirino ParisAbstract:The generalized maximum entropy method of information recovery requires that an analyst provides prior information in the form of finite bounds on the permissible values of the regression coefficients and error values for its implementation. Using a new development in the method of comparative statics, the sensitivity of the resulting coefficient and error estimates to the prior information is investigated. A Negative Semidefinite matrix reminiscent of the Slutsky-matrix of neoclassical microeconomic theory is shown to characterize the said sensitivity, and an upper bound for the rank of the matrix is derived.
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An Atemporal Microeconomic Theory and an Empirical Test of Price-Induced Technical Progress
Journal of Productivity Analysis, 2005Co-Authors: Michael R Caputo, Quirino ParisAbstract:An exhaustive comparative statics analysis of a general price taking cost-minimizing model of the firm operating under the influence of price-induced technical progress is carried out from a dual vista. The resulting refutable implications are observable and thus amenable to empirical verification, and take on the form of a symmetric and Negative Semidefinite matrix. Using data from individual cotton gins in California’s San Joaquin Valley, we empirically test the complete set of implications of the price-induced technical progress theory using both classical and Bayesian statistical procedures. We find that the data are fully consistent with the atemporal, cost-minimizing, price-induced microeconomic theory of technical progress.
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Comparative Statics of Money-Goods Specifications of the Utility Function
Journal of Economics, 2002Co-Authors: Quirino Paris, Michael R CaputoAbstract:The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and Negative Semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Sato's (1984) treatment of this problem.
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THE ECONOMIC RECORD VERSUS AER: TWENTY SIX YEARS AHEAD ON THE MONEY-GOODS MODEL
2001Co-Authors: Quirino Paris, Michael R CaputoAbstract:Author(s): Paris, Quirino; Caputo, Michael R. | Abstract: We prove that the symmetric and Negative Semidefinite modified Slutsky matrix derived by Samuelson and Sato (1984) for the money-goods model of the consumer, is identical to that derived by Pearce (1958) a quarter century before and restated sixteen years later by Berglas and Razin (1974). We also prove that these conditions are only sufficient for the problem at hand and are encompassed by a more general, modified Slutsky matrix that is necessary and sufficient as derived by Paris and Caputo (2001). These results have crucial relevance for testing the implications of consumer behavior.
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The Economic Record Versus Aer: Twenty Six Years Ahead On The Money-Goods Model
2001Co-Authors: Quirino Paris, Michael R CaputoAbstract:We prove that the symmetric and Negative Semidefinite modified Slutsky matrix derived by Samuelson and Sato (1984) for the money-goods model of the consumer, is identical to that derived by Pearce (1958) a quarter century before and restated sixteen years later by Berglas and Razin (1974). We also prove that these conditions are only sufficient for the problem at hand and are encompassed by a more general, modified Slutsky matrix that is necessary and sufficient as derived by Paris and Caputo (2001). These results have crucial relevance for test-ing the implications of consumer behavior.
Andrew R. Teel - One of the best experts on this subject based on the ideXlab platform.
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Invariance-Like Results for Nonautonomous Switched Systems
IEEE Transactions on Automatic Control, 2019Co-Authors: Rushikesh Kamalapurkar, Joel A. Rosenfeld, Anup Parikh, Andrew R. Teel, Warren E. DixonAbstract:This paper generalizes the LaSalle–Yoshizawa Theorem to switched nonsmooth systems. The Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A common candidate Lyapunov function that has a Negative Semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle–Yoshizawa-like results for the switched system. Of independent interest, are the results on approximate continuity and Filippov regularization of set-valued maps, reduction of differential inclusions using Lipschitz continuous regular functions, and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system.
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A Corollary for Switched Nonsmooth Systems with Applications to Switching in Adaptive Control.
arXiv: Systems and Control, 2016Co-Authors: Rushikesh Kamalapurkar, Joel A. Rosenfeld, Anup Parikh, Andrew R. Teel, Warren E. DixonAbstract:This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. It is established that a common candidate Lyapunov function with a Negative Semidefinite derivative is sufficient for boundedness of the system state and convergence of a positive Semidefinite function of the system state to the origin. The developed generalization is motivated by adaptive control of switched systems where the derivative of the candidate Lyapunov function is typically Negative Semidefinite.
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Invariance-like results for Nonautonomous Switched Systems
arXiv: Systems and Control, 2016Co-Authors: Rushikesh Kamalapurkar, Joel A. Rosenfeld, Anup Parikh, Andrew R. Teel, Warren E. DixonAbstract:This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A candidate common Lyapunov function that has a Negative Semidefinite derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle-Yoshizawa results for the switched system. Results for regular and non-regular candidate Lyapunov functions are presented using an appropriate generalization of the time derivative. The developed generalization is motivated by adaptive control of switched systems where the derivative of the candidate Lyapunov function is typically Negative Semidefinite.
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Stability Theorems for Delay Differential Inclusions
IEEE Transactions on Automatic Control, 2016Co-Authors: Kun-zhi Liu, Xi-ming Sun, Jun Liu, Andrew R. TeelAbstract:This technical note addresses stability problems of delay differential inclusions. A chain rule is proposed for a wide class of Lyapunov-Krasovskii functionals which are not necessarily invariantly differentiable. We also obtain an invariance-like theorem, where the derivative of the candidate functional is bounded above by a continuous Negative Semidefinite function. Several examples are given to show the effectiveness of the results.
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a nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems
IEEE Transactions on Automatic Control, 2005Co-Authors: Antonio Loria, Elena Panteley, Dobrivoje Popovic, Andrew R. TeelAbstract:A new infinitesimal sufficient condition is given for uniform global asymptotic stability (UGAS) for time-varying nonlinear systems. It is used to show that a certain relaxed persistency of excitation condition, called uniform /spl delta/-persistency of excitation (U/spl delta/-PE), is sufficient for uniform global asymptotic stability in certain situations. U/spl delta/-PE of the right-hand side of a time-varying differential equation is also shown to be necessary under a uniform Lipschitz condition. The infinitesimal sufficient condition for UGAS involves the inner products of the flow field with the gradients of a finite number of possibly sign-indefinite, locally Lipschitz Lyapunov-like functions. These inner products are supposed to be bounded by functions that have a certain nested, or triangular, Negative Semidefinite structure. This idea is reminiscent of a previous idea of Matrosov who supplemented a Lyapunov function having a Negative Semidefinite derivative with an additional function having a derivative that is "definitely nonzero" where the derivative of the Lyapunov function is zero. For this reason, we call the main result a nested Matrosov theorem. The utility of our results on stability analysis is illustrated through the well-known case-study of the nonholonomic integrator.
P. Rapisarda - One of the best experts on this subject based on the ideXlab platform.
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pick matrix conditions for sign definite solutions of the algebraic riccati equation
European Control Conference, 2001Co-Authors: H.l. Trentelman, P. RapisardaAbstract:Necessary and sufficient conditions for the existence of positive and Negative Semidefinite solutions of algebraic Riccati equations (AREs) corresponding to linear quadratic problems with an indefinite cost functional are formulated. The tests known from the literature cannot be efficiently carried out, either because they apply only to special cases, or because an infinite number of matrices of unbounded dimension should be checked for positive Semidefiniteness. The results presented in this paper, instead, characterize the extremal solutions of the ARE in terms of the finite Pick matrices induced by certain two-variable polynomial matrices associated with the equation.
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ECC - Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation
SIAM Journal on Control and Optimization, 2001Co-Authors: H.l. Trentelman, P. RapisardaAbstract:Necessary and sufficient conditions for the existence of positive and Negative Semidefinite solutions of algebraic Riccati equations (AREs) corresponding to linear quadratic problems with an indefinite cost functional are formulated. The tests known from the literature cannot be efficiently carried out, either because they apply only to special cases, or because an infinite number of matrices of unbounded dimension should be checked for positive Semidefiniteness. The results presented in this paper, instead, characterize the extremal solutions of the ARE in terms of the finite Pick matrices induced by certain two-variable polynomial matrices associated with the equation.
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All unmixed solutions of the algebraic Riccati equation using Pick matrices
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: H.l. Trentelman, P. RapisardaAbstract:Studies the existence of positive and Negative Semidefinite solutions of the algebraic Riccati equation corresponding to linear quadratic problems with an indefinite cost functional. An important role is played by certain two-variable polynomial matrices associated with the algebraic Riccati equation. We characterize unmixed solutions in terms of the Pick matrices associated with these two-variable polynomial matrices. As a corollary it turns out that the signatures of the extremal solutions are determined by the signatures of particular Pick matrices.
