895 research outputs found
Robust distributed linear programming
This paper presents a robust, distributed algorithm to solve general linear
programs. The algorithm design builds on the characterization of the solutions
of the linear program as saddle points of a modified Lagrangian function. We
show that the resulting continuous-time saddle-point algorithm is provably
correct but, in general, not distributed because of a global parameter
associated with the nonsmooth exact penalty function employed to encode the
inequality constraints of the linear program. This motivates the design of a
discontinuous saddle-point dynamics that, while enjoying the same convergence
guarantees, is fully distributed and scalable with the dimension of the
solution vector. We also characterize the robustness against disturbances and
link failures of the proposed dynamics. Specifically, we show that it is
integral-input-to-state stable but not input-to-state stable. The latter fact
is a consequence of a more general result, that we also establish, which states
that no algorithmic solution for linear programming is input-to-state stable
when uncertainty in the problem data affects the dynamics as a disturbance. Our
results allow us to establish the resilience of the proposed distributed
dynamics to disturbances of finite variation and recurrently disconnected
communication among the agents. Simulations in an optimal control application
illustrate the results
Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications
It is due to the modularity of the analysis that results for cascaded systems
have proved their utility in numerous control applications as well as in the
development of general control techniques based on ``adding integrators''.
Nevertheless, the standing assumptions in most of the present literature on
cascaded systems is that, when decoupled, the subsystems constituting the
cascade are uniformly globally asymptotically stable (UGAS). Hence existing
results fail in the more general case when the subsystems are uniformly
semiglobally practically asymptotically stable (USPAS). This situation is often
encountered in control practice, e.g., in control of physical systems with
external perturbations, measurement noise, unmodelled dynamics, etc. This paper
generalizes previous results for cascades by establishing that, under a uniform
boundedness condition, the cascade of two USPAS systems remains USPAS. An
analogous result can be derived for USAS systems in cascade. Furthermore, we
show the utility of our results in the PID control of mechanical systems
considering the dynamics of the DC motors.Comment: 16 pages. Modifications 1st Feb. 2006: additional requirement that
links the parameter-dependency of the lower and upper bounds on the Lyapunov
function, stronger condition of uniform boundedness of solutions,
modification and simplification of the proofs accordingl
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
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