5,562 research outputs found

    A zero-sum game approach for H∞ robust control of singularly perturbed bilinear quadratic systems

    Get PDF
    A zero-sum game approach for H∞ robust control of continuous-time singularly perturbed bilinear quadratic systems with an additive disturbance input is presented. By regarding the stochastic disturbance (or the uncertainty) as "the nature player", the H∞ robust control problem is transformed into a two-person zero-sum dynamic game model. By utilizing the singular perturbation decomposition method to solve the composite saddle-point equilibrium strategy of the system, the H∞ robust control strategy of the original singularly perturbed bilinear quadratic systems is obtained. A numerical example of a chemical reactor model is considered to verify the efficiency of the proposed algorithm.U radu se opisuje pristup igre nulte sume za H∞ robusno reguliranje trajnih jedinstveno perturbiranih bilinearnih kvadratnih sustava s dodatnim unosom smetnji. Smatrajući stohastičke smetnje (ili nesigurnost) kao "igrača prirode", problem H∞ robusnog reguliranja pretvara se u model dinamičke igre nulte-sume za dvije osobe. Primjenom metode dekompozicije singularne perturbacije za rješavanje složene strategije ravnoteže točke opterećenja toga sustava, dobiva se strategija H∞ robusnog reguliranja originalnih jedinstveno uznemirenih bilinearnih kvadratnih sustava. Provjera učinkovitosti predloženog algoritma daje se na numeričkom primjeru modela kemijskog reaktora

    The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations

    Get PDF
    This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.Vasile Dragan, Hiroaki Mukaidani and Peng Sh

    Stability analysis of a general class of singularly perturbed linear hybrid systems

    Full text link
    Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be mode-dependent. This means that, at switching instants, some of the slow variables can become fast and vice-versa. Firstly, we show that using a mode-dependent variable reordering we can rewrite this class of systems in a form in which the variables preserve their nature over time. Secondly, we establish, through singular perturbation techniques, an upper bound on the minimum dwell-time ensuring the overall system's stability. Remarkably, this bound is the sum of two terms. The first term corresponds to an upper bound on the minimum dwell-time ensuring the stability of the reduced order linear hybrid system describing the slow dynamics. The order of magnitude of the second term is determined by that of the parameter defining the ratio between the two time-scales of the singularly perturbed system. We show that the proposed framework can also take into account the change of dimension of the state vector at switching instants. Numerical illustrations complete our study

    Singularly Perturbed Control Systems with Noncompact Fast Variable

    Full text link
    We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in the sense of weak semilimits, to sub and supersolution of a suitable limit equation containing the effective Hamiltonian. The novelty of our contribution is that no compactness condition are assumed on the fast variable. This generalization requires, in order to perform the asymptotic proce- dure, an accurate qualitative analysis of some auxiliary equations posed on the space of fast variable. The task is accomplished using some tools of Weak KAM theory, and in particular the notion of Aubry set

    An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

    Get PDF
    This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable
    corecore