Results 71 to 80 of about 83,867 (245)
Periodic behaviour of nonlinear second order discrete dynamical systems
, 2015 In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and $g:\mathbb{Z}^+\times\mathbb{R ...
Maroncelli, Daniel, Rodriguez, Jesus
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Lyapunov exponents of hybrid stochastic heat equations [PDF]
Systems & Control Letters, 2012 In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the $p$th moment Lyapnov exponents. Moreover, several examples are established to demonstrate that unstable (deterministic or stochastic) dynamical systems can be stabilized by ...
Bao, J. H., Mao, X. R., Yuan, C. G.
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Risk‐aware safe reinforcement learning for control of stochastic linear systems
Asian Journal of Control, EarlyView.Abstract This paper presents a risk‐aware safe reinforcement learning (RL) control design for stochastic discrete‐time linear systems. Rather than using a safety certifier to myopically intervene with the RL controller, a risk‐informed safe controller is also learned besides the RL controller, and the RL and safe controllers are combined together ...
Babak Esmaeili +2 more
wiley +1 more source
Modeling and parameter estimation for fractional large‐scale interconnected Hammerstein systems
Asian Journal of Control, EarlyView.Abstract This paper addresses the challenge of modeling and identifying large‐scale interconnected systems exhibiting memory effects, hereditary properties, and non‐local interactions. We propose a fractional‐order extension of the Hammerstein architecture that incorporates Grünwald–Letnikov operators to capture complex dynamics through multiple ...
Mourad Elloumi +2 more
wiley +1 more source
Advances in Mechanical Engineering, 2019 A novel framework of rapid exponential stability and optimal feedback control is investigated and analyzed for a class of nonlinear systems through a variant of continuous Lyapunov functions and Hamilton–Jacobi–Bellman equation.
Yan Li, Yuanchun Li
doaj +1 more source
Algebraic methods for the solution of some linear matrix equations [PDF]
The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is
Djaferis, T. E., Mitter, S. K.
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Lyapunov equations and Gram matrices
Linear Algebra and its Applications, 1983 AbstractIf p is a polynomial with all roots inside the unit disc and C its companion matrix, then the Lyapunov equation X − C∗XC = P has a unique solution for every positive semidefinite matrix P. We characterize sets of vectors x0,…,xn−1 and y0,…,yn−1 such that X = G(x0,…,xn−1)= G(y0,…, yn−1)-1.
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Asian Journal of Control, EarlyView.Abstract The linear‐quadratic regulator (LQR) problem of optimal control of an uncertain discrete‐time linear system (DTLS) is revisited in this paper from the perspective of Tikhonov regularization. We show that an optimally chosen regularization parameter reduces, compared to the classical LQR, the values of a scalar error function, as well as the ...
Fernando Pazos, Amit Bhaya
wiley +1 more source
A Perron-type theorem for nonautonomous difference equations with nonuniform behavior
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We show that if the Lyapunov exponents of a linear difference equation are limits, then the same happens with the Lyapunov exponents of the solutions of the nonlinear equations for any sufficiently small nonlinear perturbation.
Hailong Zhu, Can Zhang, Yongxin Jiang
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Riemannian theory of Hamiltonian chaos and Lyapunov exponents
, 1996 This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian ...
A. H. Nayfeh +34 more
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