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This paper is concerned with a path-finding method proposed by H. J. Sussmann, known as the homotopy continuation method (HCM). Given a control system initialized at some state, the HCM can be used to find an admissible open-loop control that performs a desired state transfer. This is accomplished by lifting curves in the state space of the system to curves in the space of regular admissible controls...
The non-equal-interval direct Verhulst new information GM(1,1) model with two times fitting was built which extended equal interval to non-equal-interval and suited for general data modeling and estimating parameters of direct Verhulst GM(1,1). The new model chooses the nth component of X(0) as the starting conditions of the grey differential model. The new model need not pre-process the primitive...
We investigate an optimal consumption and investment problem where we receive a certain fixed income stream that is terminated at a random time. It turns out that the optimal strategy and the value function for this problem differ considerably from the case where our income stream is certain to continue indefinitely. More specifically, the optimal consumption policy involves a function that is not...
Stability conditions for state-delay systems are derived based on the norm of semigroup, which describes the transition of the internal state. Introducing an exact calculation method of the semigroup norm, the conditions for the internal stability and the marginal stability are characterized by non-singularity of a transcendental function. The conditions depend on the existence of time interval such...
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
We have not take great depth experimentation of individual escape which is an important means of submarine rescue in our country, mostly because of the security problem. So, the security evaluation in the use of great depth is very important. This article established the mathematical model of individual escape equipment, and figured out the pressure-curve in great depth with differential equation...
In this paper, we present a systematic approach inspired from the ergodic theory of dynamical system for the optimal control of complex fluid flows. The infinite dimensional Navier Stokes equation describing the complex fluid flow is first reduced to a finite set of coupled ordinary differential equations. We utilize Proper Orthogonal Decomposition techniques to obtain a reduced order model. The linear...
In this paper, we propose an observed-based algorithm to estimate the time course of a set of not-directly measurable gene expressions for the network motif of the multi-output feed-forward loop (MO-FFL), widespread in gene transcription networks of many organisms. The MO-FFL has been modeled according to a standard ordinary differential equations approach, providing a nonlinear model in the state...
Nonlinear receding horizon control (NRHC) attracts much attention in recent years. For NRHC, C/GMRES proposed by Otsuka is one of the most effective methods. Generalized minimal residual method (GMRES) is employed in C/GMRES, however, GMRES may become numerically unstable under some conditions in the sense of numerical calculation. This results in instability of the controlled system in the sense...
Assigning targets to multiple flight vehicles which perform a cooperative mission becomes more involved considering the complex environments. In this paper, an coordinated target assignment scheme is proposed based on a finite-time gain measure. The target assignment problem is formulated as multiple Linear Time Varying (LTV) systems. A finite-time generalized H2 measure and its performance criterion...
For control systems described by ordinary differential equations subject to almost periodic excitations the controllability properties depend on the specific excitation. Here these properties and, in particular, control sets and chain control sets are discussed for all excitations in the closure of all time shifts of a given almost periodic function. Then relations between heteroclinic orbits of an...
Bi- or even multistable behavior is a recurrent phenomenon in gene regulation networks. These networks have the capacity to operate in two or more distinct modes in a stable manner. In this work, we consider gene regulation networks with known interaction structure but unknown reaction kinetics. Additionally, it is assumed that several distinct operation modes were observed experimentally whereby...
In this paper, we consider stochastic recursive optimal control problem of the stochastic delayed system described by forward-backward stochastic differential equation with delay. By virtue of classical spike variational approach, duality method and the anticipated backward stochastic differential equation, we obtain the maximum principle of the optimal control for this problem.
In this paper, on the basis of ODE methods and trust-region methods, we propose and analyze a new curvilinear trust-region method for unconstrained optimization. The new algorithm combines elements of ODE methods with elements of trust-region methods. Moreover, the new algorithm retains the quick covergence of trust-region method.
This paper considers the optimal tracking control (OTC) problem for bilinear systems affected by sinusoidal disturbances, and gives a successive approximation approach to solve analogous problems for general bilinear systems. For a given bilinear OTC problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By iteratively solving the...
Ordinary differential equation with small parameter is considered in this paper. This kind of problem changes rapidly in both side of boundary layer. Firstly, the asymptotic solution of the problem is presented in order one. The asymptotic solution is used to solve the problem outside the boundary layer. Secondly, the analytical solution is decomposed into the smooth component and the singular component...
Feedback linearization technique is a relative mature design technique in nonlinear control system theory, the backstepping technique is a controller design technique which recently gets much favor. The feedback linearization based on backstepping technique is the combination of the two techniques mentioned, it uses backstepping design process, designs a sequence of ??virtual?? systems of relative...
In this paper, we study positive periodic solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least two positive impulsive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder...
The region of attraction of nonlinear dynamical system can be considered using an analytical R-function that can be written like an infinite series where each term of the series has the homogeneous form of degree n ?? 2 this function allows to determine and to come near to the region of attraction of a nonlinear system around the point of equilibrium located in the origin. The analytical function...
In this paper, we propose a new kind of numerical method for backward stochastic differential equation (BSDEs in short ), the idea of our method came from high-order numerical method for solving Partial differential equation (PDE). Bases on the properties of BSDEs, we fully discretize the time-space continuous problems, and use Monte Carlo method to approximate the mathematical expectation in our...
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