Search

This paper proposes a near-optimal air-to-ground missile guidance law with impact angle and impact velocity constraints based on sequential convex programming. A realistic aerodynamic model is introduced into the problem formulation, such that traditional optimization theory cannot obtain an analytical solution to the optimization problem under state constraints. The original problem is considered as an optimization problem, and the angle of attack is replaced with the angle of attack rate as a new control variable to reconstruct the problem and simplify the solving process. Next, the independent variable is changed in the differential equations to linearize and discretize the problem such that the reconstructed problem can be solved using sequential convex programming. The results obtained by numerical simulations confirmed that the proposed algorithm is valid and faster than the general-purpose nonlinear optimal control problem solver. Finally, it was verified that different impact angles and impact velocities were achieved. [ABSTRACT FROM AUTHOR]

Oscillator of single-degree-freedom is a typical model in system analysis. Oscillations resulted from differential equations with fractional order attract the interests of researchers since such a type of oscillations may appear dramatic behaviors in system responses. However, a solution to the impulse response of a class of fractional oscillators studied in this paper remains unknown in the field. In this paper, we propose the solution in the closed form to the impulse response of the class of fractional oscillators. Based on it, we reveal the stability behavior of this class of fractional oscillators as follows. A fractional oscillator in this class may be strictly stable, nonstable, or marginally stable, depending on the ranges of its fractional order. [ABSTRACT FROM AUTHOR]

The purpose of this paper is introduce several types of Levitin-Polyakwell-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Base on criterion and characterizations for these types of Levitin-Polyak well-posedness we argue on diameters and Kuratowski's, Hausdorff's, or Istrǎtescus measures of noncompactness of approximate solution sets under suitable conditions, and we prove the Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Obtain a gap function for bilevel vector equilibrium problems with equilibrium constraints using the nonlinear scalarization function and consider relations between these types of LP well-posedness for bilevel vector optimization problems with equilibrium constraints and these types of Levitin-Polyak well-posedness for bilevel vector equilibrium problems with equilibrium constraints under suitable conditions; we prove the Levitin-Polyak well-posedness for bilevel equilibrium and optimization problems with equilibrium constraints. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of nonperiodic fourth-order differential equations with general perturbation. By using the mountain pass theorem and the Ekeland variational principle, we obtain that such equations possess two homoclinic solutions. Recent results in the literature are generalized and significantly improved. [ABSTRACT FROM AUTHOR]

The differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence conditions for DE. In this paper, a sufficient condition and a corollary for the convergence of DE to the global optima are derived by using the infinite product. A DE algorithm framework satisfying the convergence conditions is then established. It is also proved that the two common mutation operators satisfy the algorithm framework. Numerical experiments are conducted on two parts. One aims to visualize the process that five convergent DE based on the classical DE algorithms escape from a local optimal set on two low dimensional functions. The other tests the performance of a modified DE algorithm inspired of the convergent algorithm framework on the benchmarks of the CEC2005. [ABSTRACT FROM AUTHOR]

In this paper, we present the existence of extremal solutions of set-valued differential equations with feedback control on semilinear Hausdorff space under Hukuhara derivative which is developed under the form DHX(t) = F(t,X(t),H(t,X(t))), X(0) = X0, for allt € [0,T] with the monotone iterative technique and we will verify that monotone sequence of approximate solutions converging uniformly to the solution of the problem, that is useful for optimization problems. [ABSTRACT FROM AUTHOR]