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A Coiflet-type wavelet-homotopy approach is implemented to investigate the large deformation of a circular plate resting on different nonlinear foundations with various boundary parameters. A parameterized and continuous boundary model for circular plate with various constraints of rotation and translation has been proposed overlooked in previous studies. Parameterized wavelet approximation of arbitrary Robin-type boundary is reconstituted without variable substitution. Comprehensive analysis on the parameterized Robin-type boundaries is conducted by Linear Programming Approach, indicating the boundary singularities are actually false corresponding to the degenerated cases of Dirichlet-type and Neumann-type ones. Highly accurate Coiflet-type solutions of the coupled governing nonlinear differential equations with integration involving in extreme bending of circular plate have been obtained performing good computational efficiency in excellent agreement with other numerical results, which implies the wavelet scheme is a high precision computation method with great potential in giving highly accurate solutions of strongly nonlinear problems. • The new Coiflet-type wavelet approach for Robin boundary conditions is proposed. • Extreme large bending of a circular plate resting nonlinear foundations is analyzed. • Highly accurate solutions with integrations and singularities are obtained. • Parameterized Robin-type boundaries are conducted by Linear Programming Approach. • Validity and efficiency of the proposed technique is provided. [ABSTRACT FROM AUTHOR]

Abstract This study investigates finite-time stability and stabilization problems for positive systems with impulses. By constructing a time-varying copositive Lyapunov function and utilizing the average impulsive interval approach, the finite-time stability criterion is established for the first time by exposing different impulsive effects. The relationship between the impulses and the length of the finite time interval is revealed via both theoretical analysis and simulations. As an extension, the finite-time L 1 gain performance is also addressed. Based on the finite-time stability results, the finite-time controller design problem is studied to guarantee the positivity and finite-time stability of the corresponding closed-loop system. The obtained criteria can be checked by the linear programming method. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results. Highlights • Finite-time stability and stabilization problems for impulsive positive systems (IPSs) are solved firstly. • Relationship between impulses and length of finite time interval is revealed deeply. • A time-varying Lyapunov copositive function (LCF) and the average impulsive interval method are utilized. • All the proposed criteria can be checked by the linear programming approach. [ABSTRACT FROM AUTHOR]

The main results of the paper are concerned with determining the optimal stationary strategies for stochastic discrete control problems on networks with discounted costs. We ground polynomial time algorithms for determining the optimal strategies of this problem using a linear programming approach. Additionally, we show that the proposed approach can be extended for Markov decision processes with a total discounted cost optimization criterion. [ABSTRACT FROM AUTHOR]