Optimal control of nonlinear dynamical systems based on a new parallel eigenvalue decomposition approach

Abstract

Summary This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two‐point boundary value problems is solved iteratively instead of solving the coupled nonlinear two‐point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower‐order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.

Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control

“…This theory for linear systems has been highly improved [26] , however, the nonlinear optimal control problem (OCP) has become a strong topic and should be deeper investigated [27][28] . Jajarmi and Baleanu [29] proposed a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. They have also investigated the convergence analysis of their suggested technique.…”

A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

“…In the end of nineteenth century basic theory of fractional calculus was developed with the studies of Liouville, Grünwald, Letnikov, and Riemann. It has been shown that fractional derivative operators are useful in describing dynamical processes with memory or hereditary properties such as creep or relaxation processes in viscoelastoplastic materials [3] , [4] , impact problem [5] , plasma physics [1] , diffusion process models [6] , [7] , [8] , [9] , chaotic systems [10] , control problems [11] , [12] , dynamics modeling of coronavirus (2019-nCov) [13] , etc .…”

On a New and Efficient Numerical Technique to Solve a Class of Discrete-time Nonlinear Optimal Control Problems

“…[21], gives a good view of nonlinear systems' dynamical behaviours [22][23]. This method was firstly developed for the analysis of dynamical systems with nonlinear terms [24][25][26], and recently it was extended for the optimal control and MPC of nonlinear dynamical systems [27][28][29]. Motivated by the remarkable advantages of the model series method, we aim to extend this technique in this paper to solve a class of discrete nonlinear OCPs.…”