Infinite horizon optimal control for nonlinear interconnected large‐scale dynamical systems with an application to optimal attitude control

Abstract

This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected largescale dynamic systems. In this method, the infinite horizon nonlinear largescale two-point boundary value problem (TPBVP), derived from Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of a uniformly convergent series. Moreover, in special cases, the proposed procedure facilitates the application of parallel processing, which improves its computational efficiency. In this study, an iterative algorithm is also presented, which has a low computational complexity and a fast convergence rate. Just a few iterations are required to obtain a suboptimal trajectory-control pair. Finally, effectiveness of the proposed approach is verified by solving the optimal attitude control problem.

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

“… In the past decades, fractional discrete time systems (or fractional difference equations) have gained much attention because of widespread applications in discrete natural phenomena . Consider the stability and synchronization of fractional discrete time systems will be our future work. In order to minimize a performance index in terms of the state and control variables, optimal control provides a powerful tool to deal with the problem of finding a control law for a given dynamic system . We will consider the optimal problem of FMCN via optimal control. …”

“…• In order to minimize a performance index in terms of the state and control variables, optimal control provides a powerful tool to deal with the problem of finding a control law for a given dynamic system. [42][43][44] We will consider the optimal problem of FMCN via optimal control.…”

Restarted State Parameterization Method For Optimal Control Problems

“…In deterministic setting, there are many text books for analytic solutions of optimal control problems such as [1][2][3][4][5][6][7]. Also, numerical methods for these problems have been provided in [8][9][10][11][12][13]. The stochastic optimal control problem has been studied in textbooks and studied by many researchers (for example see [3], [4], [8] and [9]).…”

“…Also, numerical methods for these problems have been provided in [8][9][10][11][12][13]. The stochastic optimal control problem has been studied in textbooks and studied by many researchers (for example see [3], [4], [8] and [9]). In general, an optimal control problem can be solved by one of the following methods [14]:…”

Numerical Method For Solving Optimal Control Problem Of Stochastic Volterra Integral Equations Using Block Pulse Functions

“…In deterministic setting, there are many text books for analytic solutions of optimal control problems such as [8]- [15]. Also, numerical methods for these problems have been provided in [16]- [22].…”