Robust Optimal Control of Nonlinear Systems With System Disturbance During Feedback Disruption

Abstract

In this paper, a robust optimal control problem of nonlinear systems with system disturbance during feedback disruption is considered. This is an extended work of previous time‐delay optimal control results, by adding external disturbance in the considered system. It is shown that there exists an optimal input signal which keeps the performance error within the specified bound for the longest time. Then, it is shown that such an optimal input signal can be approximated by an implementable bang‐bang input signal in terms of control performance. Two examples are given for illustration.

Numerical solution of optimal control problems governed by integro‐differential equations

“…whereẼ andF can be computed in a way similar to the construction method of the matrixC defined by Equation (6). By substituting Equations (16) and (19)-(22) into Equation (12), the integro -differential equation under discussion is reduced into the following system of algebraic equations:…”

“…Various types of optimal control problems have been investigated by these methods. Up to now, much effort has been committed to the development of various approaches for solving optimal control problems governed by ordinary differential equations [5][6][7][8][9][10][11][12][13][14]. However, a few research works have been devoted to the theoretical aspects and numerical investigation of optimal control problems described by integro-differential equations such as dynamic programming [15], direct methods based on Legendre's polynomials [16], Chebyshev's polynomials [17,18], Legendre pseudospectral approach [19], and Chebyshev pseudospectral method [20].…”

Modified bang‐bang controller for maximal and minimal time optimal control problems

“…Here, we let (m) ∶ = {x ∶ x(t) T x(t) ≤ m} and introduce the summarized version of time optimal results taken from [6,7] in the following. Theorem 1.…”

“…These two time optimal control results assure the existence of an optimal controller for each case but its actual computation is an another issue. Thus, a bang-bang controller whose each component switches between +k and −k with a finite number of switchings has been commonly employed for the actual implementation of the optimal controller [1][2][3][4][5][6][7][8].…”

“…One is to maintain the system states within a certain bound for the longest time during feedback disruption by using an open-loop controller. This is called a maximal time optimal problem and various related results have been reported [1][2][3][4][5][6]. The other is to bring the system states to near the origin in the minimal time upon the recovery of the feedback line using the latest sampled state.…”