The control parametrization enhancing transform for constrained time--delayed optimal control problems

Abstract

The Control Parametrization Enhancing Technique (cpet), is extended to a general class of constrained time-delayed optimal control problems. A model transformation approach is used to convert the time-delayed problem to an optimal control problem involving mixed boundary conditions, but without time-delayed arguments. The cpet is then used to solve this non delayed problem. Two test examples have been solved to illustrate the efficiencies of the cpet for time delayed problems.

Optimal Control of a Nonlinear Time‐Delay System in Batch Fermentation Process

“…Choosing (⋅) = (⋅) and substituting (21)-(22) into the above equation, we obtain the conclusion (19). The gradient formula (20) can be derived similarly.…”

“…Thus, the (OCP) is actually a free time optimal control problem. It is difficult to solve the (OCP) using existing numerical techniques [18][19][20]. The main difficulty is the implicit dependence of the system state on the terminal time.…”

“…Therefore, it is often impossible to obtain analytical solutions of the delayed optimal control problem and one has to resort to numerical solution methods. As a result, some successful algorithms, such as iterative dynamic programming method [18], control parameterization method [19], and measure theoretical approach [20], have been developed. However, terminal time in above optimal control problems is fixed.…”

A symplectic local pseudospectral method for solving nonlinear state‐delayed optimal control problems with inequality constraints

“…By setting Q = 40 and N = 20, we can obtain a referenced value of cost functional as J * = 164.4255645108813. In the work of Wong et al, this problem is solved by the classical control parameterization and the control parameterization enhancing technique. Moreover, this case is also studied by the shifted Legendre‐Gauss (ShLG) direct PS method in the work of Maleki and Hashim .…”

“…Continuously stirred‐tank reactors are quite widely used in chemical engineering. An optimal control problem of a system with 2‐stage continuously stirred‐tank reactors, as illustrated in Figure , has been considered in the works of Peng et al and Wong et al However, no constraint is taken into consideration in the aforementioned works. In this paper, we modify the original problem that we impose constraints on control variables.…”