The approximating sequence Riccati equation method is an efficient approach for solving the nonlinear optimal control problems, but its neglect of dynamics and necessary optimality condition makes law difficult to satisfy optimality. In this paper, pseudospectral with state-dependent coefficient optimization algorithm proposed solve defect. By introducing method, original problem transformed in...

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semi-definite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex ...

Error estimates are derived for an augmented Lagrangian approximation to an optimal control problem. Convex control constraints are treated explicitly while a Lagrange multiplier is introduced for the nonlinear system dynamics. The nonlinear optimal control problem does not fit the classical theory for estimating the error in multiplier approximations, since the natural coercivity assumption is...

Manufacturers, who re-supply a large number of customers, continually struggle with the question of how to formulate a replenishment strategy. The purpose of this paper is to determine the optimal set of routes for a group of vehicles in the transportation network under defined constraints – which is known as the Vehicle Routing Problem (VRP) – delivering new items, and resolving the invent...

When fluid flow in a pipeline is suddenly halted, a pressure surge or wave is created within the pipeline. This phenomenon, called water hammer, can cause major damage to pipelines, including pipeline ruptures. In this paper, we model the problem of mitigating water hammer during valve closure by an optimal boundary control problem involving a nonlinear hyperbolic PDE system that describes the ...

In this paper we introduce a new method to design control laws for non-linear un-deractuated systems. Our method will often work in situations where standard control techniques fail. Even when standard techniques apply, we believe that our approach will achieve better performance. This is because we produce an infinite dimensional family of control laws, whereas most control techniques only pro...

Abstract: Due to the difficulty in solving the Hamilton-Jacobi-Isaacs equation, the nonlinear optimal control approach is not very practical in general. To overcome this problem, Ezal et al. (2000) first solved a linear optimal control problem for the linearized model of a nonlinear system given in the strict-feedback form. Then, using the backstepping procedure, a nonlinear feedback controller...

Infinite time optimal controllers have been designed for a dispersion type tubular reactor model by using the framework of adaptive critic optimal control design. For the reactor control problem, which is governed by two coupled nonlinear partial differential equations, an optimal controller synthesis is presented through two sets of neural networks. One set of neural networks captures the rela...