Adaptive sequential linear programming for optimal control profiles

Linear programming is a powerful technique which can handle large number of variables and constraitns. Exploiting this strength, an algorithm is developed which uses the linear program recursively. This is an algorithm to optimize a cost function and solve for an optimal control profile. The cost function is time in case of time optimal problems or can be one of the states of the system or can be a function of the states. The states of the system are linearized about a nominal control and states. A linear programming problem is posed with perturbed controls as variables and solved to satisfy the terminal conditions. This is done with two different assumptions, the perturbed control being constant and linear in the discrete time interval. The algorithm is also modified to make it adaptive and thus more efficient. These three different approaches are implemented on few benchmark optimal control problems. The results obtained using these different approaches are compared with each other.