Optimal control problems with multiple characteristic time points in the objective and constraints

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved

A linear optimal feedback control for producing 1,3-propanediol via microbial fermentation

In this paper, we consider a multistage feedback control strategy for the production of 1,3-propanediol(1,3-PD) in microbial fermentation. The feedback control strategy is widely used in industry, and to the best of our knowledge, this is the first time it is applied to 1,3-PD. The feedback control law is assumed to be linear of the concentrations of biomass and glycerol, and the coefficients in the controller are continuous. A multistage feedback control law is obtained by using the control parameterization method on the coefficient functions. Then, the optimal control problem can be transformed into an optimal parameter selection problem. The time horizon is partitioned adaptively. The corresponding gradients are derived, and finally, our numerical results indicate that the strategy is flexible and efficient

Optimal start-up control of an evaporation system modeled as an interconnected hybrid dynamical system

The purpose of this research is to investigate the feasibility and advantageous outcomes of modeling a complicated non-linear hybrid dynamical process as an interconnected dynamical system for the purpose of solving a hybrid optimal control problem under the framework of nonlinear model predictive control. This work considers a hybrid model of the startup process of an evaporation system. In this evaporation system a liquid containing mixture of a non-volatile component A and volatile solvents B (water) and C (alcohol) is heated to evaporate the solvents and obtain component A at a higher concentration using a column that is temperature controlled by valves that control the flow of steam through a heat exchanger; valves also control the input feed inflow, vapor outflow and the drain of the concentrated product. The hybrid nature of this process was established in the work of C. Sonntag et. al. In this thesis we reformulate the mathematical model as an interconnected dynamical model with two autonomous modes. The reformulated model is then used as a constraint set for the optimization of a performance metric characterizing the startup of the evaporation process and its evolution into steady-state operation. The algorithm used to solve the optimization problem is a new version of the existing algorithms in which the model constraints and cost function computation are performed outside of the sequential quadratic (optimization) program inside fmincon in MATLAB. Extensive comparisons to the work of C. Sonntag et. al. are made

A Distributed Optimal Control Approach for Multi-agent Trajectory Optimization

<p>This dissertation presents a novel distributed optimal control (DOC) problem formulation that is applicable to multiscale dynamical systems comprised of numerous interacting systems, or agents, that together give rise to coherent macroscopic behaviors, or coarse dynamics, that can be modeled by partial differential equations (PDEs) on larger spatial and time scales. The DOC methodology seeks to obtain optimal agent state and control trajectories by representing the system's performance as an integral cost function of the macroscopic state, which is optimized subject to the agents' dynamics. The macroscopic state is identified as a time-varying probability density function to which the states of the individual agents can be mapped via a restriction operator. Optimality conditions for the DOC problem are derived analytically, and the optimal trajectories of the macroscopic state and control are computed using direct and indirect optimization algorithms. Feedback microscopic control laws are then derived from the optimal macroscopic description using a potential function approach.</p><p>The DOC approach is demonstrated numerically through benchmark multi-agent trajectory optimization problems, where large systems of agents were given the objectives of traveling to goal state distributions, avoiding obstacles, maintaining formations, and minimizing energy consumption through control. Comparisons are provided between the direct and indirect optimization techniques, as well as existing methods from the literature, and a computational complexity analysis is presented. The methodology is also applied to a track coverage optimization problem for the control of distributed networks of mobile omnidirectional sensors, where the sensors move to maximize the probability of track detection of a known distribution of mobile targets traversing a region of interest (ROI). Through extensive simulations, DOC is shown to outperform several existing sensor deployment and control strategies. Furthermore, the computation required by the DOC algorithm is proven to be far reduced compared to that of classical, direct optimal control algorithms.</p>Dissertatio

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin