### Browsing by Author "Shao, Cheng"

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Item Bio-Inspired Cooperative Optimal Control with Partially-Constrained Final State(2005) Shao, Cheng; Hristu-Varsakelis, Dimitrios; Hristu-Varsakelis, Dimitrios; ISRInspired by the process by which ants gradually optimize their foraging trails, this report investigates the cooperative solution of a class of free-final time, partially-constrained final state optimal control problems by a group of dynamic systems. A class of cooperative, pursuit-based algorithms are proposed for finding optimal solutions by iteratively optimizing an initial feasible control. The proposed algorithms require only short-range, limited interactions between group members, avoid the need for a ``global map'' of the environment on which the group evolves, and solve an optimal control problem in ``small'' pieces, in a manner which will be made precise. The performance of the algorithms is illustrated in a series of simulations and laboratory experiments.Item Biologically Inspired Algorithms for Optimal Control(2004) Shao, Cheng; Hristu-Varsakelis, Dimitrios; ISR; CDCSSIn the past few years, efforts to codify the organizing principles behind biological systems have been capturing the attention of a growing number of researchers in the systems and control community. This endeavor becomes increasingly important as new technologies make it possible to engineer complex cooperating systems that are nevertheless faced with many of the challenges long-overcome by their natural counterparts. One area in particular where biology serves as an inspiring but still distant example, involves systems in which members of a species cooperate to form collectives whose abilities are beyond those of individuals. This paper looks to the process by which ants optimize their foraging trails as inspiration for an organizing principle by which groups of dynamical systems can solve a class of optimal control problems. We explore the use of a strategy termed `local pursuit', which allows members of the group to overcome their limitations with respect to sensing range and available information through the use of neighbor-to-neighbor interactions. Local pursuit enables the group to find an optimal solution by iteratively improving upon an initial feasible control. We show that our proposed strategy subsumes previous pursuit-based models for ant-trail optimization and applies to a large array of problems, including many of the classical situations in optimal control. The performance of our algorithm is illustrated in a series of numerical experiments. Ongoing work directions related to local pursuit are also discussed in this document.Item Biologically-inspired optimal control(2005-11-14) Shao, Cheng; Hristu, Dimitrios; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Inspired by the collective activities of ant colonies, and by their ability to gradually optimize their foraging trails, this dissertation investigates the cooperative solution of a broad class of trajectory optimization problems with various types of boundary conditions. A set of cooperative control algorithms are presented and proved to converge to an optimal solution by iteratively optimizing an initially feasible trajectory/control pair. The proposed algorithms organize a group of identical control systems by imposing a type of pair-wise interaction known as "local pursuit". The bio-inspired approach taken here requires only short-range, limited interactions between group members, avoids the need for a "global map" of the environment in which the group evolves, and solves an optimal control problem in "small" pieces, in a manner which is made precise. These features enable the application of the proposed algorithms in numerical optimization, leading to an increase of the permitting size of problems that can be solved, as well as a decrease of numerical errors incurred in ill-conditioned problems. The algorithms' effectiveness is illustrated in a series of simulations and laboratory experimentsItem Biologically-Inspired Optimal Control via Intermittent Cooperation(2004) Shao, Cheng; Hristu-Varsakelis, Dimitrios; ISR; CDCSSWe investigate the solution of a large class of fixed-final-state optimal control problems by a group of cooperating dynamical systems. We present a pursuit-based algorithm -- inspired by the foraging behavior of ants -- that requires each system-member of the group to solve a finite number of optimization problems as it follows other members of the group from a starting to a final state. Our algorithm, termed "sampled local pursuit", is iterative and leads the group to a locally optimal solution, starting from an initial feasible trajectory. The proposed algorithm is broad in its applicability and generalizes previous results; it requires only short-range sensing and limited interactions between group members, and avoids the need for a "global map" of the environment or manifold on which the group evolves. We include simulations that illustrate the performance of our algorithm.Item Local Pursuit as a Bio-Inspired Computational Optimal Control Tool(2005) Shao, Cheng; Hristu-Varsakelis, Dimitrios; Hristu-Varsakelis, Dimitrios; ISR; CDCSSThis paper explores the use of a bio-inspired control algorithm, termed ``local pursuit', as a numerical tool for computing optimal control-trajectory pairs in settings where analytical solutions are difficult to obtain. Inspired by the foraging activities of ant colonies, local pursuit has been the focus of recent work on cooperative optimization. It allows a group of agents to solve a broad class of optimal control problems (including fixed final time, partially-constrained final state problems) and affords certain benefits with respect to the amount of information (description of the environment, coordinate systems, etc.) required to solve the problem. Here, we present a numerical optimization method that combines local pursuit with the well-known technique of multiple shooting, and compare the computational efficiency and capabilities of the two approaches. The proposed method method can overcome some important limitations of multiple shooting by solving an optimal control problem ``in small pieces'. Specifically, the use of local pursuit increases the size of the problem that can be handled under a fixed set of computational resources. Furthermore, local pursuit can be effective in some situations where multiple shooting leads to an ill-conditioned nonlinear programming problem. The trade-off is an increase in computation time. We compare our pursuit-based method with direct multiple shooting using an example that involves optimal orbit transfer of a simple satellite.Item Optimal Control through Biologically-Inspired Pursuit(2004) Shao, Cheng; Hristu-Varsakelis, Dimitrios; ISR; CDCSSInspired by the process by which ants gradually optimize their foraging trails, this paper investigates the cooperative solution of a class of free-final time, partially-constrained final state optimal control problems by a group of dynamic systems. A cooperative, pursuit-based algorithm is proposed for finding optimal solutions by iteratively optimizing an initial feasible control. The proposed algorithm requires only short-range, limited interactions between group members, and avoids the need for a "global map" of the environment on which the group evolves. The performance of the algorithm is illustrated in a series of numerical experiments.