Nonlinear Programming Approaches for Efficient Large-Scale Parameter Estimation with Applications in Epidemiology

The development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discrete-time and continuous-time models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in large-scale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very large-scale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with age-dependent dynamics, more complex compartment models, and spatially distributed data. However, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based decomposition and decomposition in time. These approaches show promise for certain types of estimation problems

Nonlinear Programming Approaches for Efficient Large-Scale Parameter Estimation with Applications in Epidemiology

The development of infectious disease models remains important to provide scientists with tools to better understand disease dynamics and develop more effective control strategies. In this work we focus on the estimation of seasonally varying transmission parameters in infectious disease models from real measles case data. We formulate both discrete-time and continuous-time models and discussed the benefits and shortcomings of both types of models. Additionally, this work demonstrates the flexibility inherent in large-scale nonlinear programming techniques and the ability of these techniques to efficiently estimate transmission parameters even in very large-scale problems. This computational efficiency and flexibility opens the door for investigating many alternative model formulations and encourages use of these techniques for estimation of larger, more complex models like those with age-dependent dynamics, more complex compartment models, and spatially distributed data. However, the size of these problems can become excessively large even for these powerful estimation techniques, and parallel estimation strategies must be explored. Two parallel decomposition approaches are presented that exploited scenario based decomposition and decomposition in time. These approaches show promise for certain types of estimation problems

Trajectory planning for unmanned vehicles using robust receding horizon control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 211-223).This thesis presents several trajectory optimization algorithms for a team of cooperating unmanned vehicles operating in an uncertain and dynamic environment. The first, designed for a single vehicle, is the Robust Safe But Knowledgeable (RSBK) algorithm, which combines several previously published approaches to recover the main advantages of each. This includes a sophisticated cost-to-go function that provides a good estimate of the path beyond the planning horizon, which is extended in this thesis to account for three dimensional motion; constraint tightening to ensure robustness to disturbances, which is extended to a more general class of disturbance rejection controllers compared to the previous work, with a new off-line design procedure; and a robust invariant set which ensures the safety of the vehicle in the event of environmental changes beyond the planning horizon. The system controlled by RSBK is proven to robustly satisfy all vehicle and environmental constraint under the action of bounded external disturbances. Multi-vehicle teams could also be controlled using centralized RSBK, but to reduce computational effort, several distributed algorithms are presented in this thesis. The main challenge in distributing the planning is to capture the complex couplings between vehicles.(cont.) A decentralized form of RSBK algorithm is developed by having each vehicle optimize over its own decision variables and then locally communicate the solutions to its neighbors. By integrating a grouping algorithm, this approach enables simultaneous computation by vehicles in the team while guaranteeing the robust feasibility of the entire fleet. The use of a short planning horizon within RSBK enables the use of a very simple initialization algorithm when compared to previous work, which is essential if the technique is to be used in dynamic and uncertain environments. Improving the level of cooperation between the vehicles is another challenge for decentralized planning, but this thesis presents a unique strategy by enabling each vehicle to optimize its own decision as well as a feasible perturbation of its neighboring vehicles' plans. The resulting cooperative form of the distributed RSBK is shown to result in solutions that sacrifice local performance if it benefits the overall team performance. This desirable performance improvement is achieved with only a small increase in the computation and communication requirements. These algorithms are tested and demonstrated in simulation and on two multi-vehicle testbeds using rovers and quadrotors.(cont.) The experimental results demonstrate that the proposed algorithms successfully overcome the implementation challenges, such as limited onboard computation and communication resources, as well as the various sources of real-world uncertainties arising from modeling error of the vehicle dynamics, tracking error of the low-level controller, external disturbance, and sensing noise.by Yoshiaki Kuwata.Ph.D

Efficient Robust Optimization for Robust Control with Constraints.

This paper proposes an ecient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of O(N6) per iteration of an interior-point method. We focus on the case when the disturbance set is 1-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled nite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires O(N³) time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach

Efficient robust optimization for robust control with constraints

This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed polytopic constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterise this problem as a convex program. While the reparameterised problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of O(N 6) per iteration of an interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires O(N 3) time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, which illustrate the efficiency of this approach