Results 1  10
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64
A New Computational Approach to RealTime Trajectory Generation for Constrained Mechanical Systems
, 2000
"... Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that rea ..."
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Cited by 84 (20 self)
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Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that realtime trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Realtime optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1
Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets
, 2002
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Distributed Receding Horizon Control with Application to MultiVehicle Formation Stabilization
 Automatica
, 2004
"... We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled nonseparably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed opti ..."
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Cited by 27 (4 self)
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We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled nonseparably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen su#ciently fast. The theory is applied in simulation for stabilization of a formation of vehicles.
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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Online Control Customization via OptimizationBased Control
 In SoftwareEnabled Control: Information Technology for Dynamical Systems
, 2002
"... this paper show the success of this choice for V for stabilization. An innerloop PD controller on #, # is implemented to stabilize to the receding horizon states # # T , # # T . The # dynamics are the fastest for this system and although most receding horizon controllers were found to be nomi ..."
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Cited by 20 (9 self)
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this paper show the success of this choice for V for stabilization. An innerloop PD controller on #, # is implemented to stabilize to the receding horizon states # # T , # # T . The # dynamics are the fastest for this system and although most receding horizon controllers were found to be nominally stable without this innerloop controller, small disturbances could lead to instability
Cooperative Control of MultiVehicle Systems Using Cost Graphs and Optimization
, 2003
"... We introduce a class of triangulated graphs for algebraic representation of formations that allows us to specify a mission cost for a group of vehicles. This representation plus the navigational information allows us to formally specify and solve tracking problems for groups of vehicles in formation ..."
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Cited by 17 (2 self)
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We introduce a class of triangulated graphs for algebraic representation of formations that allows us to specify a mission cost for a group of vehicles. This representation plus the navigational information allows us to formally specify and solve tracking problems for groups of vehicles in formations using an optimizationbased approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.
TwoStep Algorithms for Nonlinear Optimization with Structured Applications
 SIAM Journal on Optimization
, 1999
"... In this paper we propose extensions to trustregion algorithms in which the classical step is augmented with a second step that we insist yields a decrease in the value of the objective function. The classical convergence theory for trustregion algorithms is adapted to this class of twostep alg ..."
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Cited by 11 (7 self)
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In this paper we propose extensions to trustregion algorithms in which the classical step is augmented with a second step that we insist yields a decrease in the value of the objective function. The classical convergence theory for trustregion algorithms is adapted to this class of twostep algorithms. The algorithms can be applied to any problem with variable(s) whose contribution to the objective function is a known functional form. In the nonlinear programming package LANCELOT, they have been applied to update slack variables and variables introduced to solve minimax problems, leading to enhanced optimization eciency. Extensive numerical results are presented to show the eectiveness of these techniques. Keywords. Trust regions, line searches, twostep algorithms, spacer steps, slack variables, LANCELOT, minimax problems, expensive function evaluations, circuit optimization. AMS subject classications. 49M37, 90C06, 90C30 1 Introduction In nonlinear optimization proble...
Model Predictive Control Of A ThrustVectored Flight Control Experiment
 IN SUBMITTED: 2002 IFAC WORLD CONGRESS
, 2002
"... Model predictive control (MPC) is applied to the Caltech ducted fan, a thrustvectored flight experiment. A realtime trajectory generation software based on spline theory and sequential quadratic programming is used to implement the MPC controllers. Timing issues related to the computation and i ..."
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Cited by 11 (6 self)
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Model predictive control (MPC) is applied to the Caltech ducted fan, a thrustvectored flight experiment. A realtime trajectory generation software based on spline theory and sequential quadratic programming is used to implement the MPC controllers. Timing issues related to the computation and implementation of repeatedly updated optimal trajectories are discussed. Results show computational speeds greater than 10 Hz, 2.5 times that of the actuator dynamics. The MPC controllers successfully stabilize a step disturbance applied to the ducted fan and compare favorably to LQR methods.
Constrained Trajectory Generation For MicroSatellite Formation Flying
 In AIAA Guidance, Navigation and Control Conference
, 2001
"... Stationkeeping and reorientation control of a cluster of fullyactuated lowthrust microsatellites is considered in this paper. We propose a very general optimization based control methodology to solve constrained trajectory generation problems for stationkeeping and reorientation. By taking advan ..."
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Cited by 9 (2 self)
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Stationkeeping and reorientation control of a cluster of fullyactuated lowthrust microsatellites is considered in this paper. We propose a very general optimization based control methodology to solve constrained trajectory generation problems for stationkeeping and reorientation. By taking advantage of the fullyactuated structure of the microsatellite, it is possible to compute the control onboard the microsatellites. Performance of this methodology is reported for a typical microsatellite formation flying space mission using the Nonlinear Trajectory Generation software package.
Issues in the realtime computation of optimal control
 Mathematical and Computer Modelling
"... Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated several ways: differential inclusion, control parameterization, flatness parameterization, higherorder inclusions and so on. A plethora of techniques have been proposed for e ..."
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Cited by 8 (5 self)
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Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated several ways: differential inclusion, control parameterization, flatness parameterization, higherorder inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not portable across equivalent mathematical formulations. Further complications arise as a result of configuration and control constraints such as those imposed by obstacle avoidance or control saturation. In this paper, we present a unified framework for handling the computation of optimal controls where the description of the governing equations or that of the path constraint is not a limitation. In fact, our method exploits the advantages offered by coordinate transformations and harnesses any inherent smoothness present in the optimal system trajectories. We demonstrate how our computational framework can easily and efficiently handle different cost formulations, control sets and path constraints. We illustrate our ideas by formulating a robotics problem eight different ways that includes a differentially flat formulation subject to control saturation. This example establishes the loss of convexity in the flat formulation as well as its ramifications on computation and optimality. In addition, a numerical comparison of our unified approach to a recent technique tailored for controlaffine systems reveals that we get about 30 % improvement in the performance index.