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A multiple-shooting differential dynamic programming algorithm. Part 2: Applications

ACTA ASTRONAUTICA 2020年 173卷 460-472页

作者： Pellegrini, Etienne Russell, Ryan P. Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA 410 Calif Ave Santa Monica CA 90403 USA

A Multiple-Shooting differential dynamic programming Algorithm is applied to a variety of constrained non-linear optimal control problems, including classic benchmark problems, as well as a robotic arm problem and sensitive spacecraft trajectory optimization problems. The multiple-shooting extension presented in Part 1 is validated, as well as the Powell, Hestenes, and Rockafellar approach used in the treatment of equality and inequality path and terminal constraints. The results for example applications demonstrate the applicability of the algorithm to a variety of trajectory optimization problems. The advantages of the multiple-shooting approach over the single-shooting algorithm is evident in problems with high sensitivity. In particular, convergence of the multiple-shooting algorithm is demonstrated for complex spacecraft trajectory problems that are intractable using the single-shooting formulation.

关键词： Optimal control Trajectory optimization differential dynamic programming Multiple-shooting Augmented Lagrangian

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Low-Thrust Many-Revolution Trajectory Optimization via differential dynamic programming and a Sundman Transformation

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JOURNAL OF THE ASTRONAUTICAL SCIENCES 2018年第2期65卷 205-228页

作者： Aziz, Jonathan D. Parker, Jeffrey S. Scheeres, Daniel J. Englander, Jacob A. Univ Colorado Colorado Ctr Astrodynam Res Boulder CO 80309 USA Adv Space Boulder CO 80301 USA NASA Goddard Space Flight Ctr Code 5958800 Greenbelt Rd Greenbelt MD 20771 USA

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit angle and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are computed with the transfer duration extended up to 2000 revolutions. The flexibility of the approach to higher fidelity dynamics is shown with Earth's J(2) perturbation and lunar gravity included for a 500 revolution transfer.

关键词： Low-thrust Trajectory optimization differential dynamic programming Sundman transformation

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Large Scale Multi-Period Optimal Power Flow With Energy Storage Systems Using differential dynamic programming

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第3期37卷 1750-1759页

作者： Agarwal, Aayushya Pileggi, Larry Carnegie Mellon Univ Elect & Comp Engn Dept Pittsburgh PA 15213 USA

With theincreased penetration of renewable sources, power gridsare becoming stressed due to fluctuating generation. To alleviate stress from inconsistent sources, utilities employ energy storage systems alongside renewable sources and rely on dispatching synchronous generators. However, optimal dispatch of such devices is limited by traditional AC optimal power flow methods that do not account for time-dependent constraints, such as the state of charge of energy storage systems and generator ramping constraints. Multi-period optimal power flow is proposed as a large non-convex non-linear problem to optimally dispatch and control generators and energy storage elements across multiple time periods. In this paper, we introduce a scalable, robust framework to solve multi-period optimal power flow using a differential dynamic programming scheme that makes it capable of scaling to large systems containing energy storage devices. We demonstrate the efficacy of this solution by optimizing the SyntheticUSA testcase over a set of time periods. A robust homotopy method is applied to achieve fast simulation times that can be parallelized for further improvements.

关键词： Renewable energy sources Power system dynamics Synchronous generators Generators Planning dynamic programming Optimization differential dynamic programming energy storage multi-period optimal power flow optimization steady-state analysis

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Data-driven offset-free multilinear model predictive control using constrained differential dynamic programming

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JOURNAL OF PROCESS CONTROL 2021年 107卷 1-16页

作者： Park, ByungJun Kim, Jong Woo Lee, Jong Min Seoul Natl Univ Sch Chem & Biol Engn Inst Chem Proc 1 Gwanak Ro Seoul 08826 South Korea Tech Univ Berlin Chair Bioproc Engn Str 17 Juni 135 D-10623 Berlin Germany

Multilinear model predictive control (MLMPC) can regulate a nonlinear process with wide operating regions based on a set of linear models. Although online computational cost is reduced compare to nonlinear MPC (NMPC), it is difficult to obtain a reliable full nonlinear model or set of linear models in practice. In this paper, we propose a combination of MLMPC with differential dynamic programming (DDP), so that the system can be controlled offset-free in the absence of a full nonlinear model. DDP is a 'trajectory-centric' optimization technique that solves nonlinear optimal control problems. The trajectory can be optimized even if the full model for the system is unknown, because DDP uses only the gradients around the visited trajectory, which is easily obtained by input excitations. Moreover, the gradient information can provide linear models in the subsequent MLMPC step. In the proposed scheme, a novel model selection based on gap metric and weighting method are employed for MLMPC. We prove the offset tracking property of DDP assisted MLMPC. A continuous stirred tank reactor (CSTR) process is studied to demonstrate the effectiveness of the proposed algorithms. Simulation studies show that CDDP designed by the proposed algorithm improves the trajectory over iterations, and the resulting MLMPC achieves offset-free tracking property regardless of an initial point and a set-point in the operating region. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Model predictive control Gap metric Multilinear model predictive control differential dynamic programming

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A HYBRID ARTIFICIAL NEURAL NETWORK-differential dynamic-programming APPROACH FOR SHORT-TERM HYDRO SCHEDULING

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ELECTRIC POWER SYSTEMS RESEARCH 1995年第2期33卷 77-86页

作者： LIANG, RH HSU, YY Department of Electrical Engineering National Taiwan University Taipei Taiwan

In this paper, a hybrid artificial neural network-differential dynamic programming (ANN-DDP) method for the scheduling of short-term hydro generation is developed. The purpose of short-term hydro scheduling is to find the optimal amounts of generated powers for the hydro units in the system for the next N (N = 24 in this work) hours in the future. In the proposed method, the DDP procedures are performed offline on historical load data. The results are compiled and valuable information is obtained by using ANN algorithms. The DDP algorithm is then performed online according to the obtained information to give the hydro generation schedule for the forecasted load. Two types of ANN algorithm, the supervised learning neural network by Rumelhart et al. and the unsupervised learning neural network by Kohonen, are employed and compared in this paper. The effectiveness of the proposed approach is demonstrated by the short-term hydro scheduling of Taiwan power system which consists of ten hydro plants. It is concluded from the results that the proposed approach can significantly reduce the execution time of the conventional differential dynamic programming algorithm which is required to reach proper hydro generation schedules.

关键词： HYDRO SCHEDULING NEURAL NETWORKS differential dynamic programming

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differential dynamic-programming TECHNIQUE FOR OPTIMAL-CONTROL

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OPTIMAL CONTROL APPLICATIONS & METHODS 1994年第2期15卷 77-100页

作者： LIN, TC ARORA, JS UNIV IOWA DEPT MECH ENGNDEPT CIVIL & ENVIRONM ENGN1136 ENGN BLDGIOWA CITYIA 52242 NATL CHUNGHSING UNIV DEPT AGR MACHINERY ENGNTAICHUNG 40227TAIWAN

Continuous- and discrete-time differential dynamic programming (DDP) approaches to solve general optimal control problems are described and analysed. A comparison of the two approaches shows the continuous-time approach to be more general and flexible compared with the discrete-time approach, since it is not tied to any discretization scheme. A comparison of DDP with the non-linear programming (NLP) approach is also given. Three structural control problems - a linear model of a space structure, a single degree of freedom non-linear impact absorber and a non-linear flexible beam subjected to an impulsive load - are used to numerically evaluate the continuous- and discrete-time DDP approaches. Several grid sizes are used to show that the continuous-time approach with a reasonable number of grid points is more accurate and efficient (in most cases) than the discrete-time approach. It is therefore recommended to fully develop and evaluate the technique for the optimal control of large-scale systems.

关键词： differential dynamic programming OPTIMAL CONTROL NUMERICAL ALGORITHMS STRUCTURAL CONTROL

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Observability-Aware differential dynamic programming with Impulsive Maneuvers

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JOURNAL OF GUIDANCE CONTROL AND dynamicS 2024年第9期47卷 1905-1919页

作者： Fujiwara, Masahiro Funase, Ryu Univ Tokyo Dept Aeronaut & Astronaut 7-3-1 HongoBunkyo Ku Tokyo 1138656 Japan Japan Aerosp Explorat Agcy Inst Space andAstronaut Sci Sagamihara Kanagawa 2525210 Japan

In autonomous space systems, the reliability of navigation systems is essential. Observability in autonomous orbit determination techniques depends on the spacecraft's orbital motion, making the design of autonomous navigation systems and orbital maneuvers a coupled process. This study develops a stable and efficient algorithm based on differential dynamic programming to design maneuver sequences that improve navigation performance. Our approach incorporates the Fisher information matrix into a cost function to quantify state observability and facilitates its convergence using a semi-analytic gradient and Hessian derived under impulsive maneuvers. Two numerical examples show the validity and effectiveness of our algorithm. The results indicate the stability and efficiency in determining maneuver sequences and the improvement of state estimation accuracy along an optimized trajectory. It is also applicable to other observability-aware optimal control problems because the algorithm is independent of specific systems.

关键词： Optimal Control Problem Orbit Determination differential dynamic programming Fisher Information Matrix State Estimation Observability Active Sensing Trajectory Optimization

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PARALLEL-PROCESSING OF LARGE-SCALE DISCRETE-TIME UNCONSTRAINED differential dynamic-programming

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PARALLEL COMPUTING 1993年第9期19卷 1003-1017页

作者： CAFFEY, H LIAO, LZ SHOEMAKER, CA Cornell University Ithaca NY 14853 USA

differential dynamic programming (DDP) is an optimal control algorithm that has been used in a variety of applications involving optimization of dynamic systems. This paper discusses modifications in the serial DDP algorithm required to develop an efficient parallel algorithm. The modifications change the order of calculations in order to minimize the number of required barrier synchronization points within a time step. Because DDP is a fine-to-medium grained algorithm, previous approaches to parallel processing of DDP and related algorithms have focused on parallel processing across time steps, which results in a substantial loss of efficiency. The approach described here is most efficient for problems with a high state variable dimension. Numerical results indicate that for problems with 1000 state variables, our method can obtain a speedup of 5.3 on six processors (95.6% of the Amdahl upper bound), which is substantially higher than published results from earlier studies investigating problems of smaller state dimension and larger time dimension.

关键词： differential dynamic programming PARALLEL PROCESSING OPTIMAL CONTROL, OPTIMIZATION LARGE SCALE NUMERICAL ANALYSIS

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Discrete-Time differential dynamic programming on SO(3) With Pose Constraints

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IEEE ACCESS 2022年 10卷 112921-112933页

作者： Liu, Shu Liu, Dongpo China Acad Informat & Commun Technol Beijing 100191 Peoples R China

The motion of many robotics systems, such as the rotation of unmanned aerial vehicles, can be modeled by SO(3). However, the difficulties in the parameterization of the SO(3) makes it hard to implement the state-of-the-art collision avoidance algorithm. In this paper, we present a new method for control on SO(3) via the combination of the nonlinear state constraints and geometric control technique. We first define the nonlinear constraints for trajectory optimization on SO(3). Then we solve the trajectory optimization problem by constrained differential dynamic programming (DDP) in a Riemannian geometry framework. The first and second-order expansion of the cost function and dynamics are derived in a coordinate-free manner. The safety condition represented by nonlinear constraints is incorporated into the DDP via an active set method, where we find the active set in the backward path to obtain the optimal control policy. We validated our methods on motion planning of rigid model on SO(3) manifold where pose constraints are imposed. Our methods outperform the baseline methods in terms of convergence speed and numerical robustness to disturbance. The numerical robustness is essential when the system is initialized far from the local optimum.

关键词： Trajectory optimization Manifolds Convergence Motion planning Robot kinematics Geometry Collision avoidance Geometric control motion planning differential dynamic programming nonlinear programming

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A multiple-shooting differential dynamic programming algorithm. Part 1: Theory

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ACTA ASTRONAUTICA 2020年 170卷 686-700页

作者： Pellegrini, Etienne Russell, Ryan P. Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

Multiple-shooting benefits a wide variety of optimal control algorithms by alleviating large sensitivities present in highly nonlinear problems, improving robustness to initial guesses, and increasing the potential for parallel implementation. In this paper series, motivated by the challenges of optimizing highly sensitive spacecraft trajectories, the multiple-shooting approach is embedded for the first time in the formulation of a differential dynamic programming algorithm. Contrary to traditional nonlinear programming methods which necessitate minimal modification of the formulation in order to incorporate multiple-shooting principles, DDP requires novel non-trivial derivations, in order to include the initial conditions of the multiple-shooting subintervals and track their sensitivities. The initial conditions are updated in a necessary additional algorithmic step. A nullspace trust-region method is used for the solution of the quadratic subproblems, and equality and inequality path and terminal constraints are handled through a general augmented Lagrangian approach. The propagation of the trajectory and the optimization of its controls are decoupled through the use of State-Transition Matrices. Part 1 of the paper series provides the necessary theoretical developments and implementation details for the algorithm. Part 2 contains validation and application cases.

关键词： Optimal control Trajectory optimization differential dynamic programming Multiple-shooting Augmented Lagrangian

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