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Neighboring optimal control for periodic tasks for systems with discontinuous dynamics

Science China(Information Sciences) 2011年第3期54卷 653-663页

作者： ATKESON Christopher G. Robotics Institute Carnegie Mellon University

We propose a trajectory-based optimal control method for periodic tasks for systems with discontinuous dynamics. A general method, dynamic programming, suffers from the problem of dimensionality. We use local models of the optimal control law to construct a local controller. We combine a parametric trajectory optimization method and differential dynamic programming (DDP) to find the optimal periodic trajectory in a periodic task. By formulating the optimal control problem with an infinite time horizon, DDP generates time-invariant local models of the optimal control law. For DDP, the value function at dynamics discontinuities is approximated by a second order Taylor series. The utility of the proposed method is evaluated using simu- lated walking control of a five-link biped robot. The results show lower torques and more robustness from the proposed controller than a PD servo controller.

关键词： trajectory optimization differential dynamic programming optimal control biped walking control

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Development of methodology for the optimal operation of soil aquifer treatment systems

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WATER SCIENCE AND TECHNOLOGY 1996年第10-11期33卷 433-442页

作者： Tang, ZW Li, GH Mays, LW Fox, P Arizona State University Tempe

Soil aquifer treatment (SAT) systems are used for reclamation of sewage effluent by groundwater recharge. Increasing demand on water supplies has stimulated the production or planning of many SAT systems that will use reclaimed wastewater for groundwater recharge. These systems are comprised of a series of infiltration basins. The design and operation of soil aquifer treatment systems presently relies primarily upon judgment and experience, This research effort is developing a methodology for determining the optimal operation of SAT systems that is based upon mathematically describing the problem as a discrete-time optimal control problem. The resulting mathematical problem is a large-scale nonlinear programming problem. Solution of the problem is being accomplished by interfacing a nonlinear programming optimizer, which is solved by a differential dynamic programming algorithm, with a simulator that describes the infiltration process, unsaturated flow, effects of surface clogging and biological clogging, biological removal of nitrogen and organics. Major efforts are devoted to numerical performance of the optimization model solution, and development of the simulator. Initial results of interfacing the optimizer with the simulator without water quality concern show high convergence rate. The operation pattern determined by this method is reasonable, This new methodology will be a tool for engineers to evaluate choices regarding the potential of the design and operation of SAT systems. Copyright (C) 1996 IAWQ. Published by Elsevier Science Ltd.

关键词： clogging differential dynamic programming infiltration nitrogen removal optimization organics removal simulation soil aquifer treatment system unsaturated flow

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Airborne Bistatic Radar Trajectory Optimization for Ground Geolocation Accuracy Maximization

Airborne Bistatic Radar Trajectory Optimization for Ground G...

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IEEE Radar Conference (RadarConf)

作者： Bruna, Marsal A. Bing, Kristin F. Minges, Mark Georgia Tech Res Inst Smyrna GA 30080 USA Air Force Res Lab Wright Patterson AFB OH USA

ISBN: (纸本)9781467388238

Target detection geolocation accuracy for monostatic radars is a function of the distance to the target and sensor parameters. For bistatic radars, detection estimation errors are dependent on not only the total distance to the target but also on the platform geometry. In this paper, we present a general approach to optimize platform trajectories in order to maximize detection geolocation accuracy. By utilizing the bistatic Cramer-Rao bound, a lower bound on the estimation errors is determined. Control-limited differential dynamic programming is then used to minimize the estimation errors along a trajectory with a defined time horizon. The optimization implications of different transmitter and receiver cooperation modes are discussed.

关键词： trajectory optimization bistatic radar airborne radar Cramer-Rao lower bound differential dynamic programming

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Optimal control of xenon oscillations in load follow of a large nuclear reactor

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Annual Review in Automatic programming 1985年第PART 2期13卷 201-207页

作者： Xinping, Yang Longzhou, Fu China

The problem of xenon spatial oscillations control during the load follow of large pressure water reactors is formulated as an optimization problem. The state equations of the system are composed of the one-group diffusion equation with temperature and xenon feedbacks, the iodine-xenon dynamics equations, and an energy balance equation for the core. The resulting distributed parameter model is first coverted into a lumped one by eigenfunction expansion and then a combination method, based on differential dynamic programming and Matrix Riccati Method, is developed to obtain the optimal solution which can closely follow the desired power demand and maintain the desired flux distribution without too much control effort. Computational results show that the algorithms used in the proposed method converge for a broad spectrum of load follows. With the same precision, the combination method, comparing with DDP alone, is fairly computationally efficient. © 1986.

关键词： differential dynamic programming load follow Nuclear reactor optimization xenon oscillations

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A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

A Family of Iterative Gauss-Newton Shooting Methods for Nonl...

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25th IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

作者： Giftthaler, Markus Neunert, Michael Staeuble, Markus Buchli, Jonas Diehl, Moritz Swiss Fed Inst Technol Agile & Dexterous Robot Lab Zurich Switzerland Univ Freiburg Dept Microsyst Engn IMTEK Syst Control & Optimizat Lab Freiburg Germany

ISBN: (纸本)9781538680940

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.

关键词： Numerical Optimal Control Trajectory Optimization Multiple Shooting Quadrupedal Robots Nonlinear Model Predictive Control differential dynamic programming

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Random Search Algorithms for Optimal Control

Random Search Algorithms for Optimal Control

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作者： Joose Rajamaki Aalto University

学位级别：博士

Optimal control is an important tool in many application areas, it is for example a central tool in robotics. Many widely used methods such as differential dynamic programming (DDP) are based on differentiating the dynamics of the controlled systems and the objective function. The assumption that one would have access to a differentiable model of the entire system does not hold for many systems of interest. For example, collisions break this assumption. In this case one has to resort to random search (Monte Carlo) algorithms. This thesis presents random search algorithms that fall into two categories. The first category is locally optimal sampling based trajectory optimization methods. The second one is real-time capable Monte Carlo tree search (MCTS) methods augmented with supervised machine learning. This thesis presents sampled differential dynamic programming (SaDDP), which is a random search trajectory optimization method, derived from the differential dynamic programming algorithm. SaDDP is derived by relating the quantities of the Taylor-expansion in DDP to the statistics of a multivariate normal distribution. This allows the statistics to be recomputed from sampled data instead of utilizing differentiation to obtain them. The thesis also presents ways to regularize the SaDDP algorithm efﬁciently. The real-time capable MCTS methods presented in this thesis enable the real-time control of complicated systems, such as physics-based 3D characters. The methods perform a receding horizon lookahead search and use the data produced by the lookahead search to teach machine learning models how to better search for the actions in the future. The demonstrated combination of receding horizon search and supervised learning is fast to converge and yields robust learning. The MCTS in this thesis combines information from multiple sources. This thesis presents how to combine the information from various sources in such a way that the search adapts to the information sources

关键词： Monte Carlo Monte Carlo Tree Search differential dynamic programming

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Low-thrust Trajectory Optimization in the Circular Restricted Three Body Problem

Low-thrust Trajectory Optimization in the Circular Restricte...

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作者： Chikine, Saikiran University of Colorado at Boulder

学位级别：M.S.

The use of multi-body dynamics and dynamical systems theory for trajectory design has become increasingly prevalent to space mission design. One common multi-body dynamics model is the Circular Restricted Three-Body Problem (CR3BP), which describes the motion of a test particle under the influence of two massive primary bodies. The CR3BP yields a multitude of dynamical structures that can be leveraged for trajectory design, including libration point orbits (LPOs), invariant manifolds, and heteroclinic connections. These structures can be used to design low-energy transfers and low-thrust trajectory design for small spacecraft, such as CubeSats. Particularly, these dynamical structures can inform trajectory optimization methods to identify fuel-optimal transfers between LPOs within the CR3BP. Hybrid differential dynamic programming is used here to nd optimal low-thrust trajectories in the CR3BP. It is a modication of dynamic programming that aims to minimize a cost function in a dynamical environment, and uses quadratic expansions of the cost and the dynamics to circumvent the limitations inherent in dynamic programming. Using heteroclinic connections as a starting point, single-phase hybrid differential dynamic programming is used in this thesis to find fuel-optimal transfers between Lyapunov orbits in the Earth-Moon CR3BP and between halo orbits in the Sun-Earth CR3BP. A continuation process is used in the Sun-Earth CR3BP which uses preceding optimized trajectories to find optimal transfers to increasingly large target halo orbits. Single-phase hybrid differential dynamic programming is shown to be a robust and effective optimization approach in the CR3BP when combined with dynamical systems theory techniques, and is able to successfully find many optimal transfers for a CubeSat between Sun-Earth halo orbits.

关键词： Trajectory Optimization Aerospace engineering Three-Body Problem differential dynamic programming Astrodynamics Low-Thrust dynamical Systems

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A learning-based model predictive control scheme and its application in biped locomotion

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2022年第0期115卷

作者： Li, Jingchao Yuan, Zhaohui Dong, Sheng Sang, Xiaoyue Kang, Jian Northwestern Polytech Univ Sch Automat Xian 710129 Peoples R China Shaanxi Univ Sci & Technol Sch Elect & Control Engn Xian 710021 Peoples R China

This paper proposes a learning-based model predictive control scheme. This scheme divides the predictive model into a known nominal model and an unknown model residual. Model residual is learned using Gaussian process regression. The learned stochastic model is solved quickly using differential dynamic programming, taking into account control input constraints. The simulation results show that compared with state of art optimal control methods, this scheme has good robustness to model residual, accelerates the solution of high-dimensional problems, and can strictly constrain the control inputs according to the actual situation. Based on this learning-based model predictive control scheme, this paper also proposes an online learning gait generator for the uncertainty problem in the locomotion control of biped robots. The zero moment point is strictly constrained during training to ensure safety. The simulation results show that the gait generator is robust to unknown load and unknown external force.

关键词： Biped locomotion Learning-based model predictive control Gaussian process regression differential dynamic programming

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Optimal Control of Xenon Oscillations in Load Follow of a Large Nuclear Reactor

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IFAC Proceedings Volumes 1985年第2期18卷 201-207页

作者： Xinping Yang Longzhou Fu Department of Energy and Power Engineering Xi'an Jiaotong University Xi'an Shaanxi Province China

The problem of xenon spatial osoillationo control during the load follow of large pressure water reactors is formulated as an optimization problem. The state equations of the system are composed of the one-group diffusion equation with temperature and xenon feedbacks, the iodine-xenon dynamics equations, and an energy balance equation for the core. The resulting distributed parameter model is first coverted into a lumped one by eigenfunction expansion and then a combination method, based on differential dynamic programming and Matrix Riccati Method, is developed to obtain the optimal solution which can closely follow the desired power demand and maintain the desired flux distribution without too much control effort. Computational results show that the algorithms used in the proposed method converge for a broad spectrum of load follows. With the same precision, the combination method, comparing with DDP alone, is fairly computationally efficient.

关键词： differential dynamic programming optimization Nuclear reactor load follow xenon oscillations

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Optimal Control of Load-Following Maneuvers in a Pressurized Water Reactor

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IFAC Proceedings Volumes 1990年第8期23卷 97-102页

作者： Fuyu Chao Longzhou Fu Department of Energy & Power Engineering Xi’an Jiaotong University Xi’an Shaanxi PRC

This paper formulates the problem of load-following maneuvers in a pressurized water reactor (PWR) as a nonlinear-quadratic tracking problem in accordance with optimal control theory. An one-dimensional core model is adopted. The system model with distributed parameters is converted to a lumped one by modal expansion method. A practical combination method — STMDDF, combining differential dynamic programming (DDP) with system tau method (STM), is used to solve above problem. In the course of solving this problem, the DDP is used to deal with the strong nonlinear part of the dynamic process, and STM is employed to treat the weak nonlinear part which can be linearized around nominal value, respectively. In addition, the time interval of the strong nonlinear dynamic process can be divided into several subregions. In each subregion, an appropriate nominal trajectory for DDP can be provided by STM by the application of linearized approximation treatment. As illustrated in the examples, the provided calculating method is shown to achieve rapid convergence and shorten the computation time considerably. It is also shown that the practical reactor power can closely follow the desired load demand and meanwhile axial offset as well as axial power-peaking factor can be maintained within assigned limits with relatively less control effort.

关键词： System tau method differential dynamic programming nuclear reactors nonlinear systems numerical methods optimal control

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