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Multicriteria differential dynamic programming

IFAC Proceedings Volumes 1987年第9期20卷 431-436页

作者： Cang-pu Wu Department of Automatic Control Beijing Institute of Technology PO Box 327 Beijing PRC

The purpose of this paper is to generalize the differential dynamic programming technique to such an extent that it can tackle multicriteria optimization problems with the same advantage of overcoming the dimensionality difficulty. Fundamental concepts, underlying ideas and basic formulas which form the basis of a multicriteria differential dynamic programming algorithm are introduced and derived. The algorithm is described in detail. A fundamental convergence theorem is shown which can be applied to a wide class of multicriteria optimization problems.

关键词： Multicriteria optimization discrete time systems differential dynamic programming Pareto optimal control

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Computational Guidance Using Sparse Gauss-Hermite Quadrature differential dynamic programming

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IFAC-PapersOnLine 2019年第12期52卷 13-18页

作者： Shaoming He Hyo-Sang Shin Antonios Tsourdos School of Aerospace Transport and Manufacturing Cranfield University Cranfield MK 43 OAL UK

This paper proposes a new computational guidance algorithm using differential dynamic programming and sparse Gauss-Hermite quadrature rule. By the application of sparse Gauss-Hermite quadrature rule, numerical differentiation in the calculation of Hessian matrices and gradients in differential dynamic programming is avoided. Based on the new differential dynamic programming approach developed, a three-dimensional computational algorithm is proposed to control the impact angle and impact time for an air-to-surface interceptor. Extensive numerical simulations are performed to show the effectiveness of the proposed approach.

关键词： Computational guidance differential dynamic programming Sparse Gauss-Hermite quadrature Impact angle Impact time

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H^∞-Optimal Control via Game-Theoretic differentialdynamic programming and Gaussian Processes

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第3期204卷

作者： Sun, Wei Trafalis, Theodore B. Univ Oklahoma Norman OK 73019 USA

In this paper, we present a nonlinear H-infinity-optimal control algorithm for a systemwhose dynamics can be described by the summation of two terms: a known func-tion obtained from system modeling and an unknown function that represents themodel error induced by the disturbance and the noise that are not captured by theoriginal model. A Gaussian Process (GP) is utilized as an alternative to a super-vised artificial neural network to update the nominal dynamics of the system andprovide disturbance estimates based on data gathered through interaction with thesystem. A soft-constrained two-player zero-sum differential game that is equivalentto the disturbance attenuation problem in nonlinear H-infinity-optimal control is then for-mulated to synthesis the H(infinity )controller. The differential game is solved through theGame-Theoretic differential dynamic programming (GT-DDP) algorithm in contin-uous time. In addition we provide a proof of quadratic convergence of the proposedGT-DDP algorithm. Simulation results on a quadcopter system demonstrate the effi-ciency of the learning-based control algorithm in handling model uncertainties andexternal disturbances.

关键词： differential game differential dynamic programming Gaussian process H-infinity control

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Contact-implicit Model Predictive Control: Controlling diverse quadruped motions without pre-planned contact modes or trajectories

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2025年第3期44卷 486-510页

作者： Kim, Gijeong Kang, Dongyun Kim, Joon-Ha Hong, Seungwoo Park, Hae-Won Korea Adv Inst Sci & Technol Dept Mech Engn 291 Daehak-roYuseong-gu Daejeon 34141 South Korea MIT Dept Mech Engn Cambridge MA USA

This paper presents a contact-implicit model predictive control (MPC) framework for the real-time discovery of multi-contact motions, without predefined contact mode sequences or foothold positions. This approach utilizes the contact-implicit differential dynamic programming (DDP) framework, merging the hard contact model with a linear complementarity constraint. We propose the analytical gradient of the contact impulse based on relaxed complementarity constraints to further the exploration of a variety of contact modes. By leveraging a hard contact model-based simulation and computation of search direction through a smooth gradient, our methodology identifies dynamically feasible state trajectories, control inputs, and contact forces while simultaneously unveiling new contact mode sequences. However, the broadened scope of contact modes does not always ensure real-world applicability. Recognizing this, we implemented differentiable cost terms to guide foot trajectories and make gait patterns. Furthermore, to address the challenge of unstable initial roll-outs in an MPC setting, we employ the multiple shooting variant of DDP. The efficacy of the proposed framework is validated through simulations and real-world demonstrations using a 45 kg HOUND quadruped robot, performing various tasks in simulation and showcasing actual experiments involving a forward trot and a front-leg rearing motion.

关键词： Contact-implicit model predictive control relaxed complementarity constraint multi-contact motion planning differential dynamic programming

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Optimal planning of a dynamic pump-treat-inject groundwater remediation system

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JOURNAL OF HYDROLOGY 2007年第3-4期342卷 295-304页

作者： Chang, Liang-Cheng Chu, Hone-Jay Hsiao, Chin-Tsai Natl Chiao Tung Univ Dept Civil Engn Hsinchu 30010 Taiwan Chungchou Inst Technol Dept Informat Management Changhua 510 Taiwan

This study integrates the genetic algorithm (GA) and constrained differential dynamic programming (CDDP) to design the pump-treat-inject system. The proposed model. considers both the cost of installing wells (fixed cost) and the operating cost of pumping, injection and water treatment. To minimize the total cost white meeting the water quality constraints, the model can compute the optimal number and locations of wells, as welt as the associated optimal pumping and injection schemes. Various numerical cases reveal that the requirement to balance the total volume between pumping and injection can significantly influence the final optimal design. (C) 2007 Elsevier B.V. All rights reserved.

关键词： optimal planning differential dynamic programming genetic algorithm pump-treat-inject remediation

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A PROJECTED NEWTON METHOD IN A CARTESIAN PRODUCT OF BALLS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第1期59卷 45-69页

作者： GAWANDE, M DUNN, JC N CAROLINA STATE UNIV DEPT MATHRALEIGHNC 27695

We formulate a locally superlinearly convergent projected Newton method for constrained minimization in a Cartesian product of balls. For discrete-time,N-stage, input-constrained optimal control problems with Bolza objective functions, we then show how the required scaled tangential component of the objective function gradient can be approximated efficiently with a differential dynamic programming scheme; the computational cost and the storage requirements for the resulting modified projected Newton algorithm increase linearly with the number of stages. In calculations performed for a specific control problem with 10 stages, the modified projected Newton algorithm is shown to be one to two orders of magnitude more efficient than a standard unscaled projected gradient method.

关键词： Constrained minimization differential dynamic programming optimal control projected Newton method

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Suboptimal trajectory programming for unmanned aerial vehicles with dynamic obstacle avoidance

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2019年第10期233卷 3857-3869页

作者： Guo, Hang Fu, Wen-xing Fu, Bin Chen, Kang Yan, Jie Northwestern Polytech Univ Sch Astronaut Xian Shaanxi Peoples R China

With regard to the dynamic obstacles current unmanned aerial vehicles encountered in practical applications, an integral suboptimal trajectory programming method was proposed. It tackled with multiple constraints simultaneously while guiding the unmanned aerial vehicle to execute autonomous avoidance maneuver. The kinetics of both unmanned aerial vehicle and dynamic obstacles were established with appropriate hypotheses. Then it was assumed that the unmanned aerial vehicle was faced with terminal constraints and control constraints in the whole duration. Meanwhile, the performance index was established as minimum control efforts. The initial trajectory was generated according to optimized model predictive static programming. Next, the slack variables were introduced to transform the inequality constraints arising from dynamic obstacle avoidance into equality constraints. In addition, sliding mode control theory was utilized to determine these slack variables' dynamics by designing the approaching law of sliding mode. Then the avoidance trajectory for single or multiple dynamic obstacles was developed by this combined method. At last, a further trajectory optimization was conducted by differential dynamic programming. Consequently, the integral problem was solved step by step and numerical simulations demonstrated that the integral method possessed high computational efficiency.

关键词： dynamic obstacle avoidance optimized model predictive static programming slack variables for inequality constraints sliding model control differential dynamic programming suboptimal trajectory programming

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DESIGN OF ROBOTIC DISCRETE MINIMUM ENERGY REGULATOR

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1991年第6期138卷 509-514页

作者： BESTAOUI, Y Laboratoire de Robotique et d'Informatique Industrielle Philips Nantes France

The optimal control of manipulators is a key to the success of automated manufacturing. The problem considered here is an energy minimisation problem with given dynamics and is subject to actuator constraints. A differential dynamic programming algorithm is developed to solve the discrete-time optimal control problem. This method allows calculation of the joint reference trajectories and the design of a proportional derivative regulator. The characteristics of this new method are exposed and the simulation results shown.

关键词： ROBOTICS DISCRETE OPTIMAL CONTROL differential dynamic programming

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A MULTIOBJECTIVE APPROACH TO THE SHORT-TERM SCHEDULING OF A HYDROELECTRIC POWER-SYSTEM

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IEEE TRANSACTIONS ON POWER SYSTEMS 1995年第4期10卷 1750-1755页

作者： LYRA, C FERREIRA, LRM COPEL SOSDPPOBR-80430 CURITIBAPARANABRAZIL

This paper is concerned with the short-term scheduling of the Iguacu river hydroelectric power system, in Southern Brazil. The system comprises four plants with an unusual high coupling, held by two different utilities. Even though government regulations establishes operation guide lines, utilities have their own interests. A multiobjective framework is adopt to study the operation of the system. dynamic programming is used to find optimal solutions, with an implementation based on the concept of differential dynamic programming. A case study shows the possibility of obtaining energetic gains with the adoption of non-conventional operation rules and the need of negotiation to avoid wasting energy.

关键词： OPTIMAL HYDROELECTRIC SCHEDULING SHORT-TERM SCHEDULING MULTIOBJECTIVE OPTIMIZATION dynamic programming differential dynamic programming

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THE APPLICATION OF OPTIMAL-CONTROL METHODOLOGY TO NON-LINEAR programming-PROBLEMS

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MATHEMATICAL programming 1981年第3期21卷 331-347页

作者： MURRAY, DM YAKOWITZ, SJ Systems and Industrial Engineering Department University of Arizona Tucson USA

dynamic programming techniques have proven to be more successful than alternative nonlinear programming algorithms for solving many discrete-time optimal control problems. The reason for this is that, because of the stagewise decomposition which characterizes dynamic programming, the computational burden grows approximately linearly with the numbern of decision times, whereas the burden for other methods tends to grow faster (e.g.,n 3 for Newton's method). The idea motivating the present study is that the advantages of dynamic programming can be brought to bear on classical nonlinear programming problems if only they can somehow be rephrased as optimal control problems. As shown herein, it is indeed the case that many prominent problems in the nonlinear programming literature can be viewed as optimal control problems, and for these problems, modern dynamic programming methodology is competitive with respect to processing time. The mechanism behind this success is that such methodology achieves quadratic convergence without requiring solution of large systems of linear equations.

关键词： differential dynamic programming Discrete Optimal Control Nonlinear programming Optimization Unconstrained Optimization

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