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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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Data-driven model predictive control design for offset-free tracking of nonlinear systems

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INTERNATIONAL JOURNAL OF CONTROL 2023年第6期96卷 1408-1423页

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

We propose a design of data-driven Model Predictive Control (MPC) using a suboptimal trajectory and the linear time-varying (LTV) models from data-driven trajectory optimisation that achieves offset-free tracking. Data-driven constrained differential dynamic programming (CDDP) is exploited to improve the trajectory iteratively without the knowledge of the nonlinear model. A trajectory is divided to the transient and steady state regions, controlled by the Linear time-varying MPC (LTVMPC) and the offset-free linear MPC (LMPC), respectively. We prove the feasibility of the proposed LTVMPC in the transient region, and the offset-free tracking property of LMPC. The proposed scheme is validated to a continuous stirred tank reactor (CSTR) process. Simulation studies show that the suboptimal trajectory and LTV models are generated by CDDP, and the proposed MPC achieves offset-free tracking and disturbance rejection for a set of initial conditions and set points in the operating region.

关键词： Model predictive control gap metric linear time-varying model predictive control 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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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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Optimal control of HVAC systems using DDP and NLP techniques

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OPTIMAL CONTROL APPLICATIONS & METHODS 1996年第1期17卷 71-78页

作者： Kota, NN House, JM Arora, JS Smith, TF UNIV IOWA DEPT CIVIL & ENVIRONM ENGNIOWA CITYIA 52242 UNIV IOWA DEPT MECH ENGNIOWA CITYIA 52242

The objective of this study is to apply the differential dynamic programming (DDP) technique of optimal control to heating, ventilating and air-conditioning (HVAC) systems and to compare its performance with a non-linear programming (NLP) technique using the sequential quadratic programming method. The DDP technique is briefly described and studied. Limitations of the technique are noted. Three cases of a system that has been treated previously in the literature are optimized by the two techniques and the computational times compared, The study shows DDP to be efficient compared with NLP for the example problems. NLP is, however, more robust and general and can treat constraints on the state variables directly. Further investigation is needed for larger-scale problems to fully explore the features of the two methods.

关键词： optimal control HVAC systems non-linear programming differential dynamic programming

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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 projected Newton method optimal control differential dynamic programming

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