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Two-stage dynamic real-time optimization framework using parameter-dependent differential dynamic programming

COMPUTERS & CHEMICAL ENGINEERING 2025年 192卷

作者： Jung, Hyein Kim, Jong Woo Lee, Jong Min Seoul Natl Univ Dept Chem & Biol Engn 1 Gwanak Ro Seoul 08826 South Korea Incheon Natl Univ Innovat Ctr Chem Engn Dept Energy & Chem Engn 119 Acad Ro Incheon 22012 South Korea

The purpose of chemical process control includes proactive adjustment of the operation to make the most profit out of it. Within this context, real-time optimization (RTO) is proposed and extended to dynamic RTO (DRTO) in the hierarchical control structure, usually having model predictive control (MPC) below. However, online tractability confined the model complexity of RTO and MPC, which results in model inconsistency and, even, incompatible solutions. Here we use parameter-dependent differential dynamic programming (PDDP) to incorporate the closed-loop behavior of the controller in an RTO layer to reduce problem complexity and online computation time. The adaptive control performance of PDDP and the efficacy of closed-loop DRTO formulation with PDDP is demonstrated with the reaction-storage-separation network system control. Consequently, PDDP provides a useful parameterization method to express closed-loop system dynamics, which enables fast feedback control and integrated plant optimization.

关键词： differential dynamic programming dynamic real-time optimization Economic optimization Parametric disturbance

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Sliding mode observer-based min-max differential dynamic programming for output feedback differential games

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INTERNATIONAL JOURNAL OF CONTROL 2025年

作者： Sarbaz, Mohammad Sun, Wei Univ Oklahoma Sch Aerosp & Mech Engn 865 Asp Ave Norman OK 73019 USA

This paper studies the sliding mode observer-based min-max differential dynamic programming (DDP) method for the output feedback differential game problem. The objective of the min-max DDP refers to a game-theoretic approach where one controller aims to minimise a cost function, while the other controller seeks to maximise the same cost function. The min-max DDP relies on full knowledge of dynamics which is challenging in output feedback systems. To address this challenge, we first employ the High Order Sliding Mode (HOSM) observer to obtain unobserved states and approximate the dynamics of the nonlinear system. Then, by integrating the HOSM observer with the optimisation capabilities of min-max DDP, this paper details the update rules for the minimising and maximising controls for both players and introduces a set of backward differential equations for the second-order approximation of the value function. Finally, results of two examples are presented to show the effectiveness of the proposed methodology.

关键词： Output feedback differential games differential dynamic programming sliding mode observer optimal control

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Data-Driven Stochastic Game Theoretic differential dynamic programming

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2025年

作者： Sarbaz, Mohammad Sun, Wei Univ Oklahoma Sch Aerosp & Mech Engn Norman OK 73019 USA

This paper introduces a novel approach for designing optimal control using data-driven Stochastic Game Theoretic differential dynamic programming (SGT-DDP). The proposed method addresses unknown stochastic systems by approximating both drift and diffusion dynamics. The drift dynamics is estimated via Gaussian Process Regression (GPR) using input-output data. The diffusion dynamics is approximated from the noise data, which is extracted through subtracting the noisy output from the smoothed output. Subsequently, the binning method is combined with GPR to obtain the approximate model of the diffusion dynamics. These approximations are integrated into the SGT-DDP framework to compute optimal control policies. Simulations on benchmark nonlinear systems under unknown dynamics demonstrate the effectiveness of the method.

关键词： differential dynamic programming gaussian process regression nonlinear systems optimal control stochastic dynamics

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differential dynamic programming Based Home Energy Management Scheduler

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2020年第3期11卷 1427-1437页

作者： Jeddi, Babak Mishra, Yateendra Ledwich, Gerard Queensland Univ Technol Elect Engn & Comp Sci Brisbane Qld 4000 Australia

This paper proposes a computationally efficient home energy management scheduler (HEMS) to minimize the cost of electricity consumption (CoEC) within a home which consists of rooftop photovoltaics (PV), a battery energy storage systems, and controllable appliances. differential dynamic programming (DDP) algorithm is used and the uncertainty of PV generation and household demand along with the battery degradation is incorporated. The DDP algorithm divides the original problem space into several smaller subspaces and iteratively searches for a better solution within a subspace. The effectiveness of the developed framework is investigated through numerical simulations. The proposed HEMS minimizes the CoEC by determining an appropriate schedule of all devices ensuring an acceptable level for the customer comfort. The DPP-based HEMS is faster than the exact DP, approximate DP and mixed integer non-linear programming method. It is implemented in an intra-day setting where the BESS power is adjusted based on real-time observations of uncertain variable.

关键词： Batteries Trajectory Energy management Degradation Home appliances Uncertainty Computational modeling Battery energy storage system battery degradation controllable appliances differential dynamic programming home energy management uncertainty

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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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differential dynamic programming for finite-horizon zero-sum differential games of nonlinear systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2023年第18期33卷 11062-11084页

作者： Zhang, Bin Jia, Yingmin Zhang, Yuqi Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China Beihang Univ Res Div 7 Beijing Peoples R China

In this article, we present an iterative algorithm based on differential dynamic programming (DDP) for finite-horizon two-person zero-sum differential games. The technique of DDP is used to expand the Hamilton-Jacobi-Isaacs (HJI) partial differential equation into higher-order differential equations. Using value function and saddle point approximations, the DDP expansion is transformed into algebraic matrix equation in integral form. Based on the algebraic matrix equation, a DDP iterative algorithm is developed to learn the solution to the differential games. Strict proof is proposed to guarantee the iterative convergences of the value function and saddle point. The new algorithm is fundamentally different from existing results, in the sense that it overcome the technical obstacle to address the time-varying behavior of HJI partial differential equation. Simulation examples are given to demonstrate the effectiveness of the proposed method.

关键词： differential dynamic programming differential games finite-horizon cost function Hamilton-Jacobi-Isaacs equation iterative algorithm

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differential dynamic-programming AND SEPARABLE PROGRAMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1978年第4期24卷 617-637页

作者： OHNO, K Associate Professor Department of Applied Mathematics and Physics Kyoto University Kyoto Japan

This paper deals with differential dynamic programming for solving nonlinear separable programs. The present algorithm and its derivation are rather different from differential dynamic programming algorithms and their derivations by Mayne and Jacobson, who have not proved the convergence of their algorithms. The local convergence of the present algorithm is proved, and numerical examples are given.

关键词： differential dynamic programming nonlinear separable programs convergence proofs Kuhn-Tucker conditions iterative methods Newton's method

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differential dynamic programming for Finite-Horizon Multi-Player Non-Zero-Sum differential Games of Nonlinear Systems 12

Differential Dynamic Programming for Finite-Horizon Multi-Pl...

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IEEE 12th Data Driven Control and Learning Systems Conference (DDCLS)

作者： Zhang, Yuqi Zhang, Bin Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China

ISBN: (纸本)9798350321050

In this paper, an iterative algorithm based on differential dynamic programming (DDP) is developed to solve the finite-horizon multi-player non-zero-sum (NZS) games. By using the DDP, the coupled Hamilton-Jacobi (HJ) equations are expanded from partial differential forms to higher-order differential forms. By approximating the value functions and optimal control policies through several finite sets of basis functions, the DDP expansions are transformed into algebraic matrix equations in integral forms. Then a policy iteration (PI) algorithm is provided to solve the feedback Nash equilibrium of above NZS games. Finally, two simulation examples are given to demonstrate the feasibility of the developed algorithm.

关键词： Multi-player NZS games Feedback Nash equilibrium Coupled Hamilton-Jacobi equations differential dynamic programming Finite-horizon optimal control Policy iteration

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differential dynamic programming for Multistage Uncertain Optimal Control 7

Differential Dynamic Programming for Multistage Uncertain Op...

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7th International Joint Conference on Computational Sciences and Optimization (CSO)

作者： Qian, Xiaodong Zhu, Yuanguo Nanjing Univ Sci & Technol Dept Appl Math Nanjing 210094 Jiangsu Peoples R China

ISBN: (纸本)9781479953721

When a multistage system is transferred from one stage to the next one, it could be affected by some disturbance. This kind of system is called a multistage uncertain system if the disturbance is an uncertain factor. Based on the uncertainty theory and the equation of optimality in uncertain optimal control, a differential dynamic programming algorithm for an optimal control problem subject to a multistage uncertain system is established. The differential dynamic programming algorithm is implemented from an initial nominal control, which is provided by the genetic algorithm, to an optimal control of the problem step by step. Finally, a numerical example that the system is nonlinear with the disturbance of linear uncertain variables is given to illustrate the feasibility of the algorithm.

关键词： multistage uncertain system uncertain optimal control differential dynamic programming genetic algorithm

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Sundman-Transformed differential dynamic programming with Modified Equinoctial Elements

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JOURNAL OF THE ASTRONAUTICAL SCIENCES 2019年第4期66卷 419-445页

作者： Aziz, Jonathan D. Scheeres, Daniel J. Univ Colorado Colorado Ctr Astrodynam Res Boulder CO 80309 USA

Previous efforts addressed the challenge of low-thrust many-revolution trajectory optimization by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit anomaly and performing the optimization with differential dynamic programming (DDP). The approach may be enhanced by representing the spacecraft state with orbital elements rather than position and velocity coordinates. This paper shows how the modified equinoctial element state representation enters the DDP algorithm. Example transfers from geostationary transfer orbit (GTO) to geosynchronous orbit (GEO) demonstrate how gains in computational efficiency are possible with minimal impact to solution quality. Those gains are leveraged to compute the Pareto front of time versus delivered mass for a benchmark orbit transfer from the literature.

关键词： Low-thrust trajectory optimization differential dynamic programming Sundman transformation Modified equinoctial elements Many-revolution

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