scholarly journals Non-anticipative strategies in guarantee optimization problems under functional constraints on disturbances

2020 ◽  
Vol 30 (4) ◽  
pp. 553-571
Author(s):  
M.I. Gomoyunov ◽  
D.A. Serkov
Keyword(s):  
Dynamical System ◽  
Dynamic Programming ◽  
Differential Games ◽  
Control Strategy ◽  
Optimization Problems ◽  
Dynamic Programming Principle ◽  
Functional Constraints ◽  
Constructive Solution ◽  
The Future ◽  
Games Theory

For a dynamical system controlled under conditions of disturbances, a problem of optimizing the guaranteed result is considered. A feature of the problem is the presence of functional constraints on disturbances, under which, in general, the set of admissible disturbances is not closed with respect to the operation of “gluing up” of two of its elements. This circumstance does not allow to apply directly the methods developed within the differential games theory for studying the problem and, thus, leads to the necessity of modifying them appropriately. The paper provides a new notion of a non-anticipative control strategy. It is proved that the corresponding functional of the optimal guaranteed result satisfies the dynamic programming principle. As a consequence, so-called properties of $u$- and $v$-stability of this functional are established, which may allow, in the future, to obtain a constructive solution of the problem in the form of feedback (positional) controls.

Nonlinear Stochastic Optimal Control of MDOF Partially Observable Linear Systems Excited by Combined Harmonic and Wide-Band Noises

2019 ◽  
Vol 19 (03) ◽  
pp. 1950019 ◽  
Author(s):  
R. C. Hu ◽  
X. F. Wang ◽  
X. D. Gu ◽  
R. H. Huan
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Control Problem ◽  
Linear Systems ◽  
Control Strategy ◽  
Stochastic Optimal Control ◽  
Wide Band ◽  
Dynamic Programming Principle ◽  
Stochastic Dynamic ◽  
Partially Observable

In this paper, nonlinear stochastic optimal control of multi-degree-of-freedom (MDOF) partially observable linear systems subjected to combined harmonic and wide-band random excitations is investigated. Based on the separation principle, the control problem of a partially observable system is converted into a completely observable one. The dynamic programming equation for the completely observable control problem is then set up based on the stochastic averaging method and stochastic dynamic programming principle, from which the nonlinear optimal control law is derived. To illustrate the feasibility and efficiency of the proposed control strategy, the responses of the uncontrolled and optimal controlled systems are respectively obtained by solving the associated Fokker–Planck–Kolmogorov (FPK) equation. Numerical results show the proposed control strategy can dramatically reduce the response of stochastic systems subjected to both harmonic and wide-band random excitations.

NUMERICAL METHODS FOR DIFFERENTIAL GAMES BASED ON PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 08 (02) ◽  
pp. 231-272 ◽  
Author(s):  
M. FALCONE
Keyword(s):  
Dynamic Programming ◽  
Numerical Methods ◽  
Differential Games ◽  
Value Function ◽  
Approximation Schemes ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Feedback Controls ◽  
Dynamic Programming Approach ◽  
Discrete Time Dynamical System

In this paper we present some numerical methods for the solution of two-persons zero-sum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games.

Optimal control of a novel uninterrupted multi-speed transmission for hybrid electric mining trucks

2019 ◽  
Vol 233 (12) ◽  
pp. 3235-3245 ◽  
Author(s):  
Weiwei Yang ◽  
Jiejunyi Liang ◽  
Jue Yang ◽  
Nong Zhang
Keyword(s):  
Dynamic Programming ◽  
Real Time ◽  
Control Strategy ◽  
Dynamic Models ◽  
Fuel Efficiency ◽  
Real Time Control ◽  
Traction Motor ◽  
Time Control ◽  
Power Split ◽  
Shift Strategy

Considering the energy consumption and specific performance requirements of mining trucks, a novel uninterrupted multi-speed transmission is proposed in this paper, which is composed of a power-split device, and a three-speed lay-shaft transmission with a traction motor. The power-split device is adapted to enhance the efficiency of the engine by adjusting the gear ratio continuously. The three-speed lay-shaft transmission is designed based on the efficiency map of traction motor to guarantee the drivability. The combination of the power-split device and three-speed lay-shaft transmission can realize uninterrupted gear shifting with the proposed shift strategy, which benefits from the proposed adjunct function by adequately compensating the torque hole. The detailed dynamic models of the system are built to verify the effectiveness of the proposed shift strategy. To evaluate the maximum fuel efficiency that the proposed uninterrupted multi-speed transmission could achieve, dynamic programming is implemented as the baseline. Due to the “dimension curse” of dynamic programming, a real-time control strategy is designed, which can significantly improve the computing efficiency. The simulation results demonstrate that the proposed uninterrupted multi-speed transmission with dynamic programming and real-time control strategy can improve fuel efficiency by 11.63% and 8.51% compared with conventional automated manual transmission system, respectively.

scholarly journals Powering Mode-Integrated Energy Management Strategy for a Plug-In Hybrid Electric Truck with an Automatic Mechanical Transmission Based on Pontryagin’s Minimum Principle

2018 ◽  
Vol 10 (10) ◽  
pp. 3758 ◽  
Author(s):  
Shaobo Xie ◽  
Xiaosong Hu ◽  
Kun Lang ◽  
Shanwei Qi ◽  
Tong Liu
Keyword(s):  
Dynamic Programming ◽  
Power Unit ◽  
Energy Management ◽  
Control Strategy ◽  
Minimum Principle ◽  
Mechanical Transmission ◽  
Auxiliary Power Unit ◽  
Auxiliary Power ◽  
Pontryagin's Minimum Principle ◽  
Hybrid Electric

Pontryagin’s Minimum Principle (PMP) has a significant computational advantage over dynamic programming for energy management issues of hybrid electric vehicles. However, minimizing the total energy consumption for a plug-in hybrid electric vehicle based on PMP is not always a two-point boundary value problem (TPBVP), as the optimal solution of a powering mode will be either a pure-electric driving mode or a hybrid discharging mode, depending on the trip distance. In this paper, based on a plug-in hybrid electric truck (PHET) equipped with an automatic mechanical transmission (AMT), we propose an integrated control strategy to flexibly identify the optimal powering mode in accordance with different trip lengths, where an electric-only-mode decision module is incorporated into the TPBVP by judging the auxiliary power unit state and the final battery state-of-charge (SOC) level. For the hybrid mode, the PMP-based energy management problem is converted to a normal TPBVP and solved by using a shooting method. Moreover, the energy management for the plug-in hybrid electric truck with an AMT involves simultaneously optimizing the power distribution between the auxiliary power unit (APU) and the battery, as well as the gear-shifting choice. The simulation results with long- and short-distance scenarios indicate the flexibility of the PMP-based strategy. Furthermore, the proposed control strategy is compared with dynamic programming (DP) and a rule-based charge-depleting and charge-sustaining (CD-CS) strategy to evaluate its performance in terms of computational accuracy and time efficiency.

Trajectory control and random vibration control of nonlinear system with dielectric elastomer actuator

2018 ◽  
Vol 29 (11) ◽  
pp. 2424-2436 ◽  
Author(s):  
Yanping Tian ◽  
Yong Wang ◽  
Xiaoling Jin ◽  
Zhilong Huang
Keyword(s):  
Nonlinear System ◽  
Control Strategy ◽  
Primary Structure ◽  
Equilibrium Position ◽  
Random Vibration ◽  
Dielectric Elastomer ◽  
Control Technique ◽  
Dynamic Programming Principle ◽  
Dielectric Elastomer Actuator ◽  
Dielectric Elastomer Actuators

Dielectric elastomer actuators have gained extensive attention in scientific and industrial communities with the rapid development of soft robot technology. There still remain some questions on the control aspect of nonlinear system with dielectric elastomer actuator. The first is whether the soft actuator can successfully drive the primary structure to track an arbitrary prescribed trajectory. The second is how to suppress the random vibration around the equilibrium position when the primary structure is disturbed by external excitation. This article seeks the answers for these two questions. By directly solving the governing equation of motion, an open-loop control technique is designed to track a prescribed trajectory. The effectiveness of the trajectory tracking technique is investigated and the limitation is illustrated by the influence of inertia of the primary structure. Based on the stochastic averaging of energy envelope and stochastic dynamic programming principle, a clipped control strategy is proposed by slightly adjusting the voltage in real time to suppress the random vibration around the equilibrium position. The good effectiveness and high robustness of the clipped control strategy are verified numerically. This work may provide some guidelines for the control aspect of nonlinear systems with dielectric elastomer actuators.

Sign in / Sign up

Export Citation Format

Share Document