Semi-active bounded optimal control of uncertain nonlinear coupling vehicle system with rotatable inclined supports and MR damper under random road excitation

Ying, Z.G.,Yan, G.F.,Ni, Y.Q. Techno-Press 2018 Coupled systems mechanics Vol.7 No.6

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

Approximate Dynamic Programming-Based Dynamic Portfolio Optimization for Constrained Index Tracking

박주영,양동수,박경욱 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

Approximate Dynamic Programming-Based Dynamic Portfolio Optimization for Constrained Index Tracking

Jooyoung Park,Dongsu Yang,Kyungwook Park 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

Approximate Dynamic Programming-Based Dynamic Portfolio Optimization for Constrained Index Tracking

Park, Jooyoung,Yang, Dongsu,Park, Kyungwook Korean Institute of Intelligent Systems 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

동적 계획법을 이용한 LNG 현물시장에서의 포트폴리오 구성방법

류종현(Jong-hyun Ryu) 대한산업공학회 2015 대한산업공학회지 Vol.41 No.3

Among many energy resources, natural gas has recently received a remarkable amount of attention, particularly from the electrical generation industry. This is in part due to increasing shale gas production, providing an environment-friendly fossil fuel, and high risk of nuclear power. Because South Korea, the world’s second largest LNG importing nation after Japan, has no international natural gas pipelines and relies on imports in the form of LNG, the natural gas has been traditionally procured by long term LNG contracts at relatively high price. Thus, there is a need of developing an Asian LNG trading hub, where LNG can be traded at more competitive spot prices. In a natural gas spot market, the amount of natural gas to be bought should be carefully determined considering a limited storage capacity and future pricing dynamics. In this work, the problem to find the optimal amount of natural gas in a spot market is formulated as a Markov decision process (MDP) in risk neutral environment and the optimal base stock policy which depends on a stage and price is established. Taking into account price and demand uncertainties, the basestock target levels are simply approximated from dynamic programming. The simulation results show that the basestock policy can be one of effective ways for procurement of LNG in a spot market.

DYNAMIC PROGRAMMING FOR GENERAL LINEAR QUADRATIC OPTIMAL STOCHASTIC CONTROL WITH RANDOM COEFFICIENTS

( Shan Jian Tang ) 한국금융공학회 2014 한국금융공학회 학술발표회 Vol.2014 No.1

We are concerned with the linear-quadratic optimal stochastic control problem where all the coe_cients of the control system and the running weighting matrices in the cost functional are allowed to be predictable (but essentially bounded) processes and the terminal state-weighting matrix in the cost functional is allowed to be random. Under suitable conditions, we prove that the value field V (t, x, !), (t, x, !) ∈ [0, T] × Rn × , is quadratic in x, and has the following form: V (t, x) = hKtx, xi where K is an essentially bounded nonnegative symmetric matrix-valued adapted processes. Using the dynamic programming principle (DPP), we prove that K is a continuous semimartingale of the form and that (K, L) with L := (L1, ... ,Ld) is a solution to the associated backward stochastic Riccati equation (BSRE), whose generator is highly nonlinear in the unknown pair of processes. The uniqueness is also proved via a localized completion of squares in a self-contained manner for a general BSRE. The existence and uniqueness of adapted solution to a general BSRE was initially proposed by the French mathematician J. M. Bismut [in SIAM J. Control & Optim., 14(1976), pp. 419?444, and in S´eminaire de Probabilit´es XII, Lecture Notes in Math. 649, C. Dellacherie, P. A. Meyer, and M. Weil, eds., Springer-Verlag, Berlin, 1978, pp. 180?264], and subsequently listed by Peng [in Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), S. Chen, et al., eds., Kluwer Academic Publishers, Boston, 1999, pp. 265?273] as the first open problem for backward stochastic di_erential equations. It had remained to be open until a general solution by the author [in SIAM J. Control & Optim., 42(2003), pp. 53?75] via the stochastic maximum principle with a viewpoint of stochastic flow for the associated stochastic Hamiltonian system. The present paper is its companion, and gives the second but more comprehensive (seemingly much simpler, but appealing to the advanced tool of Doob-Meyer decomposition theorem, in addition to the DDP) adapted solution to a general BSRE via the DDP. Further extensions to the jump-di_usion control system and to the general nonlinear control system are possible.

Stochastic optimal control of coupled structures

Ying, Z.G.,Ni, Y.Q.,Ko, J.M. Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.15 No.6

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

Ying, Z.G.,Ni, Y.Q.,Ko, J.M. Techno-Press 2009 Smart Structures and Systems, An International Jou Vol.5 No.1

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.

A Dynamic Programming Approach for Emergency Vehicle Dispatching Problems

Jae Young Choi(최재영),Heung-Kyu Kim(김흥규) 한국컴퓨터정보학회 2016 韓國컴퓨터情報學會論文誌 Vol.21 No.9

In this research, emergency vehicle dispatching problems faced with in the wake of massive natural disasters are considered. Here, the emergency vehicle dispatching problems can be regarded as a single machine stochastic scheduling problems, where the processing times are independently and identically distributed random variables, are considered. The objective of minimizing the expected number of tardy jobs, with distinct job due dates that are independently and arbitrarily distributed random variables, is dealt with. For these problems, optimal static-list policies can be found by solving corresponding assignment problems. However, for the special cases where due dates are exponentially distributed random variables, using a proposed dynamic programming approach is found to be relatively faster than solving the corresponding assignment problems. This so-called Pivot Dynamic Programming approach exploits necessary optimality conditions derived for ordering the jobs partially.

A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

Z. G. Ying,Y. Q. Ni,J. M. Ko 국제구조공학회 2009 Smart Structures and Systems, An International Jou Vol.5 No.1

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semiactive parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear nonclipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.