Optimal control of a class of piecewise deterministic processes

2013 ◽  
Vol 25 (1) ◽  
pp. 1-25 ◽  
Author(s):  
M. ANNUNZIATO ◽  
A. BORZÌ
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Open Loop ◽  
Control Framework ◽  
Dichotomic Noise ◽  
Deterministic Processes ◽  
Optimality Systems ◽  
Piecewise Deterministic Processes ◽  
Tracking Objectives ◽  
Probability Density Function Pdf

A new control strategy for a class of piecewise deterministic processes (PDP) is presented. In this class, PDP stochastic processes consist of ordinary differential equations that are subject to random switches corresponding to a discrete Markov process. The proposed strategy aims at controlling the probability density function (PDF) of the PDP. The optimal control formulation is based on the hyperbolic Fokker–Planck system that governs the time evolution of the PDF of the PDP and on tracking objectives of terminal configuration with a target PDF. The corresponding optimization problems are formulated as a sequence of open-loop hyperbolic optimality systems following a model predictive control framework. These systems are discretized by first-order schemes that guarantee positivity and conservativeness of the numerical PDF solution. The effectiveness of the proposed computational control framework is validated considering PDP with dichotomic noise.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

scholarly journals Approximately Optimal Control of Nonlinear Dynamic Stochastic Problems with Learning: The OPTCON Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 181
Author(s):  
Dmitri Blueschke ◽  
Viktoria Blueschke-Nikolaeva ◽  
Reinhard Neck
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Economic Models ◽  
Open Loop ◽  
Parameter Uncertainties ◽  
Information Patterns ◽  
Loop Feedback ◽  
Dynamic Stochastic

OPTCON is an algorithm for the optimal control of nonlinear stochastic systems which is particularly applicable to economic models. It delivers approximate numerical solutions to optimum control (dynamic optimization) problems with a quadratic objective function for nonlinear economic models with additive and multiplicative (parameter) uncertainties. The algorithm was first programmed in C# and then in MATLAB. It allows for deterministic and stochastic control, the latter with open loop (OPTCON1), passive learning (open-loop feedback, OPTCON2), and active learning (closed-loop, dual, or adaptive control, OPTCON3) information patterns. The mathematical aspects of the algorithm with open-loop feedback and closed-loop information patterns are presented in more detail in this paper.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Open-loop optimal control of a class of continuous-time stochastic systems—A simulation study†

1974 ◽  
Vol 19 (6) ◽  
pp. 1165-1175 ◽  
Author(s):  
EDGAR C. TACKER ◽  
THOMAS D. LINTON ◽  
CHARLES W. SANDERS
Keyword(s):  
Optimal Control ◽  
Simulation Study ◽  
Continuous Time ◽  
Stochastic Systems ◽  
Open Loop

Unified approach for open-loop optimal control

2007 ◽  
Vol 28 (2) ◽  
pp. 59-75 ◽  
Author(s):  
Y. Imura ◽  
D. S. Naidu
Keyword(s):  
Optimal Control ◽  
Open Loop ◽  
Unified Approach

An Economic Model Predictive Control Approach for Wind Power Smoothing and Tower Load Mitigation

2018 ◽  
Author(s):  
Mohamed M. Alhneaish ◽  
Mohamed L. Shaltout ◽  
Sayed M. Metwalli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Model Predictive Control ◽  
Wind Power ◽  
Predictive Control ◽  
Economic Model ◽  
Control Algorithm ◽  
Fatigue Load ◽  
Economic Model Predictive Control ◽  
Control Framework

An economic model predictive control framework is presented in this study for an integrated wind turbine and flywheel energy storage system. The control objective is to smooth wind power output and mitigate tower fatigue load. The optimal control problem within the model predictive control framework has been formulated as a convex optimal control problem with linear dynamics and convex constraints that can be solved globally. The performance of the proposed control algorithm is compared to that of a standard wind turbine controller. The effect of the proposed control actions on the fatigue loads acting on the tower and blades is studied. The simulation results, with various wind scenarios, showed the ability of the proposed control algorithm to achieve the aforementioned objectives in terms of smoothing output power and mitigating tower fatigue load at the cost of a minimal reduction of the wind energy harvested.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

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