scholarly journals Optimal Control Implementation with Terminal Penalty Using Metaheuristic Algorithms

Automation ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 48-65
Author(s):  
Viorel Minzu
Keyword(s):  
Optimal Control ◽  
Process Model ◽  
Simulated Annealing Algorithm ◽  
Sampling Period ◽  
Open Loop ◽  
Reference Trajectory ◽  
State Variables ◽  
The Real ◽  
Real Process ◽  
Minimization Procedure

Optimal control problems can be solved by a metaheuristic based algorithm (MbA) that yields an open-loop solution. The receding horizon control mechanism can integrate an MbA to produce a closed-loop solution. When the performance index includes a term depending on the final state (terminal penalty), the prediction’s time possibly surpasses a sampling period. This paper aims to avoid predicting the terminal penalty. The sequence of the best solution’s state variables becomes a reference trajectory; this one is used by a tracking structure that includes the real process, a process model (PM) and a tracking controller (TC). The reference trajectory must be followed up as much as possible by the real trajectory. The TC makes a one-step-ahead prediction and calculates the control inputs through a minimization procedure. Therefore the terminal penalty’s calculation is avoided. An example of a tracking structure is presented. The TC may also use an MbA for its minimization procedure. The implementation is presented in two versions: using a simulated annealing algorithm and an evolutionary algorithm. The simulations have proved that the proposed approach is realistic. The tracking structure does or does not work well, depending on the PM’s accuracy in reproducing the real process.

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.

Catastrophe Theory in Explaining Price Dynamics on the Real Estate Market

2013 ◽  
Vol 21 (3) ◽  
pp. 51-61 ◽  
Author(s):  
Mirosław Belej
Keyword(s):  
Real Estate ◽  
Catastrophe Theory ◽  
Open Systems ◽  
Real Estate Market ◽  
Sensitivity Threshold ◽  
State Variables ◽  
The Real ◽  
The Real Estate ◽  
The Real Estate Market ◽  
External Stimuli

Abstract The real estate market is an open system, which implies that it is able to exchange signals with other open systems and dynamic systems. The evolution of a market system over time can be described mathematically. If the system's sensitivity threshold to external stimuli is exceeded, it becomes destabilized and moves from a near-balanced state to a state that is far from equilibrium. Those dynamic processes often induce key changes in the system's trajectory of evolution. In search of equilibrium, the system becomes transformed in a process of discontinuous and discrete changes in state variables. The above statement constitutes the research hypothesis in this article. In this study, an attempt was made to develop a mathematical model for visualizing the evolutionary path of the real estate market in the form of continuous changes interrupted by discontinuous changes. The qualitative transformation of the system will be evaluated with the use of the catastrophe theory.

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

Modeling of a Steam Turbine Including Partial Arc Admission for Use in a Process Simulation Software Environment

2011 ◽  
Author(s):  
Eric Liese
Keyword(s):  
Steam Turbine ◽  
Process Simulation ◽  
Process Model ◽  
Constant Pressure ◽  
Pressure Ratio ◽  
Simulation Software ◽  
State Variables ◽  
Steam Turbines ◽  
Software Environment ◽  
Last Stage

A dynamic process model of a steam turbine, including partial arc admission operation, is presented. Models were made for the first stage and last stage, with the middle stages presently assumed to have a constant pressure ratio and efficiency. A condenser model is also presented. The paper discusses the function and importance of the steam turbines entrance design and the first stage. The results for steam turbines with a partial arc entrance are shown, and compare well with experimental data available in the literature, in particular, the “valve loop” behavior as the steam flow rate is reduced. This is important to model correctly since it significantly influences the downstream state variables of the steam, and thus the characteristic of the entire steam turbine, e.g., state conditions at extractions, overall turbine flow, and condenser behavior. The importance of the last stage (the stage just upstream of the condenser) in determining the overall flowrate and exhaust conditions to the condenser is described and shown via results.

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

Optimal control strategies for the surface hardening of steel

2004 ◽  
Vol 120 ◽  
pp. 325-335
Author(s):  
D. Hömberg ◽  
S. Volkwein ◽  
W. Weiss
Keyword(s):  
Optimal Control ◽  
Surface Hardening ◽  
Control Strategies ◽  
Hot Spot ◽  
Orthogonal Decomposition ◽  
Phase Volume ◽  
The Finite Element Method ◽  
Optimal Temperature ◽  
Real Process ◽  
Proper Orthogonal

We discuss control strategies for the surface hardening of steel with laser or electron beam. The goal is to acchieve a prescribed hardening depth avoiding surface melting. Our mathematical model consists of a system of ODEs for the phase volume fractions coupled with the heat equation. The system is solved semi-implicitely using the finite element method. For the optimal control we discuss two approaches: model reduction using POD (Proper Orthogonal Decomposition) and a feedback control of temperature. The numerical results prove that it is not sufficient to control the surface temperature in order to obtain a uniform hardening depth. Instead the best strategy should be to compute the optimal temperature in the hot spot of the beam by solving the control problem and use this temperature as the set-point for the pyrometer control of the real process.

scholarly journals Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

2015 ◽  
Author(s):  
Jiaying Zhang ◽  
Colin R. McInnes
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Smart Structures ◽  
Polynomial Method ◽  
Reference Trajectory ◽  
Sensors And Actuators ◽  
Embedded Computing ◽  
Equal Energy ◽  
Optimal Control Method ◽  
Heteroclinic Connection

Several new methods are proposed to reconfigure smart structures with embedded computing, sensors and actuators. These methods are based on heteroclinic connections between equal-energy unstable equilibria in an idealised spring-mass smart structure model. Transitions between equal-energy unstable (but actively controlled) equilibria are considered since in an ideal model zero net energy input is required, compared to transitions between stable equilibria across a potential barrier. Dynamical system theory is used firstly to identify sets of equal-energy unstable configurations in the model, and then to connect them through heteroclinic connection in the phase space numerically. However, it is difficult to obtain such heteroclinic connections numerically in complex dynamical systems, so an optimal control method is investigated to seek transitions between unstable equilibria, which approximate the ideal heteroclinic connection. The optimal control method is verified to be effective through comparison with the results of the exact heteroclinic connection. In addition, we explore the use of polynomials of varying order to approximate the heteroclinic connection, and then develop an inverse method to control the dynamics of the system to track the polynomial reference trajectory. It is found that high order polynomials can provide a good approximation to true heteroclinic connections and provide an efficient means of generating such trajectories. The polynomial method is envisaged as being computationally efficient to form the basis for real-time reconfiguration of real, complex smart structures with embedded computing, sensors and actuators.

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.

Sign in / Sign up

Export Citation Format

Share Document