H ∞ Optimal Repetitive Controller Design for Stable Plants

1997 ◽  
Vol 119 (3) ◽  
pp. 541-547 ◽  
Author(s):  
T. E. Peery ◽  
H. O¨zbay
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Design Problem ◽  
Controller Design ◽  
Delay System ◽  
Weighting Functions ◽  
Stability Robustness ◽  
Finite Dimensional ◽  
Repetitive Controller

The repetitive controller design problem is studied for stable plants in the framework of the H∞ optimal control. For a given nominal repetitive controller, first stability robustness is optimized by solving a finite dimensional H∞ control problem. Then the nominal design is modified in an optimal way so that the performance is improved while keeping the robustness level approximately the same. This problem is formulated as a two block H∞ problem involving a delay system and two weighting functions. The resulting controller can be implemented by adding a few blocks to the existing nominal design. An example is given to illustrate the numerical aspects of this approach.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

scholarly journals Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nasser H. Sweilam ◽  
Taghreed A. Assiri ◽  
Muner M. Abou Hasan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solutions ◽  
Delay System ◽  
Variable Order ◽  
Delay Model ◽  
Standard Difference ◽  
New Formulation ◽  
Number Of Customers

<p style='text-indent:20px;'>This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.</p>

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

Constrained bilinear control problem: Application to a cancer chemotherapy model

2017 ◽  
Vol 10 (04) ◽  
pp. 1750054 ◽  
Author(s):  
El Hassan Zerrik ◽  
Nihale El Boukhari
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Sufficient Conditions ◽  
Treatment Protocol ◽  
Bilinear Model ◽  
Bilinear Control ◽  
Finite Dimensional ◽  
Quadratic Cost ◽  
Admissible Controls

The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an optimal control that minimizes a quadratic cost functional in two cases of constrained admissible controls, then we give sufficient conditions for the uniqueness of such a control, and we derive useful algorithms for the computation of the optimal control. The established results are applied to a cancer chemotherapy bilinear model in order to simulate the optimal treatment protocol using two different approaches: one based on a limited instant toxicity, and the other on a limited cumulative toxicity along the therapy session.

Combined Plant and Controller Design Using Decomposition-Based Design Optimization and the Minimum Principle

2010 ◽  
Author(s):  
James T. Allison ◽  
Sam Nazari
Keyword(s):  
Optimal Control ◽  
Design Optimization ◽  
System Design ◽  
Physical System ◽  
Design Problem ◽  
Controller Design ◽  
Minimum Principle ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Augmented Lagrangian Coordination

An often cited motivation for using decomposition-based optimization methods to solve engineering system design problems is the ability to apply discipline-specific optimization techniques. For example, structural optimization methods have been employed within a more general system design optimization framework. We propose an extension of this principle to a new domain: control design. The simultaneous design of a physical system and its controller is addressed here using a decomposition-based approach. An optimization subproblem is defined for both the physical system (i.e., plant) design and the control system design. The plant subproblem is solved using a general optimization algorithm, while the controls subproblem is solved using a new approach based on optimal control theory. The optimal control solution, which is derived using the the Minimum Principle of Pontryagin (PMP), accounts for coupling between plant and controller design by managing additional variables and penalty terms required for system coordination. Augmented Lagrangian Coordination is used to solve the system design problem, and is demonstrated using a circuit design problem.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (4) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (04) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

scholarly journals Optimal Control of a Nonlinear Time-Delay System in Batch Fermentation Process

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongsheng Yu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Batch Process ◽  
Delay System ◽  
High Yield ◽  
Time Delay System ◽  
Control Variables ◽  
Terminal Time

The main control goal in batch process is to get a high yield of products. In this paper, to maximize the yield of 1,3-propanediol (1,3-PD) in bioconversion of glycerol to 1,3-PD, we consider an optimal control problem involving a nonlinear time-delay system. The control variables in this problem include the initial concentrations of biomass and glycerol and the terminal time of the batch process. By a time-scaling transformation, we transcribe the optimal control problem into a new one with fixed terminal time, which yields a new nonlinear system with variable time-delay. The gradients of the cost and constraint functionals with respect to the control variables are derived using the costate method. Then, a gradient-based optimization method is developed to solve the optimal control problem. Numerical results show that the yield of 1,3-PD at the terminal time is increased considerably compared with the experimental data.

scholarly journals OptiDose: Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control

2021 ◽  
Author(s):  
Freya Bachmann ◽  
Gilbert Koch ◽  
Marc Pfister ◽  
Gabor Szinnai ◽  
Johannes Schropp
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Disease Progression ◽  
Dosing Regimen ◽  
Reference Function ◽  
Cost Functional ◽  
Finite Dimensional ◽  
Optimal Dosing ◽  
The Cost

AbstractProviding the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. We developed and validated an optimal dosing algorithm (OptiDose) that computes the optimal individualized dosing regimen for pharmacokinetic–pharmacodynamic models in substantially different scenarios with various routes of administration by solving an optimal control problem. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference function by minimizing a cost functional. In pharmacokinetic–pharmacodynamic modeling, the controls are the administered doses and the reference function can be the disease progression. Drug administration at certain time points provides a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease progression. Consequently, rewriting the cost functional gives a finite-dimensional optimal control problem depending only on the doses. Adjoint techniques allow to compute the gradient of the cost functional efficiently. This admits to solve the optimal control problem with robust algorithms such as quasi-Newton methods from finite-dimensional optimization. OptiDose is applied to three relevant but substantially different pharmacokinetic–pharmacodynamic examples.

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