The linear-quadratic optimal control approach to feedback control design for systems with delay

Uchida, Kenko; Shimemura, Etsujiro; Kubo, Tomohiro; Abe, Naoto

doi:10.1016/0005-1098(88)90053-2

Cited by 83 publications

(41 citation statements)

References 22 publications

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“…The methods presented in [6] is also a sensitivity approach in which the original system is embedded in a class of nondelay systems using an appropriate parameter. A reference book in the area ( [7] and references therein), discussing the Pontryagin's maximum principle or the dynamic programming method for systems with delays, states that finding a particular explicit form of the criterion must also be taken into account: the studies mostly focused on the time-optimal criterion for quadratic systems [3,[8][9][10][11].…”

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confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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In this paper, a new numerical method for solving the optimal control of linear time-varying delay systems with quadratic performance index is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions, consisting of block-pulse functions and Bernoulli polynomials, are presented. The operational matrices of integration, product, delay and the integration of the cross product of two hybrid functions of block-pulse and Bernoulli polynomials vectors are given. These matrices are then utilized to reduce the solution of the optimal control of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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confidence: 99%

Optimal Control of Delay Systems by Using a Hybrid Functions Approximation

Haddadi

Ordokhani

Razzaghi

2011

J Optim Theory Appl

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“…The term z(x,y(·)) represents the control optimal solution for a system with a time delay as obtained from the LQR technique, where N is a symmetric positive definite matrix, B is a constant matrix, P is a symmetric positive matrix, D(s) is a solution to the Generalized Riccati Equations and y(Àτ) ¼ x (t À τ). Additional details pertaining to the LQR technique can be found in the literature [143][144][145]. The flexibility index problem can be formulated similarly, as shown in Eq.…”

Section: Dynamic Feasibility and Flexibility Analysismentioning

confidence: 99%

Mathematical Tools for the Quantitative Definition of a Design Space

Rogers

Ierapetritou

2016

Methods in Pharmacology and Toxicology

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This chapter focuses on the application of process modeling to determination of design space for pharmaceutical manufacturing processes. The first two sections define design space and related terms from a regulatory perspective and discuss how these apply in practice during pharmaceutical process development. In Sect. 3, a variety of mathematical techniques that can be used to guide design space development are introduced. An emphasis is placed on the use of feasibility analysis and the relationship between process feasibility and design space. Statistical techniques, including latent variable and Bayesian methods, are also discussed in detail. For methods that have been reported in the literature for pharmaceutical manufacturing applications, an overview of the relevant case studies is provided. If methods have not yet been applied to pharmaceutical processes, potential applications for these techniques are indicated. To illustrate the applicability of these concepts to pharmaceutical manufacturing processes, a brief case study is presented in Sect. 4. A discussion of design space verification and issues related to scale-up is provided in Sect. 5. Finally a brief summary of the concepts presented and their potential role in design space development for pharmaceutical processes is given in Sect. 6. This chapter is intended to provide readers with an understanding of mathematical techniques that can be used during process development to assist in the determination of process design space. An overview of the problem formulation and solution approaches for each method are presented. More detailed mathematical developments for each technique are available in the references provided. Table 1 provides a list of symbols that are used throughout this chapter, while Table 2 describes acronyms used within this chapter.

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“…In [17,18], the linear-quadratic problem is solved for state-delay and state-and-input-delay systems, respectively, where the optimal control is obtained in the form of the integral over the previous system trajectory and depends on the system co-state satisfying a system of partial differential equations. The papers [19,20] develop the generalized Riccati approach, where the optimal control depends on the current system state and is determined by the gain matrices satisfying a set of Riccati-type differential and partial differential equations.…”

Section: Introductionmentioning

confidence: 99%