Irreducibility and reduction of nonlinear control systems: Unification and extension via pseudo-linear algebra

Kotta, Ülle; Kotta, P.; Halás, Miroslav

doi:10.1109/icarcv.2008.4795662

Cited by 3 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, there exists a configuration interesting from the analysis point of view. Note that in case of valve-controlled system differential equations are very similar to (3) vC  is an input of the system) listed in Table 5. Table 5 at the first sight seems to be reasonable, according to Theorem 3, the system is not accessible.…”

Section: Valve-controlled Scenariomentioning

confidence: 99%

“…The benefit of such a framework is that it suggests a wide range of rigorous mathematical tools and a systematic way to handle different control problems from a unified viewpoint. The approach has been successfully applied so far to address a number of problems for nonlinear control systems, including system reduction [3], realization [4] of i/o differential or difference equations, accessibility and feedback linearization of state equations [2]. On one hand, the algebraic approach requires a lot of mathematical technicalities to be used to perform analysis and obtain a solution, making this way an artificial gap between theory and practice.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Algebraic Approach for Analysis and Control of a Water Tank System

Belikov

Kotta

Tepljakov

2016

ITC

View full text Add to dashboard Cite

Modern nonlinear control theory provides various powerful frameworks. Some of them are still either out of sight of the industry or too complex to be implemented. In this paper, we present and explain the key points of an algebraic framework of differential forms. Together with Mathematica based software package NLControl it forms a powerful basis toward the employment in analysis and control of various complex processes. The application is illustrated on the basis of the laboratory model of three serially connected water tanks, and comparison with the results obtained by using classical PID controller is presented.

show abstract

Section: Valve-controlled Scenariomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algebraic Approach for Analysis and Control of a Water Tank System

Belikov

Kotta

Tepljakov

2016

ITC

View full text Add to dashboard Cite

show abstract

“…Similarly, for the number of equations in (15) the polynomials b i (δ] and b r,j (δ] in (14) play the crucial role. Besides the number of equations, the computational complexity is affected also by the choice of the monomial ordering (18) and (19). Note that the lexicographical ordering we employed is only one choice among the possible orderings one can consider here.…”

Section: Computational Complexitymentioning

confidence: 99%

“…However, knowing an input-output representation is sometimes essential for finding a solution to a specific control problem. Typical representatives are various system equivalence and controllability problems [18,19,22,26,30], model matching problems [8,15,16], observer design [9,14,21], observability and identifiability of parameters [1,29], and others. Eventually, any transfer function approach to a control problem deals, in general, with input-output properties of a system.…”

Section: Introductionmentioning

confidence: 99%