Nonlinear Control of Non-Observable Non-Flat MIMO State Space Systems Using Flat Inputs

Fritzsche, Klemens; Guo, Yuhang; Röbenack, Klaus

doi:10.1109/icstcc.2019.8886157

Cited by 10 publications

(20 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equivalently, the measure of modification is the number of equations of ( 5)-( 6) (where subsystem (6) is absent in the observable case), that we have to change by adding the flat-inputs u 1 , . .…”

Section: Resultsmentioning

confidence: 99%

“…Theorem 3.2 uses a normal form, denoted NF min , and the construction of NF min is based, as that of the forms of [20], on the following idea: a flat system is observable (with respect to its flat output and independently of the applied input signal), so we have to render the original system (Σ, h) observable. For observability we need a link from the z-subsystem towards the observed w-subsystem, but for Σ there is no such a link, see the observed-unobserved form ( 5)- (6). It follows that we have to create a link assuring observability with the help of the control vector fields, see Figure 2, where Π stands for products of some z-variables and u 1 .…”

Section: Constructing Flat Inputs For a Minimal Modification Of σmentioning

confidence: 99%

“…, ρ m ) at x 0 . We will prove that Σ can be locally, around x 0 , transformed into (5)-( 6) with the unobserved subsystem (6) given by the following chain of integrators:…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

“…. , z n−k ) = z = φ −1 • Ψ(x), with φ −1 • Ψ defined on O x 0 since φ(z) is global on R n−k , the original system (Σ, h) takes the form ( 5)-( 6) with the unobserved subsystem (6) given by (33) (which is of the form (10) with b n−k = 1).…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

“…The single-output case has been considered in [32], while the observable multi-output case has been discussed in [33], see also [7] for another approach based on the notion of unimodularity. In the recent papers [19,20] (see also [6]), the authors solved the unobservable case for which locally, around any point of an open and dense subset of the state space, we constructed control vector fields g 1 , . .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

How to minimally modify a dynamical system when constructing flat inputs?

Nicolau

Respondek

Barbot

2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

In this paper, we study the problem of constructing flat inputs for multi-output dynamical systems, in particular, we address the issue of the minimal modification of the initial dynamical system (the measure of modification being the number of equations that have to be changed by adding flat inputs). We show that in the observable case, control vector fields that distort m equations only (where m is the number of measurements) can always be constructed (and this is the minimal possible number of equations that have to be modified by adding flat inputs), while in the unobservable case, the best that we can hope for is that m + 1 equations only are modified such that they involve flat inputs. We discuss when the original output is a flat output of minimal possible differential weight for the minimally modified control system (where by the differential weight, we mean the minimal number of derivatives of components of a flat output needed to express all states and controls). We propose a solution for constructing flat inputs leading to a minimally modified control system consistent with the minimal differential weight and, moreover, for which the observable part is affected by the minimal possible number of controls (this last property being important in applications). We show that, in that case, at least 2m − 1 equations have to be affected by the flat inputs.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Constructing Flat Inputs For a Minimal Modification Of σmentioning

confidence: 99%

“…, ρ m ) at x 0 . We will prove that Σ can be locally, around x 0 , transformed into (5)-( 6) with the unobserved subsystem (6) given by the following chain of integrators:…”

Section: Proof Of Theorem 32mentioning

confidence: 99%

Section: Proof Of Theorem 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

How to minimally modify a dynamical system when constructing flat inputs?

Nicolau

Respondek

Barbot

2021

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

Flat input based canonical form observers for non‐integrable nonlinear discrete‐time systems

Fritzsche

Röbenack

2023

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

We define flat inputs for discrete‐time systems and carry over a flat input based observer design strategy for non‐integrable nonlinear continuous‐time systems to the discrete‐time case. This approach allows to design observers for nonlinear discrete‐time systems that cannot be transformed into observer canonical form, i.e., conventional observer design strategies fail. This approach is illustrated by two examples.

show abstract

Neural algorithm for optimization of multidimensional object controller parameters

Bałazy,

Lalik,

Knap

2024

Neural Comput & Applic

View full text Add to dashboard Cite

Optimal control of multivariable systems is a complex dynamic process that minimizes the cost function to obtain the optimal control strategy. Unfortunately, for nonlinear systems, it is not possible to use the traditional linear quadratic regulator (LQR), which would be optimal over the entire range of parameter variation. The problem of nonlinear multivariable systems and their optimal control is very momentous. The solution presented in this paper is based on the application of Reinforcement Learning (RL) networks in controlling a five-degree-of-freedom overhead crane system. Additionally, unlike the classical approach, the algorithm is adapted to directly analyze tabular data of inputs and outputs of the controlled model instead of analyzing its state as feedback (model-free). Implementing the new control structure for the multivariable system improved control quality compared to the classical LQR controller with linearization at the operating point. In addition to quality, the resource indicators, which in the LQR controller are represented by the matrix R, have been significantly improved. The architecture of the neural control system is presented, ensuring that over the entire range of nonlinearity, the quality of control is preserved while reducing the cost of its resource intensity. Obtaining optimal control with reduced resources for its implementation induces a wide range of applications of such neural control in engineering systems. The effectiveness of the proposed control system has been demonstrated in simulation studies. The simulation results present the system’s excellent control performance and adaptability over the entire range of object nonlinearity. The neural algorithm resulted in significantly shorter adjustment time and better control quality with significantly less system resource consumption and increased system dynamics.

show abstract

Nonlinear Control of Non-Observable Non-Flat MIMO State Space Systems Using Flat Inputs

Cited by 10 publications

References 27 publications

How to minimally modify a dynamical system when constructing flat inputs?

How to minimally modify a dynamical system when constructing flat inputs?

Flat input based canonical form observers for non‐integrable nonlinear discrete‐time systems

Neural algorithm for optimization of multidimensional object controller parameters

Contact Info

Product

Resources

About