Theoretical Study of the Nonlinear Control Algorithms with Continuous and Discrete-Time State Dependent Riccati Equation

György, Katalin; Dávid, László; Kelemen, András

doi:10.1016/j.protcy.2016.01.123

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…State feedback controller design for the problem of inverted pendulum has been shown in detail in this paper. Next, nonlinear techniques [12][13][14] and model predictive control [15] are planned to study. Figure 11.…”

Section: Discussionmentioning

confidence: 99%

State Space Based Linear Controller Design for the Inverted Pendulum

Kuczmann

2019

Acta Tech Jaur

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In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.

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Section: Discussionmentioning

confidence: 99%

State Space Based Linear Controller Design for the Inverted Pendulum

Kuczmann

2019

Acta Tech Jaur

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“…According to the SDRE theory, this can be easily accomplished if the F function in (1) can be written as [8], [13].…”

Section: B Discrete Time Sdre Methodsmentioning

confidence: 99%

“…The solution of SDRE ( 11) is only a sub-optimal solution, because there were neglected derivatives of the system matrices (A(xk) and B(xk)) [8]. If the value of the horizon (N) is infinite, the solution of the difference Riccati equation approaches the solution of the algebraic equation (Pk =Pk+1) [2].…”

Section: A Dlqrmentioning

confidence: 99%

Theoretical Study of the Unconstrained and Constrained Nonlinear Optimal Discrete Time State Feedback Control

György

Dávid

2021

Acta Universitatis Sapientiae, Electrical and Mechanical Engineering

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Majority of the optimal control techniques can only be applied successfully if the model of the controlled process is known and it is linear. If the system model is nonlinear, then this nonlinear model can be approximated with different simple, linear models. However, these models are valid only in the neighbourhood of the operating points. The success of the control algorithms is highly dependent on the used linearization methods. The aim of the paper is to compare different optimal control algorithms and linearization methods. The presented optimal control algorithms have been also tested in constrained and unconstrained versions.

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“…The application field of the Kalman algorithm has been expanded to nonlinear control systems by the so-called state-dependent Riccati equation (SDRE) approach for continuous (see [1][2][3]) and discrete (see [4][5][6][7][8][9]) cases, where the systems are formally represented as linear systems in terms of state and control, the coefficients of the matrices are the functions of the state vector (state-dependent coefficients (SDC) systems), and the quality criterion is quadratic, but the quadratic forms matrices in the criterion can also be state-dependent. In [1], the design procedure for the SDRE approach is described and its capabilities are illustrated on a benchmark problem.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [2] contains a detailed review on SDRE: the theory developed to date, characteristics, advantages, and open issues. In [4][5][6], the discrete state-dependent Riccati equation (D-SDRE) approach is described, and the corresponding control algorithms are presented and tested. In [3,[7][8][9], the development of the SDRE approach is proposed based on the asymptotic theory.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step

Danik

Dmitriev

2022

Mathematics

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For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation (PA) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA. As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation.

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Theoretical Study of the Nonlinear Control Algorithms with Continuous and Discrete-Time State Dependent Riccati Equation

Cited by 5 publications

References 3 publications

State Space Based Linear Controller Design for the Inverted Pendulum

State Space Based Linear Controller Design for the Inverted Pendulum

Theoretical Study of the Unconstrained and Constrained Nonlinear Optimal Discrete Time State Feedback Control

Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step

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