Estimation of the Region of Attraction for State-Dependent Riccati Equation Controllers

Bracci, Andrea; Innocenti, Mario; Pollini, Lorenzo

doi:10.2514/1.22122

Cited by 40 publications

(65 citation statements)

References 2 publications

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“…In this section, two different examples are presented: the first one discusses an analytic nonlinear open-loop system [4] and the other presents a nonlinear feedback control system [24] with the SDRE controller. In the first example, which gives the analytic results, we will evaluate the superiority and the effectiveness of the proposed method.…”

Section: Examplesmentioning

confidence: 99%

“…The asymptotic stability region can be found by the method of Bracci et al [4]. Briefly the procedure for this method is as follows: The Lyapunov function can be chosen to be…”

Section: A First Examplementioning

confidence: 99%

“…An analytic solution to the SDRE is generally not known [4]. This is because the algebraic state-dependent Riccati equation is solved numerically.…”

Section: Introductionmentioning

confidence: 99%

“…By determining the overvaluing matrix for the given dynamic system, the method shows the maximum boundary for the SDRE-controlled dynamic systems. However, this method is complicated from the computational standpoint for medium and high order systems [4]. Langson and Alleyne tried to find a stable upper boundary for the SDRE controlled system [17].…”

Section: Introductionmentioning

confidence: 99%

“…However, if the dimension of the system matrix is greater than two, it takes a large set of internal variables to find the optimal values for maximizing the stability region for the SDRE feedback system. Another numerical method was suggested by Bracci et al [4]. This procedure is an alternative to the method proposed by Erdem and Alleyne [14], and is based on the Lyapunov local stability theorem [25].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Chang

Chung

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Abstract-We investigate the nonlinear exponential stability of the State-Dependent Riccati Equation (SDRE)-based control. The SDRE technique is a nonlinear control method, which has emerged since the mid 1990's and has been applied to a wide range of nonlinear control problems. Despite the systematic method of SDRE, it is difficult to prove stability because the general analytic solution to the SDRE is not known. Some notable prior work has shown local asymptotic stability of SDRE by using numerical and analytical methods. In this paper, we introduce a new strategy, based on contraction analysis, to estimate the exponential stability region for SDRE controlled systems. Examples demonstrate the superiority of the proposed method.

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Section: Examplesmentioning

confidence: 99%

“…The asymptotic stability region can be found by the method of Bracci et al [4]. Briefly the procedure for this method is as follows: The Lyapunov function can be chosen to be…”

Section: A First Examplementioning

confidence: 99%

“…An analytic solution to the SDRE is generally not known [4]. This is because the algebraic state-dependent Riccati equation is solved numerically.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Chang

Chung

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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Closed-form solution to finite-horizon suboptimal control of nonlinear systems

Heydari

Balakrishnan

2014

Int. J. Robust. Nonlinear Control

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Finite-horizon optimal control of input-affine nonlinear systems with fixed final time is considered in this study. It is first shown that the associated Hamilton-Jacobi-Bellman partial differential equation to the problem is reducible to a state-dependent differential Riccati equation after some approximations. With a truncation in the control equation, a near optimal solution to the problem is obtained, and the global onvergence properties of the closed-loop system are analyzed. Afterwards, an approximate method, called Finite-horizon State-Dependent Riccati Equation (Finite-SDRE), is suggested for solving the differential Riccati equation, which renders the origin a locally exponentially stable point. The proposed method provides online feedback solution for controlling different initial conditions. Finally, through some examples, the performance of the resulting controller in finite-horizon control is analyzed.where matrices S and Q are assumed to be positive semi-definite and matrix R is a positive definite matrix. Moreover, t 0 and t f denote the fixed and given initial and final times, respectively. Problem 1Find the control history u.t / 2 R m , t 2 OEt 0 ; t f /, using which cost function (2) is minimized subject to the state equation (1).

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A novel domain of attraction based synthesis of inverse optimal control

Prasanna

Jacob

Nandakumar

2021

Intl J Robust & Nonlinear

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This article proposes a novel and systematic methodology for the inverse optimal control (IOC) of a class of input affine nonlinear systems. First, the system is represented in the pseudo-linear state-dependent coefficient (SDC) form so as to facilitate the use of matrix algebraic concepts in the design, while preserving the nonlinear system dynamics. Second, the IOC problem which seeks the solution to the Hamilton-Jacobi-Bellman equation is translated to a diagonal stability (D-stability) problem. Therefore, the general notion of D-stability, which deals with the characterization of a matrix A ∈ ℜ n×n for the existence of a diagonal matrix Γ ∈ ℜ n×n such that A T Γ + ΓA < 0, is redefined with respect to SDC factored matrices in this work. Consequently, the criteria for the existence (necessary condition) and determination of a diagonal solution (sufficient condition) are formulated in terms of the SDC matrices. It is shown in this work that these criteria can be readily met by the closed-loop system matrix Â(x) = A(x) − D, for any arbitrary domain S 𝛿 in state-space, by manipulating only the diagonal elements using the diagonal matrix D constituted by the IOC feedback. In short, the IOC feedback is designed such that the criteria for D-stability by the closed-loop system matrix Â(x) is fulfilled. Hence this novel design methodology is meaningfully named as "Inverse optimal control via diagonal stabilization" (IOC-D).The main advantages of IOC-D include: (i) guaranteed estimate of the domain of attraction (DOA), (ii) Immense flexibility of design, and (iii) guaranteed closed form solution which makes the design procedure analytic and computationally efficient. Numerical simulations validate the theoretical developments and the overall efficiency of the proposed approach.

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Estimation of the Region of Attraction for State-Dependent Riccati Equation Controllers

Cited by 40 publications

References 2 publications

Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Closed-form solution to finite-horizon suboptimal control of nonlinear systems

A novel domain of attraction based synthesis of inverse optimal control

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