Stabilization of Polynomial Systems with Bounded Actuators using Convex Optimization

Jennawasin, Tanagorn; Kawanishi, Michihiro; Narikiyo, Tatsuo

doi:10.3182/20110828-6-it-1002.03733

Cited by 8 publications

(9 citation statements)

References 10 publications

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“…We have proposed state-feedback stabilization of polynomial systems with bounded input magnitudes [10]. This method gives not only the stabilizing controller, but also Lyapunov function whose level set estimates the DOA of polynomial systems.…”

Section: A Stabilization Of Polynomial Systemsmentioning

confidence: 99%

“…The method to design the controller gain K(x) and the Lyapunov matrix P (x) is derived from the theorem [10]. Theorem 2.1: Given the compact region X and the bounds µ j , j = 1, 2, ..., m, suppose that there exist poly-…”

Section: ) Convex Stabilizing Conditionsmentioning

confidence: 99%

“…For example, input-to-state stability analysis [7] and estimating DOA for uncertain polynomial systems [8] have been developed. Moreover, polynomial state feedback and observer design methods [9] and stabilizing controller with bounded actuators [10] have been proposed. However, there is no guarantee that the dynamics of mechanical systems can be approximated by the polynomial systems sufficiently.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear controller design based on polynomial and non-polynomial representation

Tsuge

Kawanishi

Narikiyo

et al. 2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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In this paper, to synthesize stabilizing controllers for nonlinear systems we develop nonlinear controller design methods based on polynomial representation and nonpolynomial representation using particle swarm optimization(PSO). To do this we derive the stability conditions of polynomial systems and non-polynomial systems for estimating domain of attraction(DOA) with input magnitude constraints. From these conditions stabilizing controllers of polynomial systems and non-polynomial systems are synthesized by using sum of squares (SOS) and PSO techniques respectively. Finally, obtained controllers are applied to Furuta pendulum and validity of these controllers is demonstrated by numerical simulations.

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Section: A Stabilization Of Polynomial Systemsmentioning

confidence: 99%

Section: ) Convex Stabilizing Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear controller design based on polynomial and non-polynomial representation

Tsuge

Kawanishi

Narikiyo

et al. 2014

11th IEEE International Conference on Control &Amp; Automation (ICCA)

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“…The obtained PDLMIs can be relaxed into standard LMIs using the sum-of-squares (SOS) technique [12], [17], [2]. Some developments in this field have been reported in [14], [5], [6] for polynomial Lyapunov functions, and in [14], [19], [10], [7] for rational Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

An improved stabilizing condition for polynomial systems with bounded actuators: An SOS-based approach

Jennawasin

Kawanishi

Narikiyo

et al. 2012

2012 IEEE International Symposium on Intelligent Control

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Stabilization of polynomial systems is revisited in this paper. Here, we proposed a new sufficient condition for the controller design, with guaranteed bounds on the input magnitudes. In the proposed synthesis condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the resulting controller is independent of the Lyapunov matrices. Moreover, the proposed condition is convex in the decision variables and solvable via the sum-ofsquares (SOS) technique. Main contributions of the proposed approach are twofold. Firstly, parameter-dependent Lyapunov functions can be considered in robust controller design for uncertain polynomial systems. Secondly, static output-feedback design can be addressed in a computationally efficient manner.

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“…"Slack variables" method [5,6]: This methodology is based on a convex of polynomial parameter-dependent LMIs by introduction of additional variables using the elimination lemma backward. This structural relaxation LMI approach, by its essence is to expand the searching optimization space, thereby obtaining less conservative robust stability condition; II.…”

Section: Introductionmentioning

confidence: 99%

Gain-scheduled controllers design for interceptor parameter-varying system with multi-saturated constraint

Guo-long

Liang

2013

Int. J. Dynam. Control

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Based on homogeneous polynomial parameter dependent Lyapunov function (HPPDLF) theory and the algorithm that the nonlinear matrix differential equations converted into convex polyhedron state equations, the robust optimal control system is designed, for the interceptor with time-varying parameters and actuator nonlinear multisaturated constraint. First, the model of the actuator saturation operator is established, which provides the control system topology. The nonlinear differential equations with time-varying parameters converted into the linear polytopic vertex system by introduced the normalization factors of the amplitude and rate actuator saturation, and then it converted into HPPD matrix differential equations, based on HPPDLF theory and the extension of Pólya's theorem to the case of matrix-valued polynomials. The dynamic performance of the closed-loop control system is obtained by setting the minimum allowable value of the scaling factor, when solving the minimum of the maximum homothetic set in the iterative processing. Finally the simulations of the interceptor have demonstrated the effectiveness of the approach proposed.

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Stabilization of Polynomial Systems with Bounded Actuators using Convex Optimization

Cited by 8 publications

References 10 publications

Nonlinear controller design based on polynomial and non-polynomial representation

Nonlinear controller design based on polynomial and non-polynomial representation

An improved stabilizing condition for polynomial systems with bounded actuators: An SOS-based approach

Gain-scheduled controllers design for interceptor parameter-varying system with multi-saturated constraint

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