Nonlinear Control of Mismatched Uncertain Linear Systems and Application to Control of Aircraft

Singh, Sahjendra N.; Coelho, Antônio Augusto Rodrigues

doi:10.1115/1.3149673

Cited by 56 publications

(19 citation statements)

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“…Consider a linearized model of a helicopter VTOL (vertical take-off and landing) in the vertical plane with airspeed 135 konts [3]. The dynamic equation of this model can be described as respectively.…”

Section: Applicationmentioning

confidence: 99%

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Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability

Wen

Cheng

2008

Journal of the Franklin Institute

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Section: Applicationmentioning

confidence: 99%

“…One typical achievement of these researches is that the state trajectories of the controlled systems can be driven into a bounded region so that the stability of the controlled system is ensured. These researches include [2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability

Wen

Cheng

2008

Journal of the Franklin Institute

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“…The original problem here is to find a controller robustly stabilizing the closed-loop system with ρ = 1 and a decay rate of at least α = 0.1. This problem arises in control of helicopters: (Singh and Coelho 1984) and it was studied in Bhattacharyya (1987), El Ghaoui et al (1997), Tempo et al (2004).…”

Section: Stabilizationmentioning

confidence: 99%

Randomized methods based on new Monte Carlo schemes for control and optimization

Polyak

Gryazina

2009

Ann Oper Res

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We address randomized methods for control and optimization based on generating points uniformly distributed in a set. For control systems this sets are either stability domain in the space of feedback controllers, or quadratic stability domain, or robust stability domain, or level set for a performance specification. By generating random points in the prescribed set one can optimize some additional performance index. To implement such approach we exploit two modern Monte Carlo schemes for generating points which are approximately uniformly distributed in a given convex set. Both methods use boundary oracle to find an intersection of a ray and the set. The first method is Hit-and-Run, the second is sometimes called Shake-and-Bake. We estimate the rate of convergence for such methods and demonstrate the link with the center of gravity method. Numerical simulation results look very promising.

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“…The given dynamic equation is computed for typical loading and flight conditions of the VTOL helicopter at an airspeed of 135 knots (Singh and Coelho 1984). All the elements of the first three rows of both matrices change as the airspeed changes.…”

Section: Robust Control Of a Vtol Helicoptermentioning

confidence: 99%

Robust optimal parametric LQ control with a guaranteed cost bound and applications

Loh

1989

International Journal of Control

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For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closedloop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as 'robust optimal parametric LQ control with a guaranteed cost bound' and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalizesome previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helicopter. I. IntroductionThis work addresses the simultaneous robust stability and performance problem via optimal parametric linear quadratic (LQ) control of linear uncertain systems. The present work is motivated by the guaranteed cost control approach of Chang and Peng ( 1972) and the recent work of Bernstein and Haddad for robust stochastic LQ control problems (Bernstein 1987, Bernstein and Haddad 1988 a, b, and the references therein). Chang and Peng (1972) considered the robust optimal LQ control problems with a full-state feedback and showed that the solutions of a resultant modified Riccati equation are guaranteed to give both robust stability and performance over a specified range of parameter variations. Among various later extensions of this approach, Bernstein and Haddad recently extended this approach to the robust control problems for linear stochastic systems with structural real-valued parameter uncertainty (Bernstein and Haddad 1988 a, b), and for the systems with state-dependent and control-dependent white noise (Bernstein 1987). Instead of using the absolutevalue bound (Chang and Peng 1972), they utilized a quadratic Lyapunov bound suggested by Petersen and Hollot (1986) in conjunction with the guaranteed cost approach to provide a simultaneous robust stability and performance via fixed-order dynamic feedback (Bernstein and Haddad 1988 a), and further considered this problem along with a unified treatment and extension of several quadratic Lyapunov bounds developed previously for feedback control design (Bernstein and Haddad 1988 b). Explicit solutions for the robust control were then derived using the optimal projection control synthesis approach of Hyland and Bernstein (1984).In the present work, we propose to extend Chang and Peng's approach (1972) further into the robust optimal parametric LQ control problems for linear determin-

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Nonlinear Control of Mismatched Uncertain Linear Systems and Application to Control of Aircraft

Cited by 56 publications

References 0 publications

Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability

Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability

Randomized methods based on new Monte Carlo schemes for control and optimization

Robust optimal parametric LQ control with a guaranteed cost bound and applications

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