Global Output Tracking for Nonlinear Systems

Hirschorn, R.M.; Davis, Jon H.

doi:10.1137/0326074

Cited by 36 publications

(18 citation statements)

References 10 publications

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“…Statement of Problem 1: Given the dynamical system (1), with state constraints (2), and with a feedback linearizing control law u(x, β) (3) parameterized by a constant vector β ∈ R n , determine 1) the invariant set W, which is the 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 ThIP2.16 largest set of states x for a given non-saturating controller u(x, β) that will reach the origin without violating the state constraints x ∈ C, 2) β such that the feedback linearizing control law is both non-saturating (5) and stable (4).…”

Section: Problem Formulationmentioning

confidence: 99%

“…We formulate constraints that input saturation and stability place on the input parameters. Feedback linearization is a popular technique for differentially flat systems [13], [14], but can generate inputs with high-magnitude. Synthesizing non-saturating feedback linearizing control laws is a non-trivial problem [15], [16], [17] for stabilization [18] as well as for tracking [19].…”

Section: Introductionmentioning

confidence: 99%

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Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation

Oishi¹,

Mitchell

Tomlin

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-We consider feedback linearizable systems subject to bounded control input and nonlinear state constraints. In a single computation, we synthesize 1) parameterized nonlinear controllers based on feedback linearization, and 2) the set of states over which this controller is valid. This is accomplished through a reachability calculation, in which the state is extended to incorporate input parameters. While we use a HamiltonJacobi formulation, a viability approach is also feasible. The result provides a mathematical guarantee that for all states within the computed set, there exists a control law that will simultaneously satisfy two separate goals: envelope protection (no violation of state constraints), and stabilization despite saturation. We apply this technique to two real-world systems: the longitudinal dynamics of a civil jet aircraft, and a twoaircraft, planar collision avoidance scenario. The result, in both cases, is a feasible range of input parameters for the nonlinear control law, and a corresponding controlled invariant set.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation

Oishi¹,

Mitchell

Tomlin

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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show abstract

“…As opposed to the two previous examples, the safe region lies outside of the shaded region. For clarity, the invariant set calculated with dynamics (17) and initial cost function (18) is also displayed in Figure 7, and contains the invariant set calculated with the prescribed controller and initial cost function (20).…”

Section: Cooperative Collision Avoidancementioning

confidence: 99%

“…We formulate constraints that input saturation and stability place on the input parameters. Feedback linearization is a popular technique for differentially flat systems [19,20], but can generate inputs with high-magnitude. Synthesizing non-saturating feedback linearizing control laws is a non-trivial problem [21,22,23] for stabilization [24] as well as for tracking [25].…”

Section: Multi-objective Controller Synthesismentioning

confidence: 99%

“…. 20 11 Forward reachable set W rcv from Flare-30D mode under recovery dynamics which allow switching between any of four go-around modes, depending on the configuration of the flaps (F-20, F-30) and landing gear (Down, Up 13 Optimal discrete modes in (V, γ) for various altitudes. The yellow region represents Go-30U, red represents Go-30D, blue represents Go-20U, and cyan represents Go-20D.…”

Section: Telephonementioning

confidence: 99%

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Final LDRD report human interaction with complex systems: advances in hybrid reachability and control.

Oishi¹

2006

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This document describes new advances in hybrid reachability techniques accomplished during the course of a one-year Truman Postdoctoral Fellowship. These techniques provide guarantees of safety in complex systems, which is especially important in high-risk, expensive, or safety-critical systems. My work focused on new approaches to two specific problems motivated by real-world issues in complex systems: 1) multi-objecitve controller synthesis, and 2) control for recovery from error. Regarding the first problem, a novel application of reachability analysis allowed controller synthesis in a single step to achieve a) safety, b) stability, and c) prevent input saturation. By extending the state to include the input parameters, constraints for stability, saturation, and envelope protection are incorporated into a single reachability analysis. Regarding the second problem, a new approach to the problem of recovery provides a) states from which recovery is possible, and b) controllers to guide the system during a recovery maneuver from an error state to a safe state in minimal time. Results are computed in both problems on nonlinear models of single longitudinal aircraft dynamics and two-aircraft lateral collision avoidance dynamics.3 5560 4

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Prozeßführung zur Sicherung reproduzierbarer Qualität in der verfahrenstechnischen Produktion

Gilles

Friedrich²

1991

Chemie Ingenieur Technik

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Process engineering to assure reproducible quality in production. This paper presents an hierarchically structured process control concept in which product quality is regarded as the central orientation factor. The application of control engineering methods is intended to assure maintenance of the product quality specifications. The second part of the article briefly considers the present state of the art of quality assurance. Fundamental considerations concerning a well‐defined quality concept as a basis for process control are presented in the third part, prior to explanation of the process control concept and its illustration with the aid of an example.

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Global Output Tracking for Nonlinear Systems

Cited by 36 publications

References 10 publications

Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation

Computing Viable Sets and Reachable Sets to Design Feedback Linearizing Control Laws Under Saturation

Final LDRD report human interaction with complex systems: advances in hybrid reachability and control.

Prozeßführung zur Sicherung reproduzierbarer Qualität in der verfahrenstechnischen Produktion

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