Adaptive control of time-varying systems with gain-scheduling

Jang, Jinho; Annaswamy, Anuradha M.; Lavretsky, Eugene

doi:10.1109/acc.2008.4587021

Cited by 12 publications

(6 citation statements)

References 11 publications

(16 reference statements)

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“…The Lyapunov-based controller used in the following simulation studies is adaptive; explicitly compensates for parametric uncertainties, actuator dynamics, and actuator saturation; and, like all controllers, implicitly accommodates some amount of unmodeled dynamics, time delays, nonlinearities, and additional "unknown unknowns" [2], [3], [14], [16]- [21], [30].…”

Section: Lyapunov-stability-based Adaptive Controllermentioning

confidence: 99%

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Adaptive Control and the NASA X-15-3 Flight Revisited

2010

IEEE Control Syst.

130

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Section: Lyapunov-stability-based Adaptive Controllermentioning

confidence: 99%

“…The use of the projection operator in (50) guarantees stability and robustness [2], [3]. The details of the stability proof can be found in [30]. The inner-loop control input is a combination of the inputs from the pilot model d c , the baseline controller d nom , and the adaptive controller d ad , that is,…”

Section: Adaptive Controllermentioning

confidence: 99%

Adaptive Control and the NASA X-15-3 Flight Revisited

2010

IEEE Control Syst.

130

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“…These switchings introduce discontinuities and jumps in the control inputs. Adaptive control of time varying systems with gain scheduling is done in [2], [3]. The stability analysis for these systems is also performed using a time varying quadratic Lyapunov function, with some conditions on time varying Lyapunov matrix P (t) and its rateṖ (t).…”

Section: Introductionmentioning

confidence: 99%

Adaptive control of uncertain systems with gain scheduled reference models and constrained control inputs

Pakmehr

Yucelen

2014

2014 American Control Conference

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This paper develops a new state feedback model reference adaptive control approach for uncertain systems with gain scheduled reference models in a multi-input multioutput (MIMO) setting with constrained control inputs. A single Lyapunov matrix is computed for multiple linearizations of the nonlinear closed-loop gain scheduled reference system, using convex optimization tools. This approach guarantees stability of the closed-loop gain scheduled reference model. Adaptive state feedback control architecture is then developed, and its stability is proven for the case with constrained control inputs. The resulting closed-loop system is shown to have bounded solutions with bounded tracking error, with the proposed stable gain scheduled reference model. Sufficient conditions for ultimate boundedness of the closed-loop system are derived. A semi-global stability result is proved with respect to the level of saturation for open-loop unstable plants while the stability result is shown to be global for open-loop stable plants.Simulation results show that the developed adaptive controller can be used effectively to control a degraded turboshaft engine for large thrust commands, with guaranteed stability and proper tracking performance.

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“…The scheduling variable in our reference model design process is an endogenous parameter, which in the gas turbine engine case is a function of the gas turbine engine spool speeds. Some of the works dedicated to the adaptive control of systems with multiple equilibrium points and with time varying reference systems are [7,8,9,10]. Adaptive control of piecewise linear systems has been developed in [7,8].…”

Section: Introductionmentioning

confidence: 99%

Adaptive control of uncertain systems with gain scheduled reference models

Pakmehr

Yucelen

2014

2014 American Control Conference

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Firstly, a new state feedback model reference adaptive control approach is developed for uncertain systems with gain scheduled reference models in a multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback for output tracking control problem of MIMO nonlinear systems is studied and gain scheduled reference model system is used for generating desired state trajectories. Using convex optimization tools, a common Lyapunov matrix is computed for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed loop gain scheduled reference system. This approach guarantees stability of the closed-loop gain scheduled system. Adaptive state feedback control scheme is then developed, and its stability is proven. The resulting closed-loop system is shown to have bounded solutions with bounded tracking error, with the proposed stable gain scheduled reference model. Secondly, the developed control approach is improved for systems with constraints on the control inputs. The resulting closed-loop system is shown to have bounded solutions with bounded tracking error. Sufficient conditions for ultimate boundedness of the closed-loop system are derived. A semi-global stability result is proved with respect to the level of saturation for open-loop unstable plants while the stability result is shown to be global for open-loop stable plants. Thirdly, a decentralized adaptive state feedback control architecture is developed and its stability is proved. Specifically, the resulting closed-loop system is shown to have bounded solutions with bounded tracking error for all the subsystems with the proposed stable gain scheduled reference model. Simulation results are presented for each control architecture.

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Adaptive control of time-varying systems with gain-scheduling

Cited by 12 publications

References 11 publications

Adaptive Control and the NASA X-15-3 Flight Revisited

Adaptive Control and the NASA X-15-3 Flight Revisited

Adaptive control of uncertain systems with gain scheduled reference models and constrained control inputs

Adaptive control of uncertain systems with gain scheduled reference models

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