In this paper, we focus on the issue of adaptive ∞ H -control design for a class of linear parame... more In this paper, we focus on the issue of adaptive ∞ H -control design for a class of linear parameter-varying (LPV) systems based on the Hamiltonian-Jacobi-Isaac (HJI) method. By combining the idea of polynomially parameter- dependent quadratic functions and vector projection method to derive an adaptive ∞ H -control, sufficient conditions with high precision are given to guarantee both robust asymptotic stability and disturbance attenuation of the LPV systems with unknown constant parameters. The applicability of the proposed design method is illustrated on a simple example.
In this paper we design a continuous, nonlinear state feedback controller that aligns the body-fi... more In this paper we design a continuous, nonlinear state feedback controller that aligns the body-fixed thrust direction of a quadrotor helicopter with a constant desired direction given in an inertial coordinate system. The controller is designed based on an energy shaping approach and is able to saturate the control torques. Almost global asymptotic stability of the desired thrust direction is proven for arbitrary unknown moment of inertia matrices. Performance of the closed loop system is verified by simulations.
This paper presents a cascaded nonlinear state feedback control law for a quadrotor, which achiev... more This paper presents a cascaded nonlinear state feedback control law for a quadrotor, which achieves asymptotic tracking of a predefined position and heading reference trajectory. The inner-loop attitude controller and the outer-loop position controller reflect the cascade structure of the quadrotor dynamics and are designed independently using an energy shaping approach. The closed loop tracking error dynamics form a nonautonomous nonlinear cascade for whose zero equilibrium we prove almost global asymptotic stability. Experimental results show the performance of the control concept.
ABSTRACT A method to preserve stability in parametric model order reduction by matrix interpolati... more ABSTRACT A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear time-invariant systems. In the first step, system matrices of the high-dimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method. Secondly, the reduced models are made contractive by solving low-dimensional Lyapunov equations. Thirdly, they are transformed into a consistent set of generalized coordinates for accurate interpolation results. These three steps are done offline and the matrices of the local systems are stored. Finally, a stable reduced order model for a new parameter vector can be calculated online by interpolating the precomputed matrices of the local low-dimensional models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications.
This article introduces a novel way of transforming linear second order systems to first order st... more This article introduces a novel way of transforming linear second order systems to first order state space models in strictly dissipative realization. This property extends the potential for the analysis of large-scale systems in many ways: it allows for the application of efficient methods for the solution of Lyapunov equations and the guaranteed preservation of asymptotic stability during model order reduction. The transformation is easy to implement and applicable to models of very high order due to its negligible computational effort.
In this paper, we focus on the issue of adaptive ∞ H -control design for a class of linear parame... more In this paper, we focus on the issue of adaptive ∞ H -control design for a class of linear parameter-varying (LPV) systems based on the Hamiltonian-Jacobi-Isaac (HJI) method. By combining the idea of polynomially parameter- dependent quadratic functions and vector projection method to derive an adaptive ∞ H -control, sufficient conditions with high precision are given to guarantee both robust asymptotic stability and disturbance attenuation of the LPV systems with unknown constant parameters. The applicability of the proposed design method is illustrated on a simple example.
In this paper we design a continuous, nonlinear state feedback controller that aligns the body-fi... more In this paper we design a continuous, nonlinear state feedback controller that aligns the body-fixed thrust direction of a quadrotor helicopter with a constant desired direction given in an inertial coordinate system. The controller is designed based on an energy shaping approach and is able to saturate the control torques. Almost global asymptotic stability of the desired thrust direction is proven for arbitrary unknown moment of inertia matrices. Performance of the closed loop system is verified by simulations.
This paper presents a cascaded nonlinear state feedback control law for a quadrotor, which achiev... more This paper presents a cascaded nonlinear state feedback control law for a quadrotor, which achieves asymptotic tracking of a predefined position and heading reference trajectory. The inner-loop attitude controller and the outer-loop position controller reflect the cascade structure of the quadrotor dynamics and are designed independently using an energy shaping approach. The closed loop tracking error dynamics form a nonautonomous nonlinear cascade for whose zero equilibrium we prove almost global asymptotic stability. Experimental results show the performance of the control concept.
ABSTRACT A method to preserve stability in parametric model order reduction by matrix interpolati... more ABSTRACT A method to preserve stability in parametric model order reduction by matrix interpolation for the whole parameter range is proposed for high-order linear time-invariant systems. In the first step, system matrices of the high-dimensional parameter-dependent system are computed for a discrete set of parameter vectors. The local high-order systems are reduced by a projection-based reduction method. Secondly, the reduced models are made contractive by solving low-dimensional Lyapunov equations. Thirdly, they are transformed into a consistent set of generalized coordinates for accurate interpolation results. These three steps are done offline and the matrices of the local systems are stored. Finally, a stable reduced order model for a new parameter vector can be calculated online by interpolating the precomputed matrices of the local low-dimensional models. We show that this approach works without any limiting conditions concerning the structure of the large-scale model and is suitable for real-time applications.
This article introduces a novel way of transforming linear second order systems to first order st... more This article introduces a novel way of transforming linear second order systems to first order state space models in strictly dissipative realization. This property extends the potential for the analysis of large-scale systems in many ways: it allows for the application of efficient methods for the solution of Lyapunov equations and the guaranteed preservation of asymptotic stability during model order reduction. The transformation is easy to implement and applicable to models of very high order due to its negligible computational effort.
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