The modeling, analysis, and design of treatment therapies for bone disorders based on the paradigm of force-induced bone growth and adaptation is a challenging task. Mathematical models provide, in comparison to clini...
The modeling, analysis, and design of treatment therapies for bone disorders based on the paradigm of force-induced bone growth and adaptation is a challenging task. Mathematical models provide, in comparison to clinical, medical and biological approaches an structured alternative framework to understand the concurrent effects of the multiple factors involved in bone remodeling. By now, there are few mathematical models describing the appearing complex interactions. However, the resulting models are complex and difficult to analyze, due to the strong nonlinearities appearing in the equations, the wide range of variability of the states, and the uncertainties in parameters. In this work, we focus on analyzing the effects of changes in model structure and parameters/inputs variations on the overall steady state behavior using systems theoretical methods. Based on an briefly reviewed existing model that describes force-induced bone adaptation, the main objective of this work is to analyze the stationary behavior and to identify plausible treatment targets for remodeling related bone disorders. Identifying plausible targets can help in the development of optimal treatments combining both physical activity and drug-medication. Such treatments help to improve/maintain/restore bone strength, which deteriorates under bone disorder conditions, such as estrogen deficiency.
To guarantee stability of a model predictive control scheme it is essential to suitably calculate the terminal region and the terminal penalty term. In this paper we propose an approach to overcome this problem for th...
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ISBN:
(纸本)9783902661555
To guarantee stability of a model predictive control scheme it is essential to suitably calculate the terminal region and the terminal penalty term. In this paper we propose an approach to overcome this problem for the class of periodically time-varying systems. We consider both systems with periodic linear dynamics as well as systems with periodic nonlinear dynamics where the nonlinearities can be approximated with polytopic linear differential inclusions. In both cases exploiting the periodicity of the system dynamics leads to linear matrix inequality (LMI) conditions which can be used to calculate the terminal region and the terminal penalty term. The LMI conditions are shown to be less conservative than existing approaches applicable to the considered system class.
In this paper, a receding horizon control scheme able to stabilize linear periodic time-varying systems, in the sense of asymptotic convergence, is proposed. The presented approach guarantees that input constraints ar...
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This paper presents a computationally attractive nonlinear model predictive control approach for the class of continuous time Lure systems. The control law is obtained via the repeated solution of an efficient to solv...
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Nonlinear systems can be poorly or non-observable along specific state and output trajectories or in certain regions of the state space. Operating the system along such trajectories or in such regions can lead to poor...
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In ambition to minimize potential interferences between yaw stabilization and rollover prevention of an automotive vehicle, this work presents a new approach to integrate both objectives. It introduces rollover preven...
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The paper presents a moving horizon 2 control approach for the class of linear parameter-varying systems. By solving online a convex optimization problem subject to linear matrix inequality constraints the 2 gain from...
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ISBN:
(纸本)9783902661555
The paper presents a moving horizon 2 control approach for the class of linear parameter-varying systems. By solving online a convex optimization problem subject to linear matrix inequality constraints the 2 gain from the energy bounded external disturbance to the performance output is minimized at each sampling instant. The approach guarantees satisfaction of state and input constraints and it is shown that the online recalculation of the control law improves disturbance attenuation significantly when compared to a static control law.
Analysis and safety considerations of chemical and biological processes frequently require an outer approximation of the set of all feasible steady-states. Nonlinearities, uncertain parameters, and discrete variables ...
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ISBN:
(纸本)9783902661548
Analysis and safety considerations of chemical and biological processes frequently require an outer approximation of the set of all feasible steady-states. Nonlinearities, uncertain parameters, and discrete variables complicate the calculation of guaranteed outer bounds. In this paper, the problem of outer-approximating the region of feasible steady-states, for processes described by uncertain nonlinear differential algebraic equations including discrete variables and discrete changes in the dynamics, is adressed. The calculation of the outer bounding sets is based on a relaxed version of the corresponding feasibility problem. It uses the Lagrange dual problem to obtain certificates for regions in state space not containing steady-states. These infeasibility certificates can be computed efficiently by solving a semidefinite program, rendering the calculation of the outer bounding set computationally feasible. The derived method guarantees globally valid outer bounds for the steady-states of nonlinear processes described by differential equations. It allows to consider discrete variables, as well as switching system dynamics. The method is exemplified by the analysis of a simple chemical reactor showing parametric uncertainties and large variability due to the appearance of bifurcations characterising the ignition and extinction of a reaction.
Abstract To guarantee stability of a model predictive control scheme it is essential to suitably calculate the terminal region and the terminal penalty term. In this paper we propose an approach to overcome this probl...
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Abstract To guarantee stability of a model predictive control scheme it is essential to suitably calculate the terminal region and the terminal penalty term. In this paper we propose an approach to overcome this problem for the class of periodically time-varying systems. We consider both systems with periodic linear dynamics as well as systems with periodic nonlinear dynamics where the nonlinearities can be approximated with polytopic linear differential inclusions. In both cases exploiting the periodicity of the system dynamics leads to linear matrix inequality (LMI) conditions which can be used to calculate the terminal region and the terminal penalty term. The LMI conditions are shown to be less conservative than existing approaches applicable to the considered system class.
Simple design conditions are presented for decentralized output feedback controllers that achieve output consensus between nonlinear, relative degree one Multi-Agent systems (MAS) with stable zero dynamics. It is show...
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