�ݺ�ߣshows by User: LeoAsselborn

�ݺ�ߣshows by User: LeoAsselborn / http://www.slideshare.net/images/logo.gif �ݺ�ߣshows by User: LeoAsselborn / Wed, 09 Aug 2017 06:33:16 GMT �ݺ�ߣShare feed for �ݺ�ߣshows by User: LeoAsselborn Control of Discrete-Time Piecewise Affine Probabilistic Systems using Reachability Analysis /slideshow/control-of-discretetime-piecewise-affine-probabilistic-systems-using-reachability-analysis/78688168 msc16pres-170809063316
This presentation proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered class of systems contains probabilistic components (with Gaussian distribution) modeling additive disturbances and state initialization. The probabilistic reachable state sets contain all states that are reachable with a given confidence level under the effect of time-variant control laws. The control synthesis uses principles of the ellipsoidal calculus, and it considers that the system parametrization depends on the partition of the state space. The proposed algorithm uses LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints and transitions between regions of the state space are considered. The formulation of the SDP is adopted from a previous work in [1] for switched systems, in which the switching of the continuous dynamics is triggered by a discrete input variable. Here, as opposed to [1], the switching occurs autonomously and an algorithmic procedure is suggested to synthesis a stabilizing controller. An example for illustration is included.]]>
This presentation proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered class of systems contains probabilistic components (with Gaussian distribution) modeling additive disturbances and state initialization. The probabilistic reachable state sets contain all states that are reachable with a given confidence level under the effect of time-variant control laws. The control synthesis uses principles of the ellipsoidal calculus, and it considers that the system parametrization depends on the partition of the state space. The proposed algorithm uses LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints and transitions between regions of the state space are considered. The formulation of the SDP is adopted from a previous work in [1] for switched systems, in which the switching of the continuous dynamics is triggered by a discrete input variable. Here, as opposed to [1], the switching occurs autonomously and an algorithmic procedure is suggested to synthesis a stabilizing controller. An example for illustration is included.]]> Wed, 09 Aug 2017 06:33:16 GMT /slideshow/control-of-discretetime-piecewise-affine-probabilistic-systems-using-reachability-analysis/78688168 LeoAsselborn@slideshare.net(LeoAsselborn) Control of Discrete-Time Piecewise Affine Probabilistic Systems using Reachability Analysis LeoAsselborn This presentation proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered class of systems contains probabilistic components (with Gaussian distribution) modeling additive disturbances and state initialization. The probabilistic reachable state sets contain all states that are reachable with a given confidence level under the effect of time-variant control laws. The control synthesis uses principles of the ellipsoidal calculus, and it considers that the system parametrization depends on the partition of the state space. The proposed algorithm uses LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints and transitions between regions of the state space are considered. The formulation of the SDP is adopted from a previous work in [1] for switched systems, in which the switching of the continuous dynamics is triggered by a discrete input variable. Here, as opposed to [1], the switching occurs autonomously and an algorithmic procedure is suggested to synthesis a stabilizing controller. An example for illustration is included. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/msc16pres-170809063316-thumbnail.jpg?width=120&height=120&fit=bounds" /> This presentation proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered class of systems contains probabilistic components (with Gaussian distribution) modeling additive disturbances and state initialization. The probabilistic reachable state sets contain all states that are reachable with a given confidence level under the effect of time-variant control laws. The control synthesis uses principles of the ellipsoidal calculus, and it considers that the system parametrization depends on the partition of the state space. The proposed algorithm uses LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints and transitions between regions of the state space are considered. The formulation of the SDP is adopted from a previous work in [1] for switched systems, in which the switching of the continuous dynamics is triggered by a discrete input variable. Here, as opposed to [1], the switching occurs autonomously and an algorithmic procedure is suggested to synthesis a stabilizing controller. An example for illustration is included.

Control of Discrete-Time Piecewise Affine Probabilistic Systems using Reachability Analysis from Leo Asselborn

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0 Probabilistic Control of Switched Linear Systems with Chance Constraints /slideshow/probabilistic-control-of-switched-linear-systems-with-chance-constraints/78688124 ecc16pres-170809063058
An approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting is proposed in this presentation. The initial state and disturbances are assumed to be Gaussian distributed, and a time-variant hybrid control law stabilizes the system towards a goal set. The algorithmic solution computes sequences of discrete states via tree search and the continuous controls are obtained from solving embedded semi-definite programs (SDP). These program taking polytopic input constraints as well as timevarying probabilistic state constraints into account. An example for demonstrating the principles of the solution procedure with focus on handling the chance constraints is included.]]>
An approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting is proposed in this presentation. The initial state and disturbances are assumed to be Gaussian distributed, and a time-variant hybrid control law stabilizes the system towards a goal set. The algorithmic solution computes sequences of discrete states via tree search and the continuous controls are obtained from solving embedded semi-definite programs (SDP). These program taking polytopic input constraints as well as timevarying probabilistic state constraints into account. An example for demonstrating the principles of the solution procedure with focus on handling the chance constraints is included.]]> Wed, 09 Aug 2017 06:30:58 GMT /slideshow/probabilistic-control-of-switched-linear-systems-with-chance-constraints/78688124 LeoAsselborn@slideshare.net(LeoAsselborn) Probabilistic Control of Switched Linear Systems with Chance Constraints LeoAsselborn An approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting is proposed in this presentation. The initial state and disturbances are assumed to be Gaussian distributed, and a time-variant hybrid control law stabilizes the system towards a goal set. The algorithmic solution computes sequences of discrete states via tree search and the continuous controls are obtained from solving embedded semi-definite programs (SDP). These program taking polytopic input constraints as well as timevarying probabilistic state constraints into account. An example for demonstrating the principles of the solution procedure with focus on handling the chance constraints is included. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/ecc16pres-170809063058-thumbnail.jpg?width=120&height=120&fit=bounds" /> An approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting is proposed in this presentation. The initial state and disturbances are assumed to be Gaussian distributed, and a time-variant hybrid control law stabilizes the system towards a goal set. The algorithmic solution computes sequences of discrete states via tree search and the continuous controls are obtained from solving embedded semi-definite programs (SDP). These program taking polytopic input constraints as well as timevarying probabilistic state constraints into account. An example for demonstrating the principles of the solution procedure with focus on handling the chance constraints is included.

Probabilistic Control of Switched Linear Systems with Chance Constraints from Leo Asselborn

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0 Robust Control of Uncertain Switched Linear Systems based on Stochastic Reachability /slideshow/robust-control-of-uncertain-switched-linear-systems-based-on-stochastic-reachability/78688060 adhs15pres-170809062825
This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant hybrid control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over sequences of the discrete states and LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints are considered. An example for illustration is included.]]>
This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant hybrid control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over sequences of the discrete states and LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints are considered. An example for illustration is included.]]> Wed, 09 Aug 2017 06:28:24 GMT /slideshow/robust-control-of-uncertain-switched-linear-systems-based-on-stochastic-reachability/78688060 LeoAsselborn@slideshare.net(LeoAsselborn) Robust Control of Uncertain Switched Linear Systems based on Stochastic Reachability LeoAsselborn This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant hybrid control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over sequences of the discrete states and LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints are considered. An example for illustration is included. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/adhs15pres-170809062825-thumbnail.jpg?width=120&height=120&fit=bounds" /> This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant hybrid control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over sequences of the discrete states and LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints are considered. An example for illustration is included.

Robust Control of Uncertain Switched Linear Systems based on Stochastic Reachability from Leo Asselborn

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0 Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability /slideshow/probabilistic-control-of-uncertain-linear-systems-using-stochastic-reachability/78687981 rocond15-170809062534
This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.]]>
This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.]]> Wed, 09 Aug 2017 06:25:34 GMT /slideshow/probabilistic-control-of-uncertain-linear-systems-using-stochastic-reachability/78687981 LeoAsselborn@slideshare.net(LeoAsselborn) Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability LeoAsselborn This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/rocond15-170809062534-thumbnail.jpg?width=120&height=120&fit=bounds" /> This presentation proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.

Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability from Leo Asselborn

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0 Control of Uncertain Nonlinear Systems Using Ellipsoidal Reachability Calculus /LeoAsselborn/nolcos13 nolcos13-140110020821-phpapp02
This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stabilizing controllers. The method uses first-order Taylor approximation of the nonlinear dynamics and a conservative approximation of the Lagrange remainder.]]>
This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stabilizing controllers. The method uses first-order Taylor approximation of the nonlinear dynamics and a conservative approximation of the Lagrange remainder.]]> Fri, 10 Jan 2014 02:08:21 GMT /LeoAsselborn/nolcos13 LeoAsselborn@slideshare.net(LeoAsselborn) Control of Uncertain Nonlinear Systems Using Ellipsoidal Reachability Calculus LeoAsselborn This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stabilizing controllers. The method uses first-order Taylor approximation of the nonlinear dynamics and a conservative approximation of the Lagrange remainder. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/nolcos13-140110020821-phpapp02-thumbnail.jpg?width=120&height=120&fit=bounds" /> This paper proposes an approach to algorithmically synthesize control strategies for discrete-time nonlinear uncertain systems based on reachable set computations using the ellipsoidal calculus. For given ellipsoidal initial sets and bounded ellipsoidal disturbances, the proposed algorithm iterates over conservatively approximating and LMI-constrained optimization problems to compute stabilizing controllers. The method uses first-order Taylor approximation of the nonlinear dynamics and a conservative approximation of the Lagrange remainder.

Control of Uncertain Nonlinear Systems Using Ellipsoidal Reachability Calculus from Leo Asselborn

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0 Control of Uncertain Hybrid Nonlinear Systems Using Particle Filters /slideshow/adhs12/29870403 adhs12-140110020412-phpapp02
This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented.]]>
This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented.]]> Fri, 10 Jan 2014 02:04:12 GMT /slideshow/adhs12/29870403 LeoAsselborn@slideshare.net(LeoAsselborn) Control of Uncertain Hybrid Nonlinear Systems Using Particle Filters LeoAsselborn This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/adhs12-140110020412-phpapp02-thumbnail.jpg?width=120&height=120&fit=bounds" /> This paper proposes an optimization-based algorithm for the control of uncertain hybrid nonlinear systems. The considered system class combines the nondeterministic evolution of a discrete-time Markov process with the deterministic switching of continuous dynamics which itself contains uncertain elements. A weighted particle filter approach is used to approximate the uncertain evolution of the system by a set of deterministic runs. The desired control performance for a finite time horizon is encoded by a suitable cost function and a chance-constraint, which restricts the maximum probability for entering unsafe state sets. The optimization considers input and state constraints in addition. It is demonstrated that the resulting optimization problem can be solved by techniques of conventional mixed-integer nonlinear programming (MINLP). As an illustrative example, a path planning scenario of a ground vehicle with switching nonlinear dynamics is presented.

Control of Uncertain Hybrid Nonlinear Systems Using Particle Filters from Leo Asselborn

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0 Implementation of “Parma Polyhedron Library”-functions in MATLAB /slideshow/implementation-of-parma-polyhedron-libraryfunctions-in-matlab/5479537 presentation-101018142614-phpapp02
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]]> Mon, 18 Oct 2010 14:26:05 GMT /slideshow/implementation-of-parma-polyhedron-libraryfunctions-in-matlab/5479537 LeoAsselborn@slideshare.net(LeoAsselborn) Implementation of “Parma Polyhedron Library”-functions in MATLAB LeoAsselborn <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/presentation-101018142614-phpapp02-thumbnail.jpg?width=120&height=120&fit=bounds" />

Implementation of “Parma Polyhedron Library”-functions in MATLAB from Leo Asselborn

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0 https://cdn.slidesharecdn.com/profile-photo-LeoAsselborn-48x48.jpg?cb=1719870426 https://cdn.slidesharecdn.com/ss_thumbnails/msc16pres-170809063316-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/control-of-discretetime-piecewise-affine-probabilistic-systems-using-reachability-analysis/78688168 Control of Discrete-Ti... https://cdn.slidesharecdn.com/ss_thumbnails/ecc16pres-170809063058-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/probabilistic-control-of-switched-linear-systems-with-chance-constraints/78688124 Probabilistic Control ... https://cdn.slidesharecdn.com/ss_thumbnails/adhs15pres-170809062825-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/robust-control-of-uncertain-switched-linear-systems-based-on-stochastic-reachability/78688060 Robust Control of Unce...