Chris Guiver | University of Exeter in Cornwall (original) (raw)

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Papers by Chris Guiver

Research paper thumbnail of Non-dissipative boundary feedback for elastic beams

Research paper thumbnail of Model reduction by balanced truncation

Research paper thumbnail of Robust set-point regulation for ecological models with multiple management goals

Journal of Mathematical Biology, 2015

Population managers will often have to deal with problems of meeting multiple goals, for example,... more Population managers will often have to deal with problems of meeting multiple goals, for example, keeping both the total population and population densities in given stage classes at specific levels. In control engineering, such set-point regulation problems are often tackled using multiinput, multi-output PI (proportional and integral) controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multiobjective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements. Our results apply more generally to linear systems with positive state variables, including a class of infinite-dimensional systems, and thus have broad appeal.

Research paper thumbnail of The role of population inertia in predicting the outcome of stage-structured biological invasions

Mathematical Biosciences, 2015

Available online xxx 2010 MSC: 37M05 37N25 39A30 92D25 Keywords: Biological invasion Population i... more Available online xxx 2010 MSC: 37M05 37N25 39A30 92D25 Keywords: Biological invasion Population inertia Non-linear system Positive system Lyapunov functions abstract

Research paper thumbnail of A stability/instability trichotomy for non-negative Lur’e systems

Research paper thumbnail of Model reduction by balanced truncation for systems with nuclear Hankel operators

Research paper thumbnail of Controllability for positive discrete–time linear systems with positive state

Research paper thumbnail of Stability of Non-Negative Lur’e Systems

Research paper thumbnail of Bounded real and positive real balanced truncation for infinite-dimensional systems

Mathematical Control and Related Fields, 2013

ABSTRACT

Research paper thumbnail of Bounds on the dynamics of sink populations with noisy immigration

Theoretical Population Biology, 2014

Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics ... more Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources (for example, source populations, or population managers). Here we appeal to a systems and control framework to place upper and lower bounds on both the transient and future dynamics of sink populations that are subject to noisy immigration. Immigration has a number of interpretations and can fit a wide variety of models found in the literature. We apply the results to case studies derived from published models for Chinook Salmon (Oncorhynchus tshawytscha) and blowout penstemon (Penstemon haydenii).

Research paper thumbnail of Positive state controllability of positive linear systems

Systems & Control Letters, 2014

Controllability of positive systems by positive inputs arises naturally in applications where bot... more Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inputs is often overly restrictive. Relaxing this requirement, the notion of positive state controllability of positive systems is introduced. A connection between positive state controllability and positive input controllability of a related system is established and used to obtain Kalmanlike controllability criteria. In doing so we aim to encourage further study in this underdeveloped area.

Research paper thumbnail of Non-dissipative boundary feedback for Rayleigh and Timoshenko beams

Systems & Control Letters, 2010

We show that a non-dissipative feedback that has been shown in the literature to exponentially st... more We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

Research paper thumbnail of Error bounds in the gap metric for dissipative balanced approximations

Linear Algebra and its Applications, 2013

ABSTRACT

Research paper thumbnail of A Counterexample to “ Positive Realness Preserving Model Reduction With <formula formulatype="inline"> <tex Notation="TeX">${\cal H}_{\infty}$</tex></formula> Norm Error Bounds&#x201D

IEEE Transactions on Circuits and Systems I: Regular Papers, 2000

ABSTRACT

Research paper thumbnail of Integral control for population management

Journal of Mathematical Biology, 2014

We present a novel management methodology for restocking a declining population. The strategy use... more We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedback-using measurements of the population to inform management strategies and is robust to model uncertainty, an important consideration for ecological models. We demonstrate from first principles why such an approach to population management is suitable via theory and examples.

Research paper thumbnail of Non-dissipative boundary feedback for elastic beams

Research paper thumbnail of Model reduction by balanced truncation

Research paper thumbnail of Robust set-point regulation for ecological models with multiple management goals

Journal of Mathematical Biology, 2015

Population managers will often have to deal with problems of meeting multiple goals, for example,... more Population managers will often have to deal with problems of meeting multiple goals, for example, keeping both the total population and population densities in given stage classes at specific levels. In control engineering, such set-point regulation problems are often tackled using multiinput, multi-output PI (proportional and integral) controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multiobjective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements. Our results apply more generally to linear systems with positive state variables, including a class of infinite-dimensional systems, and thus have broad appeal.

Research paper thumbnail of The role of population inertia in predicting the outcome of stage-structured biological invasions

Mathematical Biosciences, 2015

Available online xxx 2010 MSC: 37M05 37N25 39A30 92D25 Keywords: Biological invasion Population i... more Available online xxx 2010 MSC: 37M05 37N25 39A30 92D25 Keywords: Biological invasion Population inertia Non-linear system Positive system Lyapunov functions abstract

Research paper thumbnail of A stability/instability trichotomy for non-negative Lur’e systems

Research paper thumbnail of Model reduction by balanced truncation for systems with nuclear Hankel operators

Research paper thumbnail of Controllability for positive discrete–time linear systems with positive state

Research paper thumbnail of Stability of Non-Negative Lur’e Systems

Research paper thumbnail of Bounded real and positive real balanced truncation for infinite-dimensional systems

Mathematical Control and Related Fields, 2013

ABSTRACT

Research paper thumbnail of Bounds on the dynamics of sink populations with noisy immigration

Theoretical Population Biology, 2014

Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics ... more Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources (for example, source populations, or population managers). Here we appeal to a systems and control framework to place upper and lower bounds on both the transient and future dynamics of sink populations that are subject to noisy immigration. Immigration has a number of interpretations and can fit a wide variety of models found in the literature. We apply the results to case studies derived from published models for Chinook Salmon (Oncorhynchus tshawytscha) and blowout penstemon (Penstemon haydenii).

Research paper thumbnail of Positive state controllability of positive linear systems

Systems & Control Letters, 2014

Controllability of positive systems by positive inputs arises naturally in applications where bot... more Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inputs is often overly restrictive. Relaxing this requirement, the notion of positive state controllability of positive systems is introduced. A connection between positive state controllability and positive input controllability of a related system is established and used to obtain Kalmanlike controllability criteria. In doing so we aim to encourage further study in this underdeveloped area.

Research paper thumbnail of Non-dissipative boundary feedback for Rayleigh and Timoshenko beams

Systems & Control Letters, 2010

We show that a non-dissipative feedback that has been shown in the literature to exponentially st... more We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

Research paper thumbnail of Error bounds in the gap metric for dissipative balanced approximations

Linear Algebra and its Applications, 2013

ABSTRACT

Research paper thumbnail of A Counterexample to “ Positive Realness Preserving Model Reduction With <formula formulatype="inline"> <tex Notation="TeX">${\cal H}_{\infty}$</tex></formula> Norm Error Bounds&#x201D

IEEE Transactions on Circuits and Systems I: Regular Papers, 2000

ABSTRACT

Research paper thumbnail of Integral control for population management

Journal of Mathematical Biology, 2014

We present a novel management methodology for restocking a declining population. The strategy use... more We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedback-using measurements of the population to inform management strategies and is robust to model uncertainty, an important consideration for ecological models. We demonstrate from first principles why such an approach to population management is suitable via theory and examples.

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