About nonnegative realizations

Nieuwenhuis, J.W.

doi:10.1016/s0167-6911(82)80024-8

Cited by 39 publications

(9 citation statements)

References 1 publication

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“…There is no guarantee that these properties hold for the positive realization problem. Related problems have been investigated in [6] for continuous systems, and in [7], [8], [9] for discrete time systems. In this paper, we treat the positive realization problem with the aid of the reachable and the observable set, and give a necessary and sufficient condition for positive realizability in terms of these sets.…”

mentioning

confidence: 99%

Reachability, Observability, and Realizability of Continuous-Time Positive Systems

Ohta¹,

Maeda²,

Kodama³

1984

SIAM J. Control Optim.

159

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This paper discusses reachability, observability, and realizability of single-input, single-output linear time-invariant systems, in which state variables and/or input (output) functions are restricted to be nonnegative to reflect physical constraints frequently encountered in real systems. We define a set reachable from the origin with nonnegative inputs, and also a set observable with nonnegative outputs. We investigate geometrical structures of the sets through convex analysis, and a duality relation between them is established.Next we consider positive realization of a given transfer function. Using the reachable set and the observable set, we give a necessary and sufficient condition for positive realizability. An example is given to demonstrate that a positive realizable transfer function does not in general have a jointly controllable and observable positive realization.

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confidence: 99%

Reachability, Observability, and Realizability of Continuous-Time Positive Systems

Ohta¹,

Maeda²,

Kodama³

1984

SIAM J. Control Optim.

159

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“…A di is asymptotically stable, and B is nonnegative and given by (8). For a given x d ∈ R m , assume there exist vectors x u ∈ R n−m + and u e ∈ R m + such that (9) holds.…”

Section: Adaptive Control For Linear Nonnegative Dynamical Systemmentioning

confidence: 99%

“…Nonnegative and compartmental models play a key role in the understanding of many processes in biological and medical sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Compartmental systems are modeled by interconnected subsystems (or compartments) which exchange variable nonnegative quantities of material with conservation laws describing transfer, accumulation, and elimination between compartments and the environment.…”

Section: Introductionmentioning

confidence: 99%

Adaptive control for nonnegative dynamical systems with arbitrary time delay

Chellaboina

Haddad²,

Ramakrishnan³

et al. 2006

2006 American Control Conference

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In this paper, we develop a direct adaptive control framework for uncertain linear nonnegative dynamical systems with unknown time delay. The specific focus of the paper is on compartmental pharmacokinetic models and their applications to drug delivery systems. In particular, we develop a LyapunovKrasovskii-based direct adaptive control framework for guaranteeing set-point regulation of the closed-loop system in the nonnegative orthant in the presence of unknown system time delay. The framework additionally guarantees nonnegativity of the control signal. Finally, we demonstrate the framework on a drug delivery model for general anesthesia involving system time delays.

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“…This result is given in the following theorem. Consider the linear uncertain dynamical system G given by (11) where A is essentially nonnegative and B is non-negative and given by (12). Assume there exists a diagonal matrix…”

Section: Adaptive Control For Linear Non-negative Uncertain Dynamicalmentioning

confidence: 99%

“…Specifically, indirect adaptive controllers utilize parameter update laws to identify unknown system parameters and adjust feedback gains to account for system variation, while direct adaptive controllers directly adjust the controller gains in response to system variations (drug administration).In this paper we develop a direct adaptive control framework for adaptive set-point regulation of linear uncertain non-negative and compartmental systems. Non-negative and compartmental dynamical systems [5][6][7][8][9][10][11][12][13][14][15][16][17][18] are composed of homogeneous interconnected subsystems (or compartments) which exchange variable non-negative quantities of material with conservation laws describing transfer, accumulation, and elimination between the compartments and the environment. It follows from physical considerations that the state trajectory of such systems remains in the non-negative orthant of the state space for nonnegative initial conditions.…”

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confidence: 99%

Adaptive control for non‐negative and compartmental dynamical systems with applications to general anesthesia

Haddad

Hayakawa

Bailey

2003

Adaptive Control & Signal

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Non-negative and compartmental dynamical system models are composed of homogeneous interconnected subsystems or compartments which exchange variable non-negative quantities of material with conservation laws describing transfer, accumulation, and elimination between the compartments and the environment. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for linear uncertain non-negative and compartmental systems. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation; that is, asymptotic set-point stability with respect to part of the closed-loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the non-negative orthant of the state space. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for non-cardiac surgery is provided to demonstrate the efficacy of the proposed approach.

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About nonnegative realizations

Cited by 39 publications

References 1 publication

Reachability, Observability, and Realizability of Continuous-Time Positive Systems

Reachability, Observability, and Realizability of Continuous-Time Positive Systems

Adaptive control for nonnegative dynamical systems with arbitrary time delay

Adaptive control for non‐negative and compartmental dynamical systems with applications to general anesthesia

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