Nonnegative Dynamical Systems Research Articles

Nonnegative Tensor-Based Linear Dynamical Systems for Recognizing Human Action from 3D Skeletons

Recently, skeleton-based action recognition has become a very important topic in the field of computer vision. It is a challenging task to accurately build a human action model and precisely distinguish similar human actions. In this paper, an action (skeleton sequence) is represented as a third-order nonnegative tensor time series to capture the original spatiotemporal information of the action. As a linear dynamical system (LDS) is an efficient tool for encoding the spatiotemporal data in various disciplines, this paper proposes a nonnegative tensor-based LDS (nLDS) to model the third-order nonnegative tensor time series. Nonnegative Tucker decomposition (NTD) is utilized to estimate the parameters of the nLDS model. These parameters are used to build extended observability sequence O∞T for the action, which implies that O∞T can be considered as the feature descriptor of the action. To avoid the limitations introduced by approximating O∞T with a finite-order matrix, we represent an action as a point on infinite Grassmann manifold comprising the orthonormalized extended observability sequences. The classification task can be performed by dictionary learning and sparse coding on the infinite Grassmann manifold. The experimental results on the MSR-Action3D, UTKinect-Action, and G3D-Gaming datasets demonstrate that the proposed approach achieves a better performance in comparison with the state-of-the-art methods.

Neuroadaptive output feedback control for nonlinear nonnegative dynamical systems with actuator amplitude and integral constraints

A neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. Specifically, the neuroadaptive controller guarantees that the control amplitude as well as the integral of the control input over a given time interval are constrained, and the physical system states remain in the nonnegative orthant of the state space. The proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of infusion rate constraints and an integral drug dosing constraint over a specified time period. Copyright © 2010 John Wiley & Sons, Ltd.

ℋ︁2 suboptimal estimation and control for nonnegative dynamical systems

AbstractLinear matrix inequalities (LMIs) provide a powerful design framework for linear control problems. In this paper, we use LMIs to develop ℋ︁2 (sub)optimal estimators and controllers for nonnegative dynamical systems. Specifically, we formulate a series of generalized eigenvalue problems subject to a set of LMI constraints for designing ℋ︁2 suboptimal estimators, static controllers, and dynamic controllers for nonnegative dynamical systems. The resulting ℋ︁2 suboptimal controllers guarantee that the closed‐loop plant system states remain in the nonnegative orthant of the state space. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.

Neural Network Adaptive Control for Nonlinear Nonnegative Dynamical Systems

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. In this paper, we develop a full-state feedback neural adaptive control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. In addition, the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state-space for nonnegative initial conditions.

Stability and dissipativity theory for nonnegative dynamical systems: a unified analysis framework for biological and physiological systems

Nonnegative dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in biological, physiological, and ecological sciences and play a key role in the understanding of these processes. In this paper we develop several results on stability, dissipativity, and stability of feedback interconnections of linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability, semistability, that is, system trajectory convergence to Lyapunov stable equilibrium points, and asymptotic stability for nonnegative dynamical systems. In addition, using linear and nonlinear storage functions with linear supply rates we develop new notions of dissipativity theory for nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems.

Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems With Time Delay

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous. However, in many engineering and life science systems, transfers between compartments are not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments. Including some information of past system states in the system model leads to infinite-dimensional delay nonnegative dynamical systems. In this note, we develop dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates. These results are then used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems with time delay.

Adaptive control for nonlinear nonnegative dynamical systems

Nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems. In this paper, we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation; that is, asymptotic set-point regulation 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 nonnegative orthant of the state space.

Optimal fixed‐structure control for linear non‐negative dynamical systems

AbstractIn this paper, we develop optimal output feedback controllers for set‐point regulation of linear non‐negative dynamical systems. Specifically, using a constrained fixed‐structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed‐loop system remain in the non‐negative orthant of the state space for non‐negative initial conditions. In addition, we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the non‐negative orthant for unconstrained optimal linear‐quadratic output feedback controllers. Output feedback controllers for compartmental systems with non‐negative inputs are also given. Copyright © 2004 John Wiley & Sons, Ltd.

On monotonicity of solutions of discrete-time nonnegative and compartmental dynamical systems

Nonnegative and compartmental dynamical system models are widespread in biological, physiological, and pharmacological sciences. Since the state variables of these systems are typically masses or concentrations of a physical process, it is of interest to determine necessary and sufficient conditions under which the system states possess monotonic solutions. In this paper, we present necessary and sufficient conditions for identifying discrete-time nonnegative and compartmental dynamical systems that only admit monotonic solutions.

Stability and dissipativity theory for discrete-time non-negative and compartmental dynamical systems

Non-negative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are non-negative. These models are widespread in engineering, biomedicine and ecology. In this paper we develop several results on stability, dissipativity and stability of feedback interconnections of discrete-time linear and non-linear non-negative dynamical systems. Specifically, using linear Lyapunov functions we first develop necessary and sufficient conditions for Lyapunov stability and asymptotic stability for non-negative systems. In addition, using linear and non-linear storage functions with linear supply rates we develop new notions of dissipativity theory for non-negative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of non-negative dynamical systems.

Stability theory for nonnegative and compartmental dynamical systems with time delay

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments. These models are widespread in biological and physical sciences and play a key role in understanding these processes. A key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments. In this paper, we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay. Specifically, asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear Lyapunov–Krasovskii functionals.

Hybrid nonnegative and computational dynamical systems

Nonnegative and Compartmental dynamical systems are governed by conservation laws and are comprised of homogeneous compartments which exchange variable nonnegative quantities of material via intercompartmental flow laws. These systems typically possess hierarchical (and possibly hybrid) structures and are remarkably effective in capturing the phenomenological features of many biological and physiological dynamical systems. In this paper we develop several results on stability and dissipativity of hybrid nonnegative and Compartmental dynamical systems. Specifically, using linear Lyapunov functions we develop sufficient conditions for Lyapunov and asymptotic stability for hybrid nonnegative dynamical systems. In addition, using linear and nonlinear storage functions with linear hybrid supply rates we develop new notions of dissipativity theory for hybrid nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of hybrid nonnegative dynamical systems.