A dynamical systems analysis of assisted and unassisted anterior and posterior hand-held load carriage

Load carriage is recognised as a primary occupational factor leading to slip and fall injuries, and therefore assessing balance maintenance during such tasks is critical in assessing injury risk. Ten males completed 55 strides under five carriage conditions: (1) unassisted anterior, (2) unassisted posterior, (3) assisted anterior, (4) assisted posterior and (5) unloaded gait (UG). Kinematic data were recorded from markers affixed to landmarks on the right side of each participant, in order to calculate segment angles for the foot, shank, thigh and pelvis. Continuous relative phase (CRP) variability was calculated for each segment pair and local dynamic stability was calculated for each segment in all three movement planes. In general, irrespective of the assistive device or movement plane, anterior load carriage was most stable (lower CRP variability and maximum finite-time Lyapunov exponents). Moreover, load carriage was less dynamically stable than UG, displaying the importance of objectively investigating safe load carriage practices.     

Neural-net-based control of dynamical systems: A case study

Multilayer perceptrons trained with the generalized delta rule or backpropagation procedure have been extensively applied in areas such as phoneme and image recognition and synthesis. Recently, many authors have reported interesting results on the application of these structures to the modeling and control of dynamical systems. In this article, we analyze the use of neural nets in a Model Reference adaptive Controller (MRAC) scheme for hydroturbine control. Several simulation results are provided, showing the feasibility of this approach and the factors involved in its design.     

Carry-over effects of backpack carriage on trunk posture and repositioning ability

Immediate effects of backpack carriage on spinal curvature and motor control in adults have been reported. However, there is a scarcity of evidence whether the effects would persist or not after the carrying load is removed. This study aimed to investigate the carry-over effects of backpack carriage on trunk posture and repositioning ability. Thirteen healthy adults were recruited and instructed to walk on a treadmill for 30 min with backpack (10% body weight) followed by 30-min unloaded walking. Participant’s trunk posture and repositioning ability were measured at different time points. During backpack carriage, reduction in lumbar lordosis and posterior pelvic tilt with significant increased cervical lordosis, thoracic kyphosis and trunk forward lean were observed. There was also a significant increase in repositioning errors in all spinal curvatures and trunk forward lean. After removal of the carrying load, there was a tendency for restoration of trunk posture and repositioning ability. However, the cervical lordosis and the repositioning error of all spinal curvatures could not be fully returned to the levels of the preload condition (all p < 0.05). The persistent changes in both spinal curvature and repositioning ability revealed an increased risk of spinal injury even after the backpack was removed, and the effects on the neck and back pain warrant future study.

Relevance to Industry

The effects of backpack carriage (10% body weight for 30 min) on the spine could not be fully restored after 30-min unloaded walking. The persistent changes in both spinal curvature and repositioning ability revealed an increased risk of spinal injury even after the backpack was removed. Proper postural reminder might be given to backpack users to alleviate the adverse effects induced after prolonged backpack carriage.     

Near-optimal control of nonlinear dynamical systems: A brief survey

For nonlinear dynamical systems, an optimal control problem generally requires solving a partial differential equation called the Hamilton–Jacobi–Bellman equation, the analytical solution of which generally cannot be obtained. However, the demand for optimal control keeps increasing, with the goal to save energy, reduce transient time, minimize error accumulation, etc. Consequently, methods were reported to approximately solve the problem leading to the so-called near-optimal control, although their technical details differ. This research direction has experienced great progress in recent years but a timely review of it is still missing. This paper serves as a brief survey for existing methods in this research direction.     

The metabolic cost of backpack and shoulder load carriage.

Eleven healthy male volunteer soldiers (mean [SD] age 24.0 [2.8] years, stature 174.1 [5.2] cm, body weight 73.2 [10.8] kg, body fat 14.2 [5.0]% and maximal oxygen uptake 4.1 [0.4] 1 min-1) walked at 4.8 km h-1 on a motor driven treadmill for 5 min at each of three gradients (0, 2.5 and 5%) whilst carrying a two-part 26 kg load either on each shoulder or strapped to a backpack frame. The load was made up of two cylinders, one weighing 18.4 kg and the other weighing 7.6 kg. For all treadmill gradients the mean (SD) backpacking heart rates and oxygen uptakes (0% gradient, 122 [10] beats min-1, 1.51 [0.11] 1 min-1; 2.5% gradient, 135 [10] beats min-1, 1.81 [0.13] 1 min-1; 5% gradient, 155 [7] beats min-1, 2.21 [0.11] 1 min-1) were significantly (p less than 0.001) lower than for shoulder load carriage (0% gradient, 130 [9] beats min-1, 1.70 [0.12] 1 min-1, 2.5% gradient, 147 [8] beats min-1; 2.01 [0.10] 1 min-1; 5% gradient 164 [9] beats min-1, 2.39 [0.11] 1 min-1). The relative oxygen cost of backpacking was 4.3-4.7% VO2 max lower than for shoulder load carriage. It is concluded that the metabolic cost of backpacking an asymmetric two part 26 kg load was significantly less than for shoulder load carriage when walking at 4.8 km h-1 on a treadmill over gradients of 0-5%.(ABSTRACT TRUNCATED AT 250 WORDS)     

Hybrid dynamical systems: robust control synthesis problems

The paper presents a new approach to robust control synthesis problems for hybrid dynamical systems. The hybrid system under consideration is a composite of a continuous plant and a discrete event controller. State and output feedback problems are considered. The main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a Riccati differential equation of the H^∞ filtering type. These results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control.     

Stability analysis of switched systems under dynamical dwell time control approach

This article investigates the stability of a class of switched systems using dynamical dwell time approach. First, the condition for stability of switched systems whose subsystems are stable are presented with dynamical dwell time approach, which is shown to be less conservative in switching law design than dwell time approach. Then the proposed approach is extended to the switched systems with both stable and unstable subsystems. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.     

A note on the control of uncertain linear dynamical systems with constrained control input

A method is presented to design a stabilizing saturated state feedback controller for linear continuous-time systems with bounded uncertainty acting via the input channel.     

A control problem for affine dynamical systems on a full-dimensional polytope

Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.     

Multi-objective analysis for assessing simultaneous changes in regional spinal curvatures under backpack carriage in young adults

Change in sagittal spinal curvature from the neutral upright stance is an important measure of the heaviness and correctness of backpack use. As current recommendations, with respect to spinal profile, of backpack load thresholds were based on the significant curvature change in individual spinal region only, this study investigated the most critical backpack load by assessing simultaneously the spinal curvature changes along the whole spine. A motion analysis system was used to measure the curvature changes in cervical, upper thoracic, lower thoracic and lumbar regions with backpack load at 0, 5, 10, 15 and 20% of body weight. A multi-objective goal programming model was adopted to determine the global critical load of maximum curvature change of the whole spine in accordance with the maximum curvature changes of the four spinal regions. Results suggested that the most critical backpack load was 13% of body weight for healthy male college students.

Practitioner Summary: As current recommendations of backpack load thresholds were based on the significant curvature change in individual spinal region only, this study investigated the backpack load by considering simultaneously the spinal curvature changes along the whole spine. The recommendation, in terms of the global critical load, was 13% of body weight for healthy male college students.     

Hierarchical control of cooperative nonlinear dynamical systems

Cooperative control methods that are scalable with low computational cost are crucial for networked dynamical systems to respond quickly in unknown or cluttered environments. In an attempt to make the problem tractable, many existing cooperative controls are designed with oversimplified assumptions and/or without the capabilities of rapidly handling different environmental and dynamical constraints. In this article, proposed is a two-level hierarchical, cooperative control framework using a divide-and-conquer strategy so that challenges can be separately handled at different levels. It is scalable and has low computational cost. Based on a simplified homogeneous double-integrator dynamic model, the top-level planner first computes cooperative trajectories satisfying obstacle avoidance requirements. Then at the lower level, state and control constraints, nonlinear dynamics and self-collision/obstacle avoidance as related to the real system are addressed through a bio-inspired fast trajectory planning algorithm. The stability of the overall hierarchical structure is proven. Two examples, a differential-drive ground vehicle formation control and an unmanned aerial vehicle formation flight, are used to illustrate the advantages of the proposed hierarchical framework.     

Discrete dynamical systems with symmetries: Computer analysis

Discrete dynamical systems and mesoscopic lattice models are considered from the standpoint of their symmetry groups. Universal specific features of deterministic dynamical system behavior associated with nontrivial symmetries of these systems are specified. Group nature of soliton-like moving structures of the “spaceship” type in cellular automata is revealed. Study of lattice models is also considerably simplified when their symmetry groups are taken into account. A program in C for group analysis of systems of both types is developed. The program, in particular, constructs and investigates phase portraits of discrete dynamical systems modulo symmetry group and seeks dynamical systems possessing special features, such as, for example, reversibility. For mesoscopic lattice models, the program computes microcanonical distributions and looks for phase transitions. Some computational results and observations are presented.     

On the control of discrete-event dynamical systems

We study a class of problems related to the supervisory control of a discrete-event system (DES), as formulated by Ramadge and Wonham, and we focus on the computational effort required for their solution. While the problem of supervisory control of a perfectly observed DES may be easily solved by dynamic programming, the problem becomes intractable (in the sense of complexity theory) when imperfectly observed systems are considered. Research supported by the Army Research Office (Grant No. DAAL03-86-K-0171) and by an NSF PYI award, with matching funds from Bellcore Inc.     

Robust control of set-valued discrete-time dynamical systems

This paper presents results obtained for the control of set-valued discrete-time dynamical systems. Such systems model nonlinear systems subject to persistent bounded noise. A robust control problem for such systems is introduced. The problem is formulated as a dynamic game, wherein the controller plays against the set-valued system. Both necessary and sufficient conditions in terms of (stationary) dynamic programming equalities are presented. The output feedback problem is solved using the concept of an information state, where a decoupling between estimation and control is obtained. The methods yield a conceptual approach for constructing controlled-invariant sets and stabilizing controllers for uncertain nonlinear systems     

Stability analysis of non-linear dynamical systems

This paper examines the possibility of using non-linear comparison systems in the stability analysis of non-linear dynamical systems. Stability criteria and estimates of the stability region of non-linear comparison systems are established. It is shown that the use of non-linear comparison systems may lead to less conservative results than those obtained by linear ones.     

A dissipative dynamical systems approach to stability analysis of time delay systems

In this paper the concepts of dissipativity and the exponential dissipativity are used to provide sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite‐dimensional linear dynamical system and an infinite‐dimensional time delay operator, we show that the time delay operator is dissipative with respect to a quadratic supply rate and with a storage functional involving an integral term identical to the integral term appearing in standard Lyapunov–Krasovskii functionals. Finally, using stability of feedback interconnection results for dissipative systems, we develop sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides a dissipativity theoretic interpretation of Lyapunov–Krasovskii functionals for asymptotically stable dynamical systems with arbitrary time delay. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity analysis of stochastic dynamical systems

A new, efficient algorithm is developed for the sensitivity analysis of a general class of stochastic dynamical systems. The algorithm is based on an idea of the likelihood ratio method that utilizes a probability density information for the sensitivity analysis, and on the Fokker-Planck or Kolmogorov's forward equation for computing the evolution of probability densities. The ideas of stochastic sensitivity analysis and likelihood ratio method are presented and combined to derive the sensitivity of average values of the performance functional with respect to system parameters. The present algorithm avoids the time consuming Monte Carlo or stochasic simulations, and, instead, sensitivity gradients of the probability density function and performance functional are directly computed during single-run simulation.     

An impulsive dynamical systems framework for reset control systems

Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyse several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence on the initial condition (well-posedness). The work scope is about reset control systems with a linear and time-invariant base system, and a zero-crossing resetting law. A necessary and sufficient condition for existence and uniqueness of solutions, based on the well-posedness of reset instants, is developed. As a result, it is shown that reset control systems (with strictly proper plants) do not have Zeno solutions. It is also shown that full reset and partial reset (with a special structure) always produce well-posed reset instants. Moreover, a definition of continuous dependence on the initial condition is developed, and also a sufficient condition for reset control systems to satisfy that property. Finally, this property is used to analyse sensitivity of reset control systems to sensor noise. This work also includes a number of illustrative examples motivating the key concepts and main results.     

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.