A rigorous model of reflex function indicates that position and force feedback are flexibly tuned to position and force tasks

This study aims to quantify the separate contributions of muscle force feedback, muscle spindle activity and co-contraction to the performance of voluntary tasks (“reduce the influence of perturbations on maintained force or position”). Most human motion control studies either isolate only one contributor, or assume that relevant reflexive feedback pathways during voluntary disturbance rejection tasks originate mainly from the muscle spindle. Human ankle-control experiments were performed, using three task instructions and three perturbation characteristics to evoke a wide range of responses to force perturbations. During position tasks, subjects (n = 10) resisted the perturbations, becoming more stiff than when being relaxed (i.e., the relax task). During force tasks, subjects were instructed to minimize force changes and actively gave way to imposed forces, thus becoming more compliant than during relax tasks. Subsequently, linear physiological models were fitted to the experimental data. Inhibitory, as well as excitatory force feedback, was needed to account for the full range of measured experimental behaviors. In conclusion, force feedback plays an important role in the studied motion control tasks (excitatory during position tasks and inhibitory during force tasks), implying that spindle-mediated feedback is not the only significant adaptive system that contributes to the maintenance of posture or force

A dynamic network approach to identification of physical systems

System identification problems utilizing a prediction error approach are typically considered in an input/output setting, where a directional cause-effect relationship is presumed and transfer functions are used to estimate the causal relationships. In more complex interconnection structures, as e.g. appearing in dynamic networks, the cause-effect relationships can be encoded by a directed graph. Physical dynamic networks are most commonly described by diffusive couplings between node signals, implying that cause-effect relationships between node signals are symmetric and therefore can be represented by an undirected graph. This paper shows how (prediction error) identification methods developed for linear dynamic networks can be configured to identify components in (undirected) physical networks with known topology

Closed-loop identification of multivariable processes with part of the inputs controlled

\u3cp\u3eIn many multivariable industrial processes a subset of the available input signals is being controlled. In this paper it is analysed in which sense the resulting partial closed-loop identification problem is actually a full closed-loop problem, or whether one can benefit from the presence of non-controlled inputs to simplify the identification problem. The analysis focuses on the bias properties of the plant estimate when applying the direct method of prediction error identification, and the possibilities to identify (parts of) the plant model without the need of simultaneously estimating full-order noise models.\u3c/p\u3

Detecting nonlinear modules in a dynamic network:a step-by-step procedure\u3csup\u3e⁎\u3c/sup\u3e

\u3cp\u3eAdopting a dynamic network viewpoint allows one to analyze and identify subsystems of a complex interconnected system. When studying a network of dynamic systems, it is important to know if significant nonlinear behavior is present in a dynamic network under study and where the nonlinearity is located in the network. This work extends the Best Linear Approximation framework from the closed-loop to the networked setting. The framework is illustrated using a practical step-by-step estimation and analysis procedure. It is shown how nonlinear behavior can be quantified and located in a dynamic network using this framework.\u3c/p\u3

A local direct method for module identification in dynamic networks with correlated noise

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes

Allocation of Excitation Signals for Generic Identifiability of Dynamic Networks

This paper studies generic identifiability of dynamic networks, in which the edges connecting the vertex signals are described by proper transfer functions, and partial vertices are excited by designed external signals. We assume that the topology of the underlying graph is known, and all the vertex signals are measured. We show that generic identifiability of a directed network is related to the existence of a set of disjoint directed pseudo-trees that cover all the edges of the underlying graph, based on which, an excitation allocation problem is studied, aiming to select the minimal number excitation signals to achieve the generic identifiability of the whole network. An algorithmic procedure thereby is devised for selecting locations of the external signals such that all the edges can be consistently estimated

Excitation allocation for generic identifiability of a single module in dynamic networks: A graphic approach

For identifiability of a single module in a dynamic network, excitation signals need to be allocated at particular nodes in the network. Current techniques provide analysis tools for verifying identifiability in a given situation, but hardly address the synthesis question: where to allocate the excitation signals to achieve generic identifiability. Starting from the graph topology of the considered network model set, a new analytic result for generic identifiability of a single module is derived based on the concept of disconnecting sets. For the situation that all node signals are measured, the vertices in a particular disconnecting set provide the potential locations to allocate the excitation signals. Synthesis approaches are then developed to allocate excitation signals to guarantee generic identifiability

Some asymptotic properties of multivariable models identified by equation error techniques

\u3cp\u3eSome interesting properties are derived for simple equation-error-identification techniques - least squares and basic instrumental variable methods - applied to a class of linear, time-invariant, time-discrete multivariable models. The system at hand is not supposed to be contained in the chosen model set. Assuming that the input is unit variance white noise, it is shown that the Markov parameters of the system are estimated asymptotically unbiased over a certain interval around t equals 0.\u3c/p\u3

Some asymptotic properties of multivariable models identified by equation error techniques

\u3cp\u3eSome interesting properties are derived for simple equation error identification techniques, least squares and basic instrumental variable methods, applied to a class of linear time-invariant time-discrete multivariable models. The system at hand is not supposed to be contained in the chosen model set. Assuming that the input is unit-variance white noise, it is shown that the Markov parameters of the system are estimated asymptotically unbiased over a certain interval around t equals 0.\u3c/p\u3