Initial Condition Response Research Articles

Model order reduction for bilinear control systems with inhomogeneous initial conditions

This work focuses on the model order reduction problem for bilinear control systems with nonzero initial conditions. Based on the Volterra series analysis, the system response can be decomposed into three parts. The first two parts are the zero input response and zero initial condition response of the system. The third part describes the response which couples the effect of the nonzero initial condition and the nonzero input. The system corresponding to the third part is a bilinear control system with a special time-varying input coefficient matrix. We show that such a system is equivalent to a time-invariant bilinear control system, and conventional model reduction methods can be applied to reduce it. We propose to reduce each of the component responses independently and then combine them to approximate the full system response. This method is of high flexibility and shows promising results.

Nucleus Accumbens Dopamine D1-Receptor-Expressing Neurons Control the Acquisition of Sign-Tracking to Conditioned Cues in Mice.

Following repeated pairings, the reinforcing and motivational properties (incentive salience) of a reward can be transferred onto an environmental stimulus which can then elicit conditioned responses, including Pavlovian approach behavior to the stimulus (a sign-tracking response). In rodents, acquisition of sign-tracking in autoshaping paradigms is sensitive to lesions and dopamine D1 receptor antagonism of the nucleus accumbens (NAc) of the ventral striatum. However, currently, the possible roles of dorsal striatal subregions, as well as of the two major striatal neuron types, dopamine D1-/D2-expressing medium spiny neurons (MSNs), in controlling the development of conditioned responses is still unclear and warrants further study. Here, for the first time, we used a transgenic mouse line combined with striatal subregion-specific AAV virus injections to separately express tetanus toxin in D1-/D2- MSNs in the NAc, dorsomedial striatum, and dorsolateral striatum, to permanently block neurotransmission in these neurons during acquisition of an autoshaping task. Neurotransmission blocking of NAc D1-MSNs inhibited the acquisition of sign-tracking responses when the initial conditioned response for each conditioned stimulus presentation was examined, confirming our initial hypothesis. These findings suggest that activity in NAc D1-MSNs contributes to the attribution of incentive salience to conditioned stimuli.

Non-lethal effects of predators on body growth and health state of juvenile lizards, Psammdromus algirus

Predation risk does not necessarily increase predation rates because prey may be able to behave differentially to cope with higher predation risk. However, antipredatory behaviors may be costly, leading to negative, although non-lethal, effects of predators on prey. We examined in outdoor enclosures whether an experimental increase in predation pressure, which did not increase direct mortality, but forced individuals to increase antipredatory behaviors, may have significant non-lethal effects on body growth and health state of juvenile lizards, Psammodromus algirus. Simulated persistent predator attacks resulted in slower rates of body size growth and body mass gain of juvenile lizards, which may greatly affect their future survival. However, juvenile lizards were able to maintain their initial body condition and immune response regardless of predation risk level. Moreover, our data suggested that experience of lizards with their home range “environment” might allow them to compensate the negative effects of temporal high predation risk on body condition when predation risk subsequently decreased. Finally, juvenile lizards with greater immune responses showed smaller increments in body size, but larger increments in body mass and body condition, at the end of the control treatment. In contrast, there was no relationship between immunity and growth after the experimental treatment.

Identification of linear time-invariant systems based on initial condition responses

Forced responses are commonly used for system identification, but only initial condition responses may be available when a system has no controllable inputs or forced responses cannot be practically measured. It is therefore meaningful to analyse whether initial condition responses can be used to estimate the system matrix. In this work, the identifiability of the nth order (n > 1) linear time-invariant systems from initial condition responses is analysed. Systems with only one measurable state (OMS systems) and those with n measurable states (NMS systems) are considered. Analysis indicates that one initial condition response is not sufficient to uniquely determine the system matrix of an OMS system and n initial condition responses are necessary. The identifiability of an OMS system with data from n independent initial condition responses is equivalent to that of an NMS system with only one initial condition response. Explicit formulations and a non-iterative algorithm are developed for both OMS and NMS systems.

On-line Reconfigurability Evaluation for Actuator Faults Using Input/Output Data

Control reconfigurability, from the fault tolerance point of view, defines the capacity of the control system to allow restoration of performance in the presence of faults. For its evaluation it is required to calculate the controllability gramian. This calculation is usually carried on before control system be implemented, i.e., off-line. Instead, the on-line evaluation of the control reconfigurability from input/output data could be useful for the fault tolerance redesign. The contribution of the paper is to propose a way of calculating on-line the controllability gramian from input/output data in order to evaluate an index based on the control reconfigurability. The paper aims to estimate the reconfigurability for a linear system under partial loss of control effectiveness. The controllability gramian could be computed in direct form from the initial condition response. For practical aspects, an identification algorithm is proposed in order to compute the system controllability gramian, independently of initial conditions. An example is presented to illustrate the method.

STABILITY ANALYSIS OF CLOSED-LOOP INPUT SHAPING CONTROL

Input shaping is a vibration control technique that operates by filtering reference commands so that the modified (or shaped) command does not excite the system's natural frequencies. Usually input shaping is limited to a filtering operation outside of any feedback loops. However, this implementation prevents input shaping from effecting some vital control applications including disturbance rejection, initial condition response, etc. Therefore, some research has suggested using input shapers within feedback loops. This paper will present some initial investigations toward the fundamental understanding of how input shapers utilized within feedback loops affect closed loop stability.

Effect of prismatic joint inertia on dynamics of kinematic chains

In this paper the effect of prismatic joint inertia on dynamics of planar kinematic chains with friction is investigated. The mathematical model of a planar kinematic chain consisting of a prismatic joint sliding along a link that is connected to a revolute joint is developed using Lagrange’s equations. The influence of the slider inertia on the position of the application point of the joint forces is analyzed. The influence of the slider link inertia on the dynamic response of a spatial robot arm with feedback control is analyzed using Kane’s formulation. Larger values of the initial condition response characteristics are observed for larger values of the slider link inertia. Also, the effect of the prismatic joint inertia on the dynamic parameters of a planar mechanism is exemplified using inverse dynamics based on the Newton–Euler method. Numerical results are obtained and compared for zero and larger values of the prismatic joint inertia at different speeds. The numerical simulations reveal that the effect of slider inertia may be negligible at low speeds, but becomes significant at high speeds.

Unified initial condition response analysis of Lur'e systems and linear time-invariant systems

A unified framework to the initial condition response (ICR) analysis of non-linear time-varying systems of the Lur'e type and linear time-invariant (LTI) systems is considered. To quantify the transient behaviour resulting from initial conditions, an ICR measure is defined. An appropriate upper bound for the ICR measure can be calculated based upon the condition number of a positive definite matrix, associated with a quadratic Lyapunov function. Owing to the particular structure of the Lur'e systems, bounding the ICR measure is transformed into a minimization problem, constrained by either two simultaneous Lyapunov matrix inequalities or a single algebraic Riccati inequality. In the LTI case, the ICR measure is merely the supremum of the induced norm of the state transition matrix and its calculation involves solving a Lyapunov matrix equation. The ICR measure bound is significant from the engineering standpoint since it enables the calculation of the non-saturating domain of the state variables. In the LTI case, this bound also provides a quantification of impulse and unit step responses. The results are illustrated by several examples.

Behavioural correlates of conditioned ventilatory responses to hypoxia in rats

To examine the possible contribution of behavioural arousal to ventilatory conditioning, we performed a differential conditioning experiment using two odours as the paired conditioned stimulus (CS+) and unpaired conditioned stimulus (CS−) and a hypoxic mixture (7.5% O 2) as the unconditioned stimulus (US) in 24 adult male rats. Vanillin was the CS+ and rose the CS− in half the rats, and vice versa in the other half. Each rat underwent 26 paired CS+/hypoxia trials and 26 CS− trials in alternation, followed by two CS+ only and two CS− trials to test for conditioning. Analysis of breathing variables and behavioural scores during the test showed two qualitatively different conditioned responses. The initial conditioned response was characterised by short breath durations (TT), frequent sniffing episodes, and arousal responses. Following this, a specific, conditioned increase in tidal volume (VT) and levelling off of sniffing and motor activities occurred. The early TT-response and late VT-response to CS+ both contributed to an increase in ventilation (VI). The present data show that the association of an odour and hypoxia elicits a biphasic ventilatory conditioned response, of which the first component is integrated into conditioned arousal.

The role of mesoprefrontal dopamine neurons in the acquisition and expression of conditioned fear in the rat

The mesoprefrontal dopamine neurons are sensitive to physical, pharmacological and psychological stressors. In this report, the role of these neurons in the response to classical fear conditioning was investigated. 6-Hydroxydopamine lesions to the medial prefrontal cortex reduced dopamine levels to about 13% of controls but did not alter behavior during the acquisition of fear conditioning. As expected, conditioned fear increased dopamine metabolism (3,4-dihydroxyphenylacetic acid/dopamine ratio) in the nucleus accumbens in sham-lesion rats. The medial prefrontal 6-hydroxydopamine lesions did not alter this effect. During the expression, however, lesioned rats demonstrated a delayed extinction of the conditioned response without an overall increase in the initial conditioned response. This effect was consistent in rats receiving 6-hydroxydopamine lesions before or after the acquisition period. The calculated rates of extinction showed that the 6-hydroxydopamine lesioned rats had a reduced rate of extinction, but not acquisition, of fear conditioning. The results presented in this manuscript indicate that the mesoprefrontal dopamine neurons are involved in co-ordinating the normal extinction of a fear response but do not alter the acquisition of fearful behaviors. These data are consistent with the conclusion that the mesoprefrontal dopamine neurons are involved in maintaining the animal's response adaptability with regards to stress-related changes in the external environment.

Analysis and Control of a Flywheel Energy Storage System With a Hybrid Magnetic Bearing

This article presents the design, dynamic analysis, and control of a flywheel energy storage system. At the heart of the system is a hybrid magnetic bearing. The bearing consists of ring and disk shaped permanent magnets, and a synthetic ruby sphere on a sapphire plate. The bearing is shown to be stable without active control. Equations of motion for the flywheel are derived in a sensor based coordinate system. The resulting equations are non-singular around the nominal operating condition and are feedback linearizable without the need for a coordinate transformation. A method of modeling rotor imbalance as a set of sinusoidal disturbances of magnitudes that do not depend on rotational speed is also presented. To reject large external disturbances active control is applied to the flywheel. Two nonlinear control laws are applied and are shown to improve the initial condition response of the inherently stable system.

Development of hypoglycemia and hyperglycemia as a function of number of trials in insulin conditioning

A neutral environment paired with insulin injections can develop the capacity to elicit glycemic changes. However, both conditioned hypoglycemia and conditioned hyperglycemia have been reported under apparently similar circumstances. The present study examined conditioned glycemic changes as a function of the number of conditioning trials and the novelty of the conditioning environment. Adult, male Wistar rats were injected with either insulin or physiological saline every second day, in either a novel or a familiar environment. On the test day, all rats were injected with saline and blood was collected 20 minutes later for determination of glucose levels. In rats given insulin in the novel environment, conditioned hypoglycemia was observed after two trials but was replaced by conditioned hyperglycemia after five trials. No conditioning at all occurred in the familiar environment. The two conditioned responses observed were interpreted as reflecting two unconditioned responses brought about by insulin—a hypoglycemic response to the central detection of insulin, and a hyperglycemic response to the detection of (insulin-induced) hypoglycemia. Taken in conjunction with previous experiments in which both conditioned response patterns have occurred, the present results suggest that the homeostatic response of hyperglycemia can become strong enough to overcome the initial conditioned response of hypoglycemia, but that its establishment depends on the use of a novel conditioned stimulus and a larger number of conditioning trials.

Persistency of excitation in the presence of possibly unbounded signals

This note develops an explicit characterization of the concept of persistency of excitation for time-invariant linear systems in the presence of possibly unbounded signals. This result can be used to establish exponential convergence for a range of adaptive control algorithms. A feature of our proof is a particular technique for dealing with the initial condition response.

Acute tolerance to the effects of n-butanol and n-hexanol in goldfish

1. The success-rate of a conditioned response in goldfish was tested as a function of time after single additions of n-butanol and n-hexanol at different concentrations. 2. The same response, also tested as a function of time, was made during the approach to a final concentration of 15 mM n-butanol by one, two, three or six equal concentration steps. 3. Following a step increase in alcohol concentration, the initial conditioned response success-rate decreased (except for the step 0–2.5 mM of n-butanol) and was related both to the initial concentration and to the size of the step. 4. Recovery from decreased success-rates was observed for final concentrations of less than 15 mM n-butanol (by step) and 1.06 mM hexanol. The recovery was almost complete for the lower final concentrations, but only partial for 12.5 and 15.00 mM butanol. After single steps to a final concentration of 15 mM butanol there was no evidence of recovery by 5 h. Concentrations of 20 mM butanol, 1.35 mM hexanol produced fully anaesthetised fish. 5. The uptake of n-butanol in the brain of the fish was measured as a function of time following step changes in concentration from 0–10, 0–15 and 0–20 mM butanol. 6. A set of ‘dose response’ curves relating the conditioned response success-rate and brain concentration were calculated at different times from the above data; these show a shift to the right with increasing time. Thus, goldfish show the phenomenon of acute tolerance to n-butanol and n-hexanol.