State-dependent Gain Research Articles

State Observer Design for Monitoring the Degree of Polymerization in a Series of Melt Polycondensation Reactors

A nonlinear reduced-order state observer is applied to estimate the degree of polymerization in a series of polycondensation reactors. The finishing stage of polyethylene terephthalate synthesis is considered in this work. This process has a special structure of lower block triangular form, which is properly utilized to facilitate the calculation of the state-dependent gain in the observer design. There are two possible on-line measurements in each reactor. One is continuous, and the other is slow-sampled with dead time. For the slow-sampled titration measurement, inter-sample behavior is estimated from an inter-sample output predictor, which is essential in providing continuous corrections on the observer. Dead time compensation is carried out in the same spirit as the Smith predictor to reduce the effect of delay in the measurement outputs. By integrating the continuous-time reduced-order observer, the inter-sample predictor and the dead time compensator together, the degree of polymerization is accurately estimated in all reactors. The observer performance is demonstrated by numerical simulations. In addition, a pre-filtering technique is used in the presence of sensor noise.

Formation control of multiple Euler-Lagrange systems via null-space-based behavioral control

This paper addresses the formation control problem of multiple Euler-Lagrange systems with model uncertainties in the environment containing obstacles. Utilizing the null-space-based (NSB) behavioral control architecture, the proposed problem can be decomposed into elementary missions (behaviors) with different priorities and implemented by each individual system. A class of novel coordination control algorithms is constructed and utilized to achieve accurate formation task while avoiding obstacles and guaranteeing the model uncertainty rejection objective. By using sliding mode control and Lyapunov theory, the formation performance in closed-loop multi-agent systems is proven achievable if the state-dependent gain of the obstacle avoidance mission is appropriately designed. Finally, simulation examples demonstrate the effectiveness of the algorithms.

Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system’s physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.

視覚を用いた多項式空間上の受動性に基づく液面振動制御実験

In this paper, we propose a pseudo-passivity based control on polynomial space. First, we identify a model of a liquid sloshing system using a robotic vision and convert the model into a physical system on a polynomial space. Second, we design a passivity based control with a state-dependent gain to stabilize the horizontal surface asymptotically on polynomial space. Finally, we confirm the validity of the proposed method by visual feedback for the liquid sloshing system.

Sliding Mode Speed Control for Induction Motor Drives with State-Dependent Gain Method

The main obstacle of conventional sliding mode control is caused by discontinuous function of high control activity which is known as chattering phenomenon. In this research, the chattering phenomenon is significantly reduced by a newly developed algorithm. A fast sigmoid function with varying boundary layer algorithm is designed as a state-dependent to replace the discontinuous function in conventional sliding mode control. It is known that the switching gain of sliding mode control is proportional to the chattering level, and normally a large switching gain is applied to handle the uncertainties. This research proposes a state-dependent sliding mode control which is the switching gain and boundary layer is proportional to the sigmoid function of the sliding mode controller. As a result, the boundary layer and the switching gain will change depend on uncertainties of the motor drives system. The induction motor is controlled by vector control strategy, using indirect field orientation and Space Vector Pulse Width Modulation technique. Experimental result have proved that the proposed state-dependent sliding mode control able to deal with external load disturbances as well as effectively free from chattering phenomenon compared to conventional sliding mode control. The proposed algorithm and the vector control strategy are developed in digital signal processing board. The results have confirmed that the state-dependent sliding mode control is superior with regard to external load disturbances and variation in the reference speed setting when compared to conventional sliding mode control and fixed boundary layer sliding mode control.

Robust adaptive neural control for a class of uncertain MIMO nonlinear systems

In this paper, a novel robust adaptive neural control scheme is proposed for a class of uncertain multi-input multi-output nonlinear systems. The proposed scheme has the following main features: (1) a kind of Hurwitz condition is introduced to handle the state-dependent control gain matrix and some assumptions in existing schemes are relaxed; (2) by introducing a novel matrix normalisation technique, it is shown that all bound restrictions imposed on the control gain matrix in existing schemes can be removed; (3) the singularity problem is avoided without any extra effort, which makes the control law quite simple. Besides, with the aid of the minimal learning parameter technique, only one parameter needs to be updated online regardless of the system input–output dimension and the number of neural network nodes. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Cellular mechanisms of brain state–dependent gain modulation in visual cortex

During locomotion, visual cortical neurons fire at higher rates to visual stimuli than during immobility while maintaining orientation selectivity. The mechanisms underlying this change in gain are not understood. We performed whole cell recordings from layer 2/3 and layer 4 visual cortical excitatory neurons as well as from parvalbumin-positive and somatostatin-positive inhibitory neurons in mice free to rest or run on a spherical treadmill. We found that the membrane potential of all cell types became more depolarized and (with the exception of somatostatin-positive interneurons) less variable during locomotion. Cholinergic input was essential for maintaining the unimodal membrane potential distribution during immobility, while noradrenergic input was necessary for the tonic depolarization associated with locomotion. Our results provide a mechanism for how neuromodulation controls the gain and signal-to-noise ratio of visual cortical neurons during changes in the state of vigilance.

State–dependent system identification for control of a hydraulically–actuated nuclear decommissioning robot

This article considers the identification of state–dependent parameter (SDP) models for the hydraulically actuated dual–manipulators of a mobile robot used for nuclear decommissioning tasks. A unified framework for calibration, data collection and system identification is developed, and utilized to investigate potential state–dependencies. The latter are associated with nonlinear system dynamics and can cause irregular joint movements when the device is controlled using linear control algorithms. The analysis suggests that a univariate SDP model is suitable for control design. The model has a state–dependent gain, characterized directly from experimental data using a numerically optimized polynomial function of the delayed input variable. In order to demonstrate the practical utility of the SDP model, closed–loop results using a novel non–minimal regulator for joint control are briefly considered.

Visualizing Neuromodulation In Vivo: TANGO-Mapping of Dopamine Signaling Reveals Appetite Control of Sugar Sensing

Behavior cannot be predicted from a "connectome" because the brain contains a chemical "map" of neuromodulation superimposed upon its synaptic connectivity map. Neuromodulation changes how neural circuits process information in different states, such as hunger or arousal. Here we describe a genetically based method to map, in an unbiased and brain-wide manner, sites of neuromodulation under different conditions in the Drosophila brain. This method, and genetic perturbations, reveal that the well-known effect of hunger to enhance behavioral sensitivity to sugar is mediated, at least in part, by the release of dopamine onto primary gustatory sensory neurons, which enhances sugar-evoked calcium influx. These data reinforce the concept that sensory neurons constitute an important locus for state-dependent gain control of behavior and introduce a methodology that can be extended to other neuromodulators and model organisms.

Energy Shaping Nonlinear Acceleration Control for a Mobile Inverted Pendulum Utilizing Instability

A nonlinear controller for accelerating a mobile inverted pendulum (MIP) with interconnection and damping assignment passivity-based control (IDA-PBC) is proposed. For underactuated systems, nonlinear partial differential equations (PDEs) must be solved to derive the IDA-PBC and it is a difficult task in general. However, this study shows that the MIP can be properly described as a full actuated port-Hamiltonian system focusing only on the pendulum dynamics. The controller is derived without solving the PDEs. Although our controller is for only the pendulum part of the system, the translational acceleration can be indirectly controlled utilizing the relation between the inclination of the pendulum and the acceleration arising from instability of the system. The controller can achieve various properties through energy shaping procedure of the IDA-PBC. Especially an energy function which will lead to safe operation of the MIP is proposed in this study. The function ensures that motion of the pendulum is restricted in a predefined region and converges to a desired pendulum angle. The controller also gets the pendulum back to the desired angle with a large state-dependent gain when the pendulum comes close to fall over. Effectiveness of the controller is verified through simulations.

C308 エネルギー整形非線形制御による倒立振子型移動体の不安定性を利用した加速制御(OS7 非線形制御理論とその応用3)

A nonlinear controller for accelerating a mobile inverted pendulum (MIP) with interconnection and damping assignment passivity-based control (IDA-PBC) is proposed. For underactuated systems, nonlinear partial differential equations (PDEs) must be solved to derive the IDA-PBC and it is a difficult task in general. However, this study shows that the MIP can be properly described as a full actuated port-Hamiltonian system focusing only on the pendulum dynamics. The controller is derived without solving the PDEs. Although our controller is for only the pendulum part of the system, the translational acceleration can be indirectly controlled utilizing the relation between the inclination of the pendulum and the acceleration arising from instability of the system. The controller can realize various properties through energy shaping procedure of the IDA-PBC. Especially an energy function which will lead to safe operation of the MIP is proposed in this study. The function ensures that motion of the pendulum is restricted in a predefined region and converges to a desired pendulum angle. The controller also gets the pendulum back to the desired angle with a large state-dependent gain when the pendulum comes close to fall over. Effectiveness of the controller is verified through simulations.

316 エネルギー整形非線形制御による倒立振子型移動体の不安定性を利用した加速制御と実機検証

A nonlinear controller for accelerating a mobile inverted pendulum (MIP) with interconnection and damping assignment passivity-based control (IDA-PBC) has been proposed by the authors in a previous study. For an underactuated system such as a MIP, nonlinear partial differential equations (PDEs) must be solved to derive the IDA-PBC and it is a difficult task in general. However, the authors have shown that the MIP can be properly described as a full actuated port-Hamiltonian system focusing only on the pendulum dynamics. The controller is derived without solving the PDEs. Although our controller is for only the pendulum part of the system, the translational acceleration can be indirectly controlled utilizing the relation between the inclination of the pendulum and the acceleration arising from instability of the system. The controller can realize various properties through energy shaping procedure of the IDA-PBC. Especially an energy function which will lead to safe operation of the MIP is used in this study. The function ensures that motion of the pendulum is restricted in a predefined region and converges to a desired pendulum angle. The controller also gets the pendulum back to the desired angle with a large state-dependent gain when the pendulum comes close to fall over. Effectiveness of the controller is verified through experiments.

Background synaptic activity modulates spike train correlation

Event Abstract Back to Event Background synaptic activity modulates spike train correlation Ashok L. Kumar1*, Maurice J. Chacron2 and Brent Doiron3 1 Carnegie Mellon University, Center for the Neural Basis of Cognition, United States 2 McGill University, Department of Physiology, Canada 3 University of Pittsburgh, Department of Mathematics, United States Sensory neurons have many synaptic inputs, not all of which directly transmit sensory information. Instead, some inputs serve to modulate the neuronal response to relevant stimuli. One example of neural modulation is that the intensity of background synaptic input determines the postsynaptic neuron's leak conductance and membrane potential variability. This in turn controls the gain of its firing rate response to an excitatory stimulus [1]. State dependent gain control in sensory neurons is necessary for proper stimulus processing in low and high contrast environments, and allows attentional state to modulate signal transfer. Most work that characterizes the modulatory influence of background activity has focused on single cell responses, but it is reasonable to expect that such activity may also modulate population responses. We study how background activity shapes correlations between pairs of neurons using simulations, a theory from non-equilibrium statistical mechanics, and data recorded from electrosensory pyramidal neurons in weakly electric fish. We find that increasing background activity can decrease the output spike train correlation of two neurons over long time scales but increase pairwise synchrony on short time scales. We study these effects in simulated integrate-and-fire neurons. Using a linear response theory [2,3], we find that changes in correlation are related to single cell response properties including gain and integration timescale. We first demonstrate these changes in correlation using pairs of model neurons receiving partially correlated conductance-based synaptic activity. The neuron pairs received low or high levels of background activity, and spike train statistics were compared for these two states. We next demonstrate similar state-dependent changes in a recurrent network of neurons in which correlations arise through coupling. Finally, we test our predictions on simultaneously recorded extracellular spike data from primary sensory nucleus in the electrosensory system of weakly electric fish. We induce a state change in the neuronal response properties by driving the animal with stimuli mimicking a prey or a communication signal [4]. Consistent with our theoretical findings, the timescale and correlation of recorded neuron pairs vary depending on these processing states. The findings connect state-dependent changes in single cell response properties, such as firing rate gain, to changes in correlated activity in a neuronal population.

Nonlinear observer design for state and disturbance estimation

A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov's auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor.

On Robust, Multi-Input Sliding-Mode Based Control with a State-Dependent Boundary Layer

This paper proposes a nonlinear multi-input control law using sliding mode concepts for continuous-time, uncertain, linear systems. The control law introduces a state-dependent layer around the sliding mode plane to remove chattering. This layer combines two types of boundary layers: a constant layer and a sector-shaped layer. The states will always enter the state-dependent boundary layer and the choice of the sliding mode will be seen to determine the ultimate system performance. A proof of stability shows ultimate boundedness. The controller is applied to a nonlinear simulation model of a cart-pendulum and exhibits a high degree of robustness. The new boundary layer in connection with a novel dynamically changing, state-dependent gain can be used to obtain a narrow boundary-layer shape in the operating region of interest. This permits rejection of disturbances without chattering of the control and improves on the performance expected of a sliding-mode control with constant boundary layer.

Nonlinear observer design in the presence of delayed output measurements

The present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements. The proposed nonlinear observer possesses a state-dependent gain which is computed from the solution of a system of first-order singular partial differential equations, and in particular, consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time-instants within the time-delay window introduced by the available output measurements. Therefore, the proposed nonlinear observer exhibits a chain-like structure that explicitly reflects and takes into account the magnitude of the output delay. Furthermore, a set of conditions is derived under which convergence of the estimation error to zero is established. Finally, the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example.

On the Nonlinear Dynamic State Reconstruction Problem for Chemical/Biochemical Reaction Systems in the Presence of Model Uncertainty

A new approach to the unmeasurable state reconstruction problem for nonlinear chemical reaction systems in the presence of model uncertainty is proposed. In particular, a new robust nonlinear state estimation method is developed that explicitly uses all the available useful information associated with: (i) a dynamic model inevitably characterized by uncertainty, and (ii) a set of sensor measurements in order to accurately reconstruct other key quantities/variables that cannot be measured on-line due to physical and/or technical limitations. The problem of interest is conveniently formulated and addressed within the context of singular partial differential equations (PDE) theory, leading to a nonlinear state estimator that possesses a state-dependent gain computed through the solution of a system of first-order singular PDEs. A set of necessary and sufficient conditions is presented that ensure the existence and uniqueness of a locally analytic solution to the aforementioned system of singular PDEs, and a series solution method that can be easily implemented via a MAPLE code is developed. Under these conditions, the convergence of the estimation error or the mismatch between the actual unmeasurable states and their estimates is analyzed and characterized in the presence of model uncertainty. Finally, the performance of the proposed nonlinear etimator and its convergence properties are evaluated in an illustrative biochemical reaction system that exhibits nonlinear behavior coupled with parametric uncertainty, and the estimation objective is to accurately reconstruct the unmeasurable substrate concentration using the available cell mass concentration measurements and the model of the system under consideration.

Nonlinear Observer Design for Process Monitoring

The present work proposes a systematic nonlinear observer design framework for process monitoring. The objective is to accurately monitor key process variables associated with process safety or product quality, by designing a model-based nonlinear observer that directly utilizes the available information coming from continuous-time on-line process output measurements. The nonlinear observer possesses a state-dependent gain which is computed from the solution of a system of first-order linear partial differential equations (PDEs). Depending on whether the process operates in continuous or batch mode, a different mathematical treatment and solution scheme for the system of PDEs is needed. Within the proposed design framework, both full-order and reduced-order observers are studied. Finally, the performance of the proposed observer is evaluated in two chemical-engineering examples: (1) a catalytic batch reactor where the objective is to accurately estimate the catalyst activity and (2) an exothermic CSTR that exhibits steady-state multiplicity and the heat released by the reaction needs to be closely monitored.

A nonlinear autoregressive signal model with state-dependent gain

Abstract This paper describes a nonlinear AR model in which the nonlinearity appears as a multiplicative state-dependent function on the input noise term. This structure allows to gain some control on the shape of the output probability density function. A sufficient condition for the stability of such a model is given, as well as a sub-optimal parameter estimation scheme. The model is then applied to real signals issued from temperature variation sensors.