State-dependent Gain Research Articles

Event-Triggered Distributed Average Tracking Control for Lipschitz-Type Nonlinear Multiagent Systems.

This article investigates the event-triggered distributed average tracking (ETDAT) control problems for the Lipschitz-type nonlinear multiagent systems with bounded time-varying reference signals. By using the state-dependent gain design approach and event-triggered mechanism, two types of ETDAT algorithms called: 1) static and 2) adaptive-gain ETDAT algorithms are developed. It is the first time to introduce the event-triggered strategy into DAT control algorithms and investigate the ETDAT problem for multiagent systems with Lipschitz nonlinearities, which is more practical in real physical systems and can better meet the needs of practical engineering applications. Besides, the adaptive-gain ETDAT algorithms do not need any global information of the network topology and are fully distributed. Finally, a simulation example of the Watts-Strogatz small-world network is presented to illustrate the effectiveness of the adaptive-gain ETDAT algorithms.

Robust proportional–integral control of submersible autonomous robotized vehicles by backstepping-averaged sub-gradient sliding mode control

This study presents a novel robust controller strategy for submersible autonomous robotized vehicles (SARV). This controller applies the averaged sub-gradient (ASG) descendant method to optimize the tracking of well-posed reference trajectories. The motion control form of the SARV is done in three stages (cascade-like control design). The phases consist of using the translation velocities as pseudo controllers to adjust the SARV position, regulating the angular velocities to attain the requested translation velocities, and using the proposed ASG to control the thrusters to get the needed angular velocities. ASG implementation optimizes a convex cost function depending on the integral of the tracking error using the ASG method. The application of Barbalat’s lemma justifies the tracking error is converging the origin asymptotically. A class of integral sliding mode controllers with a variable state-dependent gain solves the tracking of the designed reference trajectories in each of the three stages. The sliding surface depends on the tracking error for each pseudo-controller, its integral, and the cost function average. The optimization of the cost function can be done without complete knowledge of the SARV dynamics. A numerical example is presented in this study to confirm the suggested control design’s effectiveness based on the cost function’s time evolution analysis. The forced motion by the proposed controller is compared with the movement obtained by a proportional–integral–derivative (PID) controller. The proposed controller exhibits a better tracking of the reference trajectory than the PID version.

Robust Control of a Bimorph Piezoelectric Robotic Manipulator Considering Ellipsoidal-Type State Restrictions

The current study presents an adaptive control approach to solve the tracking trajectory problem for a robotic manipulator that uses a gripper based on bimorph piezoelectric actuators. The development of an adaptive gain state feedback form that considers the state restrictions is proposed using a novel class of barrier Lyapunov function that drives the effective control of joints and piezoelectric actuators. The proposed method allows for the inclusion of complex combinations of state restrictions in the Lyapunov function, yielding the construction of differential forms for the gains in the controller that can handle the evolution of trajectories of the robotic arm inside the restricted region. The proposed control design successfully tracks reference trajectories for both joints of the robotic arm as well as the motion of the piezoelectric device during several operative scenarios. A comprehensive experimental study evaluates the effect of introducing state-dependent gain considering state restrictions of the ellipsoidal type. The comparison of the mean square error confirms the contributions of the developed control action, showing better tracking quality for less control power with the same evaluation, which is a desirable characteristic in the controlled motion of micromanipulators. The proposed controller solves the tracking trajectory problem for the micromanipulation system, satisfies the motion restrictions, and allows better tracking performance to be enforced. Furthermore, comparison of the obtained trajectories seems to validate the proposed controller’s contribution concerning a feedback form with fixed gains.

A Distributed Dynamical System for Optimal Resource Allocation Over State-Dependent Networks

This paper focuses on investigating the nonsmooth resource allocation problem based on distributed dynamical systems over state-dependent communication networks. Taking into account the coupling of supply-demand constraint, a potential-based Lagrangian function containing local multipliers is reformulated by the exact penalty method. By virtue of the primal-dual subgradient flow, a distributed differentiated projected dynamical system with a state-dependent gain is proposed. It is shown that the connectivity of communication networks can be preserved under the proposed system. Furthermore, it is proved that the system converges to the optimal resource allocation with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/t)$</tex-math></inline-formula> convergence rate. Finally, the theoretical results are substantiated through simulations of economic dispatch problems in the IEEE 30-bus system and IEEE 118-bus system.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Event-Triggered Cooperative Tracking for Lipschitz-Type Multi-Agent Systems: An ARE-Based Approach

This brief studies the event-triggered cooperative tracking problem for multiple autonomous agents described by Lipschitz-type nonlinear dynamics. A new kind of event-triggered cooperative tracking strategy is developed by using model-based local sampled state information and the state-dependent gain approach. Compared with some event-triggered cooperative tracking strategies in existing works, the dynamics of agents is extended to Lipschitz-type nonlinearity in this brief, which can better meet the practical engineering needs. Besides, the cooperative tracking algorithms overcome the infeasibility of linear matrix inequality (LMI) conditions, and the cooperative tracking problem can be addressed by only solving an algebraic Riccati equation (ARE), which is feasible if the system is stabilizable. Finally, a simulation example is presented to verify the theoretical analysis and the effectiveness of the control strategy.

Adaptive sliding-mode trajectory tracking control for state constraint master–slave manipulator systems

This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master–slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional–derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.

Distributed Time-Varying Optimization With State-Dependent Gains: Algorithms and Experiments

This brief addresses distributed continuous-time optimization problems with time-varying objective functions. The goal is for multiple agents to cooperatively minimize the sum of local time-varying objective functions with only local interaction and information while explicitly taking into account distributed adaptive gain design. Here, the optimal point is time varying and creates an optimal trajectory. First, for the unconstrained case, a distributed nonsmooth algorithm coupled with a state-dependent gain is proposed. It is shown that the interaction gain for each agent can be computed according to the variation of the Hessian and gradient information of the convex local objective functions so that the algorithm can solve the time-varying optimization problem without imposing a bound on any information about the local objective functions. Second, for the case where there exist common time-varying linear equality constraints, an extended algorithm is presented, where local Lagrangian functions are introduced to address the equality constraints. The asymptotic convergence of both algorithms to the optimal solution is proved. Numerical simulations are presented to illustrate the theoretical results. In addition, the one proposed algorithm is experimentally implemented and validated on a multi-Crazyflie platform.

Mechanisms underlying gain modulation in the cortex.

Cortical gain regulation allows neurons to respond adaptively to changing inputs. Neural gain is modulated by internal and external influences, including attentional and arousal states, motor activity and neuromodulatory input. These influences converge to a common set of mechanisms for gain modulation, including GABAergic inhibition, synaptically driven fluctuations in membrane potential, changes in cellular conductance and changes in other biophysical neural properties. Recent work has identified GABAergic interneurons as targets of neuromodulatory input and mediators of state-dependent gain modulation. Here, we review the engagement and effects of gain modulation in the cortex. We highlight key recent findings that link phenomenological observations of gain modulation to underlying cellular and circuit-level mechanisms. Finally, we place these cellular and circuit interactions in the larger context of their impact on perception and cognition.

A Robust [K,KL] Sector for Nonlinear System

This brief suggests an approach to design a robust ${[\mathcal {K,KL}]}$ sector for nonlinear system subjected to parametric/model uncertainty and this design relies on the Matrosov’s results. The nonlinear surface to decide the boundaries of a sector is designed by using a control-Lyapunov function. Here, a Hands-Off control consists of constant and state-dependent gain is used to force the state vectors to the interior of robust ${[\mathcal {K,KL}]}$ sector and shows asymptotic stability with minimum support to the nonlinear system by avoiding the redundant control effort. The usefulness of the proposed design is illustrated by a nonlinear electronic circuit.

Echo State Network-Based Backstepping Adaptive Iterative Learning Control for Strict-Feedback Systems: An Error-Tracking Approach

In this article, an echo state network (ESN)-based backstepping adaptive iterative learning control scheme is proposed for nonlinear strict-feedback systems performing the same operation repeatedly over a finite-time interval. Different from most of the output tracking approaches, an error-tracking approach is presented using the backstepping technique, such that the tracking error can follow a prespecified error trajectory without any requirement on the initial value of system states. Then, a novel Lyapunov function is constructed to deal with the unknown state-dependent gain function of the controller design. The uncertain nonlinearities are approximated by employing ESNs with simple feedback structures, and the weight update laws are developed by combining the parameter adaptation in the time domain and iteration domain. Moreover, the proposed control scheme is further extended to handle the strict-feedback systems with input saturations. Through the Lyapunov-like synthesis, the closed-loop stability and error convergence of the proposed error-tracking control scheme are analyzed in the presence of the approximation errors. Numerical simulations are provided to verify the effectiveness of the proposed scheme.

Brain State-dependent Gain Modulation of Corticospinal Output in the Active Motor System

The communication through coherence hypothesis suggests that only coherently oscillating neuronal groups can interact effectively and predicts an intrinsic response modulation along the oscillatory rhythm. For the motor cortex (MC) at rest, the oscillatory cycle has been shown to determine the brain's responsiveness to external stimuli. For the active MC, however, the demonstration of such a phase-specific modulation of corticospinal excitability (CSE) along the rhythm cycle is still missing. Motor evoked potentials in response to transcranial magnetic stimulation (TMS) over the MC were used to probe the effect of cortical oscillations on CSE during several motor conditions. A brain-machine interface (BMI) with a robotic hand orthosis allowed investigating effects of cortical activity on CSE without the confounding effects of voluntary muscle activation. Only this BMI approach (and not active or passive hand opening alone) revealed a frequency- and phase-specific cortical modulation of CSE by sensorimotor beta-band activity that peaked once per oscillatory cycle and was independent of muscle activity. The active MC follows an intrinsic response modulation in accordance with the communication through coherence hypothesis. Furthermore, the BMI approach may facilitate and strengthen effective corticospinal communication in a therapeutic context, for example, when voluntary hand opening is no longer possible after stroke.

Finite-Time Coordination Under State-Dependent Communication Graphs With Inherent Links

This brief investigates distributed coordination control problems under a state-dependent communication graph with several inherent links. In the network, an interaction arises between two agents if either their states differ by less than a fixed range or an inherent communication link exists between them. By considering that each agent has a state-dependent control gain, a nonlinear consensus protocol is proposed for single-integrator modeled multi-agent systems. With the validity of some initial condition, the communication graph is shown to be connected at any time, which guarantees asymptotic consensus. It is further shown that this result can apply to the opinion consensus problem. This brief also provides a novel approach to finite-time coordination protocols synthesis. By simply multiplying a time-varying gain, any coordination protocol can be transformed into a finite-time protocol. A simulation example is presented to illustrate the effectiveness of the theoretical result.

The Non-Smoothness Problem in Disturbance Observer Design: A Set-Invariance-Based Adaptive Fuzzy Control Method

This work removes the critical assumptions of continuity, differentiability, and state-independent boundedness, which are typical of compounded disturbances in disturbance observer-based adaptive designs. Crucial in removing such assumptions are a novel observer-based design with state-dependent gain in place of a constant one, and a novel set-invariance design. The designs use different a priori knowledge of the disturbance, but they can both handle state-dependent (e.g., possibly unbounded) disturbances, as well as non-smooth (e.g., non-differentiable and jump discontinuous) disturbances. The tracking error is proven to be as small as desired by appropriately choosing design parameters. For the second design, which uses the least a priori knowledge of the disturbance, stability is proven by enhancing Lyapunov theory with an invariant-set mechanism, so as to construct an appropriate compact set resulting an invariant set for the closed-loop trajectories.

Cooperative Semiglobal Robust Output Regulation of Non-Introspective Nonlinear Agents With Partial Normal Form and State-Dependent High-Frequency Gain

This paper investigates cooperative semig-lobal robust output regulation problem for a class of non-introspective nonlinear multiagent systems. Each agent of this class is allowed to have a partial normal form , instead of only the conventional normal form, with a state-dependent high-frequency gain. Besides, all agents are unaccessible to the controller states of their neighbors. In this setting, if the uniform detectability assumption in the sense of [25] is satisfied, then a robust distributed regulator can be designed with the employment of a distributed nonlinear internal model and a novel distributed extended lower-power high-gain observer, such that the numerical implementation problem is solved and the regulated output of each agent asymptotically converges to the desired reference input robustly with guaranteed domain attraction.

Finite-Time Distributed Average Tracking for Second-Order Nonlinear Systems.

This paper studies the distributed average tracking (DAT) problem for multiple reference signals described by the second-order nonlinear dynamical systems. Leveraging the state-dependent gain design and the adaptive control approaches, a couple of DAT algorithms are developed in this paper, which are named finite-time and adaptive-gain DAT algorithms. Based on the finite-time one, the states of the physical agents in this paper can track the average of the time-varying reference signals within a finite settling time. Furthermore, the finite settling time is also estimated by considering a well-designed Lyapunov function in this paper. Compared with asymptotical DAT algorithms, the proposed finite-time algorithm not only solve finite-time DAT problems but also ensure states of physical agents to achieve an accurate average of the multiple signals. Then, an adaptive-gain DAT algorithm is designed. Based on the adaptive-gain one, the DAT problem is solved without global information. Thus, it is fully distributed. Finally, numerical simulations show the effectiveness of the theoretical results.

Adaptive sliding-mode control with integral compensation for robotic devices with state constraints

Abstract The aim of this study was to design a discontinuous controller with adaptive gains, based on the sliding-mode theory. The adaptive controller solved the trajectory tracking problem for a class of systems with state constraints, specifically for a class of multi-articulated robot manipulator with a constraint work-space. The controller implemented a state dependent adaptive gain that grows in value when the trajectories approach the boundary of the set that characterized the states constraints. The design of the adaptive gain guaranteed the existence of a finite-time stable equilibrium point for a special sliding surface depending on the tracking trajectory error. The specific law used to adjust the gain was obtained by a Lyapunov-based stability analysis. Some numerical simulations proved that the sliding-mode controller showed a superior performance, measured by the mean square value of the tracking result, compared to the non-adaptive gain first order sliding-mode controller.

State-dependent parameter model identification for inverse dead-zone control of a hydraulic manipulator

The robotic platform in this study has dual, seven-function, hydraulically actuated manipulators, which are being used for research into assisted tele-operation for common nuclear decommissioning tasks, such as pipe cutting. The article concerns the identification of state-dependent parameter (SDP) models for joint angle control. Compared to earlier SDP analysis of the same device, the present work proposes a new way of representing the state-dependent gain and parametrises this using novel regret-regression methods. A mechanistic interpretation of this model yields dead-zone and angular velocity saturation coefficients, and facilitates SDP-based control with an inverse dead-zone. This approach integrates the input signal calibration, system identification and nonlinear control system design steps, using a relatively small data-set, allowing for straightforward recalibration when the dynamic characteristics have changed due to age and use, or after the installation of replacement parts.

Fast Terminal Sliding-Mode Control With an Integral Filter Applied to a Van Der Pol Oscillator

This paper proposes a procedure for designing a fast terminal sliding-mode control involving an integral filter that guarantees a finite time of convergence to zero dynamics, robustness against polynomial bounded uncertainties, and external disturbances. It reduces the chattering effect by employing a state-dependent gain and adds an integral filter to smooth the input control signal. We suggest a simplified algorithm to design the controller. To test the performance of the algorithm, we use a Van der Pol chaotic oscillator synchronization with perturbations in the states. Finally, we compare the performance of the method by using the proposed controller with the filter turned-on and turned-off.

Complete identification of four giant interneurons supplying mushroom body calyces in the cockroach Periplaneta americana.

Global inhibition is a fundamental physiological mechanism that has been proposed to shape odor representation in higher-order olfactory centers. A pair of mushroom bodies (MBs) in insect brains, an analog of the mammalian olfactory cortex, are implicated in multisensory integration and associative memory formation. With the use of single/multiple intracellular recording and staining in the cockroach Periplaneta americana, we succeeded in unambiguous identification of four tightly bundled GABA-immunoreactive giant interneurons that are presumably involved in global inhibitory control of the MB. These neurons, including three spiking neurons and one nonspiking neuron, possess dendrites in termination fields of MB output neurons and send axon terminals back to MB input sites, calyces, suggesting feedback roles onto the MB. The largest spiking neuron innervates almost exclusively the basal region of calyces, while the two smaller spiking neurons and the second-largest nonspiking neuron innervate more profusely the peripheral (lip) region of the calyces than the basal region. This subdivision corresponds well to the calycal zonation made by axon terminals of two populations of uniglomerular projection neurons with dendrites in distinct glomerular groups in the antennal lobe. The four giant neurons exhibited excitatory responses to every odor tested in a neuron-specific fashion, and two of the neurons also exhibited inhibitory responses in some recording sessions. Our results suggest that two parallel olfactory inputs to the MB undergo different forms of inhibitory control by the giant neurons, which may, in turn, be involved in different aspects of odor discrimination, plasticity, and state-dependent gain control. J. Comp. Neurol. 525:204-230, 2017. © 2016 Wiley Periodicals, Inc.