State-dependent Control Research Articles

Chapter 7 - Breathing during sleep

The depth, rate, and regularity of breathing change following transition from wakefulness to sleep. Interactions between sleep and breathing involve direct effects of the central mechanisms that generate sleep states exerted at multiple respiratory regulatory sites, such as the central respiratory pattern generator, respiratory premotor pathways, and motoneurons that innervate the respiratory pump and upper airway muscles, as well as effects secondary to sleep-related changes in metabolism. This chapter discusses respiratory effects of sleep as they occur under physiologic conditions. Breathing and central respiratory neuronal activities during nonrapid eye movement (NREM) sleep and REM sleep are characterized in relation to activity of central wake-active and sleep-active neurons. Consideration is given to the obstructive sleep apnea syndrome because in this common disorder, state-dependent control of upper airway patency by upper airway muscles attains high significance and recurrent arousals from sleep are triggered by hypercapnic and hypoxic episodes. Selected clinical trials are discussed in which pharmacological interventions targeted transmission in noradrenergic, serotonergic, cholinergic, and other state-dependent pathways identified as mediators of ventilatory changes during sleep. Central pathways for arousals elicited by chemical stimulation of breathing are given special attention for their important role in sleep loss and fragmentation in sleep-related respiratory disorders.

Fully Distributed Control for a Class of Uncertain Multi-Agent Systems with a Directed Topology and Unknown State-Dependent Control Coefficients

To address the control of uncertain multi-agent systems (MAS) with completely unknown system nonlinearities and unknown control coefficients, a global consensus method is proposed by constructing novel filters and barrier function-based distributed controllers. The main contributions are as follows. Firstly, a novel two-order filter is designed for each agent to produce informational estimates from the leader, such that a connectivity matrix is not used in the controller’s design, solving the difficultly caused by the time-varying control coefficients in a MAS with a directed graph. Secondly, combined with the novel filters, barrier functions are used to construct the distributed controller to deal with the completely unknown system nonlinearities, resulting in the global consensus of the MAS. Finally, it is rigorously proved that the consensus of the MAS is achieved while guaranteeing the prescribed tracking-error performance. Two examples are given to verify the effectiveness of the proposed method, in which the simulation results demonstrate the claims.

Homogeneous constrained finite-time controller for double integrator systems: Analysis and experiment

In this paper, the finite-time control problem for a class of double integrator systems under state constraints is investigated. Different from the traditional finite-time control methods with constant gains, an improved finite-time controller with state-dependent gains is designed. The main challenges lie in the finite-time stability analysis of the resultant closed-loop system caused by state-dependent control gains and how to make the system states keep in the constrained region. Based on the homogeneous system theory, the finite-time stability of the closed-loop system under state constraints is proved. In addition to the finite-time convergence, it is also shown that the states of the system always are kept in the constrained region. Finally, the developed finite-time controller is applied to buck converter and the validity of the proposed method is verified through a DC–DC buck converter under voltage and current constraints.

Trajectory-Tracking Controller Design of Rotorcraft Using an Adaptive Incremental-Backstepping Approach

This paper treats a robust adaptive trajectory-tracking control design for a rotorcraft using a high-fidelity math model subject to model uncertainties. In order to control the nonlinear rotorcraft model which shows strong inter-axis coupling and high nonlinearity, incremental backstepping approach with state-dependent control effectiveness matrix is utilized. Since the incremental backstepping control suffers from performance degradation in the presence of control matrix uncertainties due to change of flight conditions, control system robustness is improved by combining the least squares parameter estimator to estimate time varying uncertainties contained in the control effectiveness matrix. Also, by selecting a suitable gain set by investigating the error dynamics, a uniform trajectory-tracking performance over operational flight envelope of the rotorcraft is ensured without resorting to the conventional gain scheduling method. To evaluate the proposed controller, comparative results between IBSC and Adaptive IBSC are provided in this paper with sequential maneuvers from the ADS-33E-PRF. The proposed method shows improved tracking performance under variations in control effective matrix in the flight simulation. Robust and stable parameter estimation is also guaranteed due to the implementation of the DF-RLS algorithm for the least squares estimator.

Service Scheduling for Random Requests With Deadlines and Linear Waiting Costs

We study service scheduling problems in a slotted system where jobs arrive according to a Bernoulli process and leave within two slots after arrival. Service costs are quadratic in service rates, and there is also a linear waiting cost. We frame the problems as average cost Markov decision processes. While the studied system is a linear system with quadratic costs, it has state-dependent control and a non-standard cost function structure, rendering the optimization problem complex. We obtain explicit optimal policies in the case when all the jobs are of the same size. In particular, we show that the optimal policy is linear or piece-wise linear in the system state, depending on the system parameters. We then consider a scenario where each service request comes from a rational agent interested in optimizing his/her service and waiting cost, and we obtain a symmetric Nash equilibrium. We extend our study to a scenario where job sizes can take distinct values, and job arrivals constitute a Markov chain. Here, we provide an algorithm that yields the optimal policy, but it is of exponential complexity. Finally, we propose an approximate policy of linear complexity for general job size distributions and derive its performance bound.

NDNF interneurons in layer 1 gain-modulate whole cortical columns according to an animal’s behavioral state

Processing of sensory information in neural circuits is modulated by an animal's behavioral state, but the underlying cellular mechanisms are not well understood. Focusing on the mouse visual cortex, here we analyze the role of GABAergic interneurons that are located in layer 1 and express Ndnf (L1 NDNF INs) in the state-dependent control over sensory processing. We find that the ongoing and sensory-evoked activity of L1 NDNF INs is strongly enhanced when an animal is aroused and that L1 NDNF INs gain-modulate local excitatory neurons selectively during high-arousal states by inhibiting their apical dendrites while disinhibiting their somata via Parvalbumin-expressing interneurons. Because active NDNF INs are evenly spread in L1 and can affect excitatory neurons across all cortical layers, this indicates that the state-dependent activation of L1 NDNF INs and the subsequent shift of inhibition in excitatory neurons toward their apical dendrites gain-modulate sensory processing in whole cortical columns.

Nonlinear SDRE based adaptive fuzzy control approach for age-specific drug delivery in mixed chemotherapy and immunotherapy

Determination of a near-optimal personalized drug delivery scenario in mixed chemotherapy and immunotherapy based on the age of cancer patients was presented in this paper. For this purpose, a mathematical model for cancer dynamics is considered in the form of ordinary differential equations (ODE) which contains cancer cells, tumor cells, and chemotherapy drug intervention. This model is modified by adding immunotherapy intervention effects to alter cancer dynamics. We consider two patients with known and unknown model parameters which are mentioned as a reference and unknown patients respectively. The nonlinear composite adaptive controller is introduced by compounding State Dependent Riccati Equation (SDRE) and Model Reference Adaptive Control (MRAC) techniques for achieving the drug delivery of an unknown patient. The drug delivery scenario for a reference patient with a known mathematical model and parameters is determined via the SDRE technique and then for any unknown patient, the personalized mixed therapy protocol is achieved using the treatment regimen of the reference patient as a reference model in MRAC. To reduce the side effects of chemotherapy drugs, we determine drug maximum dose limits using fuzzy control by considering the age of cancer patients. We regarded patients in four age groups of child, young, middle-aged, and old. In the proposed methodology, unknown patients are considered as a black-box simulator and the mathematical model parameters of the patient are not essential for the design of drug administration protocol and we only need patients’ age. After chemotherapy, the treatment is completed by immunotherapy to avoid cancer relapse. The effect of reference and unknown patient ages in obtaining drug delivery protocol is deeply surveyed. Numerical simulations confirm the effectiveness, robustness, and flexibility of the proposed strategy for patients of different ages. The Proposed algorithm can be an effective tool to aid oncologists in prescribing age-specific optimal treatment protocols for cancer patients.

Changing the Cortical Conductor's Tempo: Neuromodulation of the Claustrum.

The claustrum is a thin sheet of neurons that is densely connected to many cortical regions and has been implicated in numerous high-order brain functions. Such brain functions arise from brain states that are influenced by neuromodulatory pathways from the cholinergic basal forebrain, dopaminergic substantia nigra and ventral tegmental area, and serotonergic raphe. Recent revelations that the claustrum receives dense input from these structures have inspired investigation of state-dependent control of the claustrum. Here, we review neuromodulation in the claustrum—from anatomical connectivity to behavioral manipulations—to inform future analyses of claustral function.

Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown quantized input and control directions subject to actuator failures

This article addresses an adaptive backstepping control design for uncertain fractional-order nonlinear systems in the strict-feedback form subject to unknown input quantization, unknown state-dependent control directions, and unknown actuator failure. The system order can be commensurate or noncommensurate. The total number of failures is allowed to be infinite. The Nussbaum function is used to deal with the problem of unknown control directions. Compared with the existing results, the control gains can be functions of states and the knowledge of quantization parameters and characteristics of the actuator failure are unknown. By applying the backstepping control approach based on the frequency-distributed model, it is proved that all the closed-loop signals remain bounded and the output tracking error converges to the origin asymptotically. Finally, the effectiveness of the proposed controller is demonstrated by two simulation examples.

Feedback control of charged ideal fluids

The theory of controlled mechanical systems of Bloch et al (2001 IEEE Trans. Control Syst. Technol. 45 2253–70; Bloch et al 2001 Int. J. Robust Nonlinear Control 11 191–214; Bloch et al 1992 Automatica 28 745–56; Bloch et al 1997 Current and Future Directions in Applied Mathematics) and Krishnaprasad P S (1985 Nonlinear Anal. Theor. Methods Appl. 9 1011–35) is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and depends on the Eulerian state of the controlled system. Moreover, the control is set up so that the corresponding closed loop equations are Lie–Poisson. This implies that the energy–momentum method of Arnold V (1966 Ann. Inst. Fourier 16 319–61) and Holm et al (1985 Phys. Rep. 123 1–116) can be used to find a stabilizing control. As an example the case of planar parallel shear flow with an inflection point is treated. A state dependent feedback control is constructed which stabilizes the system for an arbitrarily long channel.

Nonlinear state-dependent pulse control for an SIRS epidemic model with varying size and its application to the transmission of brucellosis

As the disease spreads, it will inevitably cause important damage to the life and health of the population, resulting in changes in the population quantity. In addition, in some economically underdeveloped areas, limited medical resources will also have an important impact on the prevention and control of diseases. Based on these, a susceptible-infected-recovered-susceptible (SIRS) epidemic model is established, where state-dependent pulse control strategy, varying total population and limited medical resources are introduced. By using the qualitative theory of ordinary differential equation, differential inequality techniques, Poincaré map, and other methods, some sufficient conditions of the existence and orbital asymptotical stability of positive order-1 or order-2 periodic solution are obtained in various situations. Theoretical results imply that the proportion of infected class can be controlled at a desired low level for a long time and disease will not break out among population. Finally, based on realistic parameters of brucellosis in ruminants, numerical simulations have been performed to expalin/extend our analytical results and the feasibility of the state-dependent feedback control strategy.

Synchronization on a limit cycle of multi-agent systems governed by discrete-time switched affine dynamics

Abstract This paper addresses the problem of synchronizing a group of interacting discrete-time switched affine systems with centralized control laws. Two different state-dependent control laws are proposed, based on recent literature on switched affine systems and are evaluated on an academical example with a multi-agent system.

Facilitating Numerical Solutions of Inhomogeneous Continuous Time Markov Chains Using Ergodicity Bounds Obtained with Logarithmic Norm Method

The problem considered is the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time Markov chains with discrete state space and time varying intensities. Numerical solution techniques can benefit from methods providing ergodicity bounds because the latter can indicate how to choose the position and the length of the “distant time interval” (in the periodic case) on which the solution has to be computed. They can also be helpful whenever the state space truncation is required. In this paper one such analytic method—the logarithmic norm method—is being reviewed. Its applicability is shown within the queueing theory context with three examples: the classical time-varying M/M/2 queue; the time-varying single-server Markovian system with bulk arrivals, queue skipping policy and catastrophes; and the time-varying Markovian bulk-arrival and bulk-service system with state-dependent control. In each case it is shown whether and how the bounds on the rate of convergence can be obtained. Numerical examples are provided.

Robust state dependent Riccati equation variable impedance control for robotic force-tracking tasks

Industrial robots are increasingly used in highly flexible interaction tasks, where the intrinsic variability makes difficult to pre-program the manipulator for all the different scenarios. In such applications, interaction environments are commonly (partially) unknown to the robot, requiring the implemented controllers to take in charge for the stability of the interaction. While standard controllers are sensor-based, there is a growing need to make sensorless robots (i.e., most of the commercial robots are not equipped with force/torque sensors) able to sense the environment, properly reacting to the established interaction. This paper proposes a new methodology to sensorless force control manipulators. On the basis of sensorless Cartesian impedance control, an Extended Kalman Filter (EKF) is designed to estimate the interaction exchanged between the robot and the environment. Such an estimation is then used in order to close a robust high-performance force loop, designed exploiting a variable impedance control and a State Dependent Riccati Equation (SDRE) force controller. The described approach has been validated in simulations. A Franka EMIKA panda robot has been considered as a test platform. A probing task involving different materials (i.e., with different stiffness properties) has been considered to show the capabilities of the developed EKF (able to converge with limited errors) and controller (preserving stability and avoiding overshoots). The proposed controller has been compared with an LQR controller to show its improved performance.

Vehicle tip-over prevention using gain-scheduled State-dependent Riccati Equation–based anti-rollover controller

The most hazardous kind of vehicle crash among all road accidents is vehicle rollover. Present-day rollover prevention systems in commercial vehicles mitigate rollover by preventing any wheel lift-off from the ground. These systems make use of actuators such as differential brakes and demand all the wheels on the ground for satisfactory operation. Such systems are not effective in recovering a vehicle from intense rollover scenarios where the wheels on one side are lifted off the ground, and the vehicle is about to rollover to the other side after reaching the tip-over point. A few studies have investigated the possibility of reinstating a vehicle at the tip-over point with the wheels on a side lifted off. The high complexity and computation time of the optimal control strategies such as nonlinear model predictive controller make it unsuitable for real-time implementations. This study proposes a novel gain-scheduled State-dependent Riccati Equation–based optimal anti-rollover controller for reinstating a vehicle from the tip-over point. An inverted double pendulum on a cart vehicle model is used as the plant model. The anti-rollover controller is found to be presentable as a two-dimensional gain-scheduled lookup table with specific state dependencies in existence. It eliminates the necessity of solving the nonlinear performance index minimization problem online. State-dependent Riccati Equation method adequately accounts for the nonlinearities involved, yet possesses a small computational time per sample. The anti-rollover controller is evaluated with a 10 degrees of freedom full vehicle model with a nonlinear pure slip tyre model that incorporates the dynamical effects neglected in the controller formulation. Finally, the anti-rollover controller is evaluated in real-life initial conditions using a sophisticated pick-up truck model obtained from TruckSim® software through a co-simulation with the anti-rollover controller setup in MATLAB®/Simulink® environment. The State-dependent Riccati Equation controller was found to be effective in reinstating the higher-order models from the tip-over point in all the case studies conducted.

Markovian bulk-arrival and bulk-service queues with general state-dependent control

We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored.

Constrained Utility Deviation-Risk Optimization and Time-consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton-Jacobi-Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.

On a Class of Lur’e Dynamical Systems with State-Dependent Set-Valued Feedback

Using a new implicit discretization scheme, we study in this paper the existence and uniqueness of strong solutions for a class of Lur’e dynamical systems where the set-valued feedback depends on both the time and the state. This work is a generalization of Tanwani et al. (SIAM J. Control Opti. 56(2), 751–781, 2018) where the time-dependent set-valued feedback is considered to acquire weak solutions. Obviously, strong solutions and implicit discretization scheme are nice properties, especially for numerical simulations. Conditions guarantying the exponential attractivity of solutions are provided. The obtained results can be used to study the time-varying Lur’e systems with errors in data or under the state-dependent controls applied to the moving sets. Our work is new even the set-valued feedback depends only on the time.

Dynamical analysis of a two-species competitive system with state feedback impulsive control

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

Constrained Utility Deviation-Risk Optimization and Time-Consistent HJB Equation

In this paper we propose a unified utility deviation-risk model which covers both utility maximization and mean-variance analysis as special cases. We derive the time-consistent Hamilton--Jacobi--Bellman (HJB) equation for the equilibrium value function and significantly reduce the number of state variables, which makes the HJB equation derived in this paper much easier to solve than the extended HJB equation in the literature. We illustrate the usefulness of the time-consistent HJB equation with several examples which recover the known results in the literature and go beyond, including a mean-variance model with stochastic volatility dependent risk aversion, a utility deviation-risk model with state dependent risk aversion and control constraint, and a constrained portfolio selection model. The numerical and statistical tests show that the utility and deviation-risk have a significant impact on the equilibrium control strategy and the distribution of the terminal wealth.