We consider a sampled-data control system where a wireless sensor transmits its measurements to a controller over a communication channel. We assume that the sensor has a harvesting element to extract energy from the environment and store it in a rechargeable battery for future use. The harvested energy is modelled as a first-order Markovian stochastic process conditioned on a scenario parameter describing the harvesting environment. The overall model can then be represented as a Markov decision process, and a suitable transmission policy providing both good control performance and efficient energy consumption is designed using reinforcement learning approaches. Finally, supervisory control is used to switch between trained transmission policies depending on the current scenario. Also, we provide a tool for estimating an unknown scenario parameter based on measurements of harvested energy, as well as detecting the time instants of scenario changes. The above problem is solved based on Bayesian filtering and smoothing.

We address the problem of event-triggered networked control of nonlinear systems under simultaneous deception and Denial-of-Service (DoS) attacks. By DoS attacks, we refer to disruptions in the communication channel that prevent sensor measurements from reaching the controller. When the system undergoes a deception attack, the controller receives a modified output, deviating from the sensor’s original measurement. We implement the input delay approach and the Lyapunov-Krasovskii technique to obtain sufficient conditions, expressed in terms of linear matrix inequalities (LMIs), that characterize the duration of the DoS interruptions under which input-to-state stability (ISS) of the closed-loop system is preserved. Furthermore, we explore scenarios involving simultaneous attacks, where the DoS is modeled as a stochastic Bernoulli process. The closed-loop system is then considered as a stochastic impulsive system. In a similar manner, we derive conditions to ensure mean-square ISS for this case. A numerical example illustrates the efficiency of the results.

The problem of event-triggered sampled-data control of nonlinear systems with sector-bounded nonlinearities is considered. We assume that sensors transmit their measurements to the controller over a communication channel, where the success of transmissions is defined by an i.i.d. Bernoulli process. For the analysis of the closed-loop system stability, we use the Lyapunov–Krasovskii technique. As a result, we obtain stability conditions in terms of linear matrix inequalities (LMIs), which can be used to design the appropriate triggering parameters. A global strictly positive minimum inter-event time is guaranteed to exist by design with the proposed triggering condition. A numerical example demonstrates the efficiency of the event-triggered approach in reducing the number of transmissions compared to periodic sampling, where the period is the enforced minimum time in the event-triggering condition.

We consider a wireless control system where sensors transmit their measurements to a controller over a fading channel. We assume that each sensor is equipped with a rechargeable battery and can harvest energy from the environment or other energy sources. To predict the harvested energy, we consider a stationary Markovian model conditioned on a scenario and estimate the unknown parameters based on empirical measurements. The transmission energy is assumed to be inversely proportional to the communication channel gain, which is described by a compound distribution. To increase energy efficiency, we use a continuous event-trigger allowing the sensors to transmit new data only when certain conditions are satisfied. Finally, we analyze the exponential stability of the closed-loop nonlinear system with multiple sector-bounded nonlinearities based on the input-delay method and Lyapunov–Krasovskii technique.

In this paper we study the problem of how quantization may affect the maximum likelihood estimation of the parameters of a probability density function representing a compound distribution. We consider and compare three different approaches to design a variable quantizer allowing to guarantee a predefined loss of Fisher information which is used as a measure of the information loss due to quantization. We also propose the approximations which characterize the asymptotic behavior of the loss allowing a significant reduction of the computational complexity.

It is well-known that the state-feedback control law based on the speed gradient method can stabilize the pendulum's energy. This control employs measurements of the pendulum's angular displacement and angular velocity. In the present paper, we aim to stabilize the pendulum's energy by using the angular measurement only. We suggest a time-delay implementation of the above state-feedback control law. The resulting delayed static output-feedback practically stabilizes the pendulum's energy. We propose a precise characterization of the energy deviation bound that depends on the delay value. A numerical example demonstrates the efficiency of the results.

This letter considers the problem of how uniform quantization affects the maximum likelihood estimation of the parameters of a probability density function representing a compound distribution. As a measure of the information loss due to quantization, the loss of Fisher information is used. The main contribution of this letter is the approximation which characterizes the asymptotic behavior of the loss allowing a significant reduction of the computational complexity. We further investigate how to choose the quantization interval to guarantee a predefined loss of Fisher information. An extensive numerical simulation demonstrates the efficiency of the approximation.

The problem of pendulum’s energy control in presence of an irregular input disturbance is considered. A feedback control law is chosen based on the speed gradient method. The main contribution of the paper is in studying the complex behavior of the previously designed system under irregular disturbances. The main result is precise estimates for an initial set and a limit set (attractor) as well as the conditions guaranteeing the following: all the solutions starting in the initial set will enter the limit set in a finite time.

The problem of event-triggered sampled-data nonlinear control of Hamiltonian system is considered by the example of controlling the pendulum's energy. A feedback control law based on the speed gradient method is chosen. The main contribution consists in precisely characterizing energy deviation bounds depending on event-trigger switching parameter.

In the paper the results of first experimental studies with the setup are described, including motor parameters identification, state estimation and control of rotation velocity. The presented results demonstrate that the setup is useful for study and for control of complex nonlinear oscillatory systems.

The paper combines authors’ previous results on extending Emilia Fridman’s method to a class of nonlinear systems with sector bounded nonlinearity with the recent results of A. Selivanov and E. Fridman on a switching approach to event-triggered control. In this paper the sampled-data control under continuous event-trigger is considered. The closed-loop system is represented as the system switching between periodic and event-triggered sampling. Applying Fridman’s method and Yakubovich’s S-procedure the problem is reduced to feasibility analysis of linear matrix inequalities. Particularly it is demonstrated that the event-trigger can reduce the network workload by the example on synchronization of Chua’s circuits.

SummaryThis paper is devoted to the evaluation of sampling interval providing robust exponential stability of nonlinear system with sector‐bounded nonlinearities. It extends our previous results (R. E. Seifullaev, A. L. Fradkov. Sampled‐data control of nonlinear oscillations based on LMIs and Fridman's method. In 5th IFAC International Workshop on Periodic Control Systems, 95‐100. Caen, France. 2013). The proposed approach exploits E. Fridman's method for linear systems based on a general time‐dependent Lyapunov–Krasovskii functional. With classical results of V. A. Yakubovich about S‐procedure, the problem is reduced to feasibility analysis of linear matrix inequalities. The results are illustrated by example: the pendulum system with friction and sector‐bounded multiple nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd.

The paper combines authors’ previous results on extending Emilia Fridman’s method to a class of nonlinear systems with sector bounded nonlinearity with the recent results of A.Selivanov and E.Fridman on a switching approach to event-triggered control. In this paper the sampled-data control under continuous event-trigger is considered. The closed-loop system is represented as the system switching between periodic and event-triggered sampling. Applying Fridman’s method and Yakubovich’s S-procedure the problem is reduced to feasibility analysis of linear matrix inequalities. Particularly it is demonstrated that the event-trigger can reduce the network workload by the example on synchronization of Chua’s circuits.

The problem of controlling a nonlinear system to an invariant manifold using quantized state feedback is considered by the example of controlling the pendulum's energy. A feedback control law based on the speed gradient algorithm is chosen. The main result consisting in precisely characterizing allowed quantization error bounds and resulting energy deviation bounds is presented.

The E.M. Fridman method for analysis of the hybrid linear systems by passing to a system with sawtoothed delay and using the nonstationary Lyapunov-Krasovskii functionals and descriptor variables was extended to the nonlinear multivariable Lur’e systems. Consideration was given to the discrete control in the form of a feedback with bounded above variable step of discretization. At that, in the system equations the control function was multiplied by a bounded scalar nonlinear function. This case corresponds to numerous oscillators such as the “pendulum on cart” system. On the basis of the classical results obtained by V.A. Yakubovich on losslessness of the S-procedure, the problem of estimating the upper boundary of the discretization step comes to analyzing the system of linear matrix inequalities for solvability.

Stability conditions for sampled-data nonlinear control system with linear output feedback are studied. The case of sector bounded nonlinearities and uncertain sampling with the known upper bound on the sampling intervals is considered. Stability analysis is performed by input delay approach based on time-dependent Lyapunov-Krasovskii functionals refined by Emilia Fridman in 2010 (Fridman's method) and extended by Seifullaev and Fradkov in 2013 to nonlinear control systems with sector bounded nonlinearity (Lurie systems). Based on classical results of V.A. Yakubovich about S-procedure the problem is reduced to feasibility analysis of linear matrix inequalities. Linear output feedback controller design is based on the Passification method. The results are illustrated by example showing that both bounds on the sampling interval and accuracy of those bounds depend essentially on the controller choice.

An attempt to evaluate accuracy of Fridman's sampling interval estimates for nonlinear discrete-continuous systems where the controlled plant belongs to a class of cascade passifiable Lurie systems. Numerical results obtained for master-slave configuration of two mobile robots demonstrate good accuracy of Fridman's estimates: error of the sampling interval estimate is less than 25% of the value obtained from extensive simulation. In contrast, the error obtained by conventional method from quadratic Lyapunov function is more than 75% of the value obtained from simulation.

The master-slave synchronization problem for two cart-pendulum systems when both measurement and control signals are transmitted via intranet communication channel is examined. The speed-gradient method for exciting master system and linear state feedback for slave system is used. Theoretical analysis is performed by the nonlinear extension of Fridman's method. Experimental results are presented for a cart-pendulum system constructed from Lego. Theoretical bound for sampling interval guaranteeing synchronization is about h=0.1 sec. Such bounds are positive for control over intranet and very negative for control over internet. However experiments show that real values of the communication delays are even bigger.

Emilia Fridman's method based on time-dependent Lyapunov-Krasovsii functionals is extended to nonlinear control systems with sector bounded nonlinearity. Furthermore, this paper considers sampled-data feedback control under uncertain sampling with the known upper bound on the sampling intervals, where the control function is multiplied by bounded scalar nonlinear function in system equation. This special case corresponds to many oscillator control systems, for example, cart-pendulum system. The problem is reduced to feasibility analysis of linear matrix inequalities based on classical results of V.A. Yakubovich about S-procedure.