H. J. Kushner and P. G. Dupuis. Springer-Verlag, New York/Heidelberg, May 1992. 439 pp., DM 98. ISBN 3-540-97834-8

Numerical methods for stochastic control problems in continuous time

This paper first offers a transversal view through microfluidics theory and applications, starting from a brief overview on microfluidic systems and related theoretical issues, covering different kinds of phenomena, from continuous to multiphase flow. Multidimensional models, from lumped parameters to numerical models and computational solutions, are then considered as preliminary tools for the characterization of spatio-temporal dynamics in microfluidic flows. Following these, experimental approaches through original monitoring opto-electronic interfaces and systems are discussed. Finally, a vision of two phase microfluidic phenomena is given through nonlinear analyses applied to experimental time series.

Reinforcement Learning and Adaptive Dynamic Programming for Feedback Control

The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

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Comparison of Riemann and Lebesque sampling for first order stochastic systems

Development of microgrids and wide spread deployment of renewable generation and energy storage systems have highlighted the need for distributed control schemes to achieve maximum utilization and coordination among all the connected resources. In DC microgrids, the key goals of system-wide control are droop-based current sharing and network dc-voltage regulation. These may be achieved using a consensus algorithm secondary control that a) averages all the node voltages dynamically and maintains them at a nominal value and b) based on information from neighboring source currents to converge to a consensus in current sharing. Achieving the dynamic consensus may impose significant communication burden when implemented using conventional periodic communication methods. In this paper, an event-triggered communication based dynamic consensus algorithm is proposed that helps achieve both the stated goals of proportional current sharing along with average DC voltage regulation in a DC microgrid. The convergence and stability of the modified dynamic consensus algorithm and event triggering condition is proven using Lyapunov's stability criterion. The proposed control is applied to a DC microgrid system for secondary control of voltage and current regulation, and the performance of the proposed technique is validated under various operating conditions and disturbance in the communication system in both simulation and hardware environment.

Event-Triggered Communication Based Distributed Control Scheme for DC Microgrid

Self-learning robust optimal control for continuous-time nonlinear systems with mismatched disturbances.

This technical note proposes a procedure to control an uncertain discrete-time networked system using an aperiodic stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric uncertainty. Aperiodic exchange of information is done due to bandwidth constraint of the communication network. An event-triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks. In event-triggered control, the control input is computed and actuated at the system end only when a pre-specified event condition is violated. The robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost-functional. It is shown that the robust control law with aperiodic information ensures input-to-state stability (ISS) of the original system in the presence of mismatched uncertainty. Deriving the event-triggering condition for a discrete-time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note. A numerical example is given to prove the efficacy of the proposed event-based control algorithm over the conventional periodic one.

Stabilization of Uncertain Discrete-Time Linear System With Limited Communication

Stepper motor is found in a lot of applications such as computer peripherals, business machines, process control, machine tools and robotics. Especially in different areas of robotics, process control like silicon processing, I.C. Bonding and Laser trimming applications, it is necessary to control the stepper motor from remote places. The present paper describes a remote angular position control system of stepper motor using DTMF (Dual-Tone Multi-Frequency) Technology as an alternative means of communication using Radio Frequency (RF) with advantages of simplicity and audibility. DTMF Technology has been used here to implement acoustic communication for controlling the angular position of the stepper motor remotely anywhere in the world through mobile phone network. The desired value of angular position signals, in terms of DTMF tones have been generated by using a mobile phone. The microcontroller has been used to implement the control algorithm after receiving the DTMF tone. Since no extra transmitting and receiving device is needed except mobile phone, the system is very much simple, rugged, and cost effective. The experimental results indicate that the system has high resolution, repeatability and error is also within tolerable limit.

Remote Position Control System of Stepper Motor Using DTMF Technology

This paper proposes a framework to design an event-triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event-triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and mismatched system uncertainties. Derivation of event-triggering rule with a non-zero positive inter-event time and corresponding stability criteria for uncertain event-triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results.

Model Based Robust Control Law for Linear Event-Triggered System

This paper proposes a framework to design an event-triggered based robust control law for nonlinear uncertain robot manipulator. Load variations and unmodeled system dynamics of manipulator are the primary sources of both system and input uncertainties. A static event-triggering rule is employed to realize the proposed robust control law. Derivation of static event-triggering rule with a positive inter-event time and corresponding stability criteria for uncertain manipulator dynamics are the key contribution of this paper. Validation of proposed control technique is carried out numerically on a two-link SCARA type robot manipulator. Simulation results show that measurement error norm is always bounded by the state dependent threshold and also ensures that asymptotic convergence of manipulator states in the presence of both system and input uncertainty.

An event-triggered based robust control of robot manipulator

A conceptual design methodology is proposed for event-triggered based communication for wide-area damping controller in power systems. The event-triggering mechanism is adopted to reduce the communication burden between the origin of the remote signal and the wide-area damping controller (WADC) location. The remote signal is transmitted to the WADC only when an event-triggering condition based on a predefined system output, is satisfied. The triggering condition is derived from a stability criterion, and is monitored continuously by a separate event-monitoring unit located at the origin of the remote signal. The stability of the resulting closed-loop system is guaranteed via the input-to-state stability technique. The proposed event-triggered WADC is implemented on two typical test power systems – two area four machine and IEEE 39-bus 10-machine. The validation of proposed mechanism is carried out through non-linear simulation studies on MATLAB/Simulink platform. The numerical results show the efficacy of the controller in managing the communication channel usage without compromising the stated system stability objectives.

Niladri Sekhar Tripathy

Papers

Stabilization of Uncertain Discrete-Time Linear System With Limited Communication

Remote Position Control System of Stepper Motor Using DTMF Technology

Model Based Robust Control Law for Linear Event-Triggered System

An event-triggered based robust control of robot manipulator

Event-triggered communication in wide-area damping control: a limited output feedback-based approach