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IN THIS ISSUE

### Research Papers

J. Dyn. Sys., Meas., Control. 2017;139(9):091001-091001-18. doi:10.1115/1.4036033.

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial-state stabilization of stochastic dynamical systems. Partial asymptotic stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation, and hence, guaranteeing both partial stability in probability and optimality. The overall framework provides the foundation for extending optimal linear-quadratic stochastic controller synthesis to nonlinear-nonquadratic optimal partial-state stochastic stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time-varying stochastic systems with quadratic and nonlinear-nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine stochastic nonlinear systems using an inverse optimality framework tailored to the partial-state stochastic stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091002-091002-6. doi:10.1115/1.4036236.

The Udwadia–Kalaba methodology is a possible way of explicitly obtaining the equations of motion of constrained systems. From these equations of motion, one can estimate the necessary forces in the constraint to keep the system in a given motion. Hence, the Udwadia–Kalaba methodology can also apply to active tracking control of subsystems or the control of points of a structure. In this work, one investigates experimentally the benefits and drawbacks of such control strategy by applying it to the control of out-of-plane vibrations of a cantilever beam. The beam is excited by a shaker mounted near the clamped end of the beam. A second shaker applies the control forces in the free end of the beam, where an accelerometer is used for feedback. The vibration behavior of the beam under excitation/control is measured by a laser vibrometer. Results show that the methodology changes the dynamic behavior of the structure by changing its boundary conditions at the point of control, thus shifting natural frequencies and mode shapes. Results also show that the successful implementation of the method experimentally is sensitive to the quality of modeling of the structure.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091003-091003-10. doi:10.1115/1.4036031.

One of the main challenges in robotics applications is dealing with inaccurate sensor data. Specifically, for a group of mobile robots, the measurement of the exact location of the other robots relative to a particular robot is often inaccurate due to sensor measurement uncertainty or detrimental environmental conditions. In this paper, we address the consensus problem for a group of agent robots with a connected, undirected, and time-invariant communication graph topology in the face of uncertain interagent measurement data. Using agent location uncertainty characterized by norm bounds centered at the neighboring agent's exact locations, we show that the agents reach an approximate consensus state and converge to a set centered at the centroid of the agents' initial locations. The diameter of the set is shown to be dependent on the graph Laplacian and the magnitude of the uncertainty norm bound. Furthermore, we show that if the network is all-to-all connected and the measurement uncertainty is characterized by a ball of radius r, then the diameter of the set to which the agents converge is 2r. Finally, we also formulate our problem using set-valued analysis and develop a set-valued invariance principle to obtain set-valued consensus protocols. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approximate consensus protocol framework.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091004-091004-11. doi:10.1115/1.4036034.

This paper introduces a two-scale command shaping strategy for reducing vibrations in conventional and hybrid electric vehicle (HEV) powertrains during engine restart. The approach introduces no additional system components and thus few additional costs. The torque profile from an electric machine (EM) is tailored to start the internal combustion engine (ICE) while minimizing residual vibrations. It is shown that the tailored EM torque profile, composed of a linear combination of constant and time-varying components, results in significant mitigation of powertrain vibrations and smoother ICE startup. The time-varying EM torque component is calculated using an analytical ICE model and a perturbation technique for separating scales, which isolates the ICE nonlinear response. Command shaping is then applied to the linear problem at the remaining scale. Simulation results suggest a promising and straightforward technique for reducing vibrations and improving drivability during ICE restart. Furthermore, two-scale command shaping may also be useful in mitigating other HEV-related drivability issues associated with powertrain mode changes (e.g., blending of hybrid power sources, engaging and disengaging of clutches, etc.).

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091005-091005-13. doi:10.1115/1.4036367.

The energy that is needed for operating a self-powered device is provided by the energy excess in the system in the form of kinetic energy, or a combination of regenerative and renewable energy. This paper addresses the energy exchange issues pertaining to regenerative and renewable energy in the development of a self-powered dynamic system. A rigorous framework that explores the supply and demand of energy for self-powered systems is developed, which considers uncertainties and optimal bounds, in the context of optimal uncertainty quantification. Examples of regenerative and solar-powered systems are given, and the analysis of self-powered feedback control for developing a fully self-powered dynamic system is discussed.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091006-091006-7. doi:10.1115/1.4035927.

In this paper, we consider the adaptive control problem for a class of systems governed by linear time-varying interval differential equations having unknown (interval) parameters. Using the fact that system output posses lower and upper bounds, we have converted the interval differential equation into two sets of ordinary differential equations that describe the behavior of lower and upper bounds of system output. With this approach, interval analysis could be replaced by real analysis, and hence, adaptive control of interval systems can be treated as an ordinary adaptive control problem. Using variation arguments, we have developed the necessary conditions of optimality for the equivalent adaptive control problem. Finally, we present a numerical example to illustrate the effectiveness of the proposed (interval) control scheme.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091007-091007-15. doi:10.1115/1.4036030.

This paper introduces a new method to monitor battery state of health (SOH). In particular, the side reaction current density is estimated as a direct SOH indicator for the first time and its estimation is formulated as an inaccessible subsystem identification problem, where the battery health subsystem is treated as an inaccessible subsystem with the side reaction current density as the output. Inaccessibility in this context refers to the fact that the inputs and outputs of the subsystem are not measurable in situ. This subsystem is identified using retrospective-cost subsystem identification (RCSI) algorithm, and the output of the identified battery health subsystem provides an estimate for the side reaction current density. Using an example parameter set for a LiFePO4 battery, simulations are performed to obtain estimates under various current profiles. These simulations show promising results in identifying the battery health subsystem and estimating the side reaction current density with RCSI under ideal conditions. Robustness of the algorithm under nonideal conditions is analyzed. Estimation of the side reaction current density using RCSI is shown to be sensitive to nonideal conditions that cause errors in the measurement or estimation of the battery voltage. A method for quantitatively assessing the impact of nonideal conditions on the side reaction current estimation accuracy is provided. The proposed estimation technique, including the method for estimating the side reaction current density using RCSI and the framework analyzing its robustness, can also be applied to other parameter sets and other battery chemistries to monitor the SOH change resulting from any electrochemical-based degradation mechanism that consumes cyclable Li-ions.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091008-091008-11. doi:10.1115/1.4036074.

Battery energy storage systems (BESSs) have been integrated with wind turbines to mitigate wind intermittence and make wind power dispatchable as traditional power sources. This paper presents two phases of optimizations, namely, power scheduling and real-time control that allows an integrated wind turbine and BESS to provide the grid with consistent power within each dispatch interval. In the power scheduling phase, the desired battery state of charge (SOC) under each wind speed is first determined by conducting an offline probabilistic analysis on historical wind data. With this information, a computationally efficient one-step-ahead model predictive approach is developed for scheduling the integrated system power output for the next dispatch interval. In the real-time control phase, novel control algorithms are developed to make the actual system power output match the scheduled target. A wind turbine active power controller is proposed to track the reference power set point obtained by a steady-state optimization approach. By combining an internal integral torque control and a gain-scheduled pitch control, the proposed active power controller can operate around a desired tip speed ratio (TSR) without an accurate knowledge of turbine power coefficient curve. Compared to the conventional power scheduling and real-time controller, implementing the new methodology significantly reduces the ramp rate, generator torque changing rate, battery charging rate, and the power output deviation from the scheduled target. BESSs with various capacities and different wind profiles are considered to demonstrate the effectiveness of the proposed algorithms on battery sizing.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091009-091009-8. doi:10.1115/1.4036233.

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of large-scale systems with time-varying delays in the interconnected terms and state and input delays. The upper bounds of interconnection terms with time-varying delays and external disturbances are assumed to be completely unknown. By integrators inclusion, a dynamic input delay compensator is established for input delay compensation and it is used as a practical method for state calculation x(t + R). Also, a method is presented for a class of decentralized feedback controllers, which can evolve the closed-loop system error uniformly bounded stable. As a numerical example, the proposed technique is applied to an unstable open-loop system to show the feasibility and effectiveness of the method.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091010-091010-12. doi:10.1115/1.4036230.

This paper presents a new switching antiwindup compensation design to maximize the domain of attraction for a supercavitating vehicle subject to actuator saturation. The dive-plane dynamics of the vehicle are considered. By applying the linear differential inclusion expression of saturated feedbacks, conditions under which the compensator locally stabilizes the closed-loop system are then derived. The design of antiwindup gains on maximizing the system's domain of attraction is finally formulated and solved as an iterative optimization problem with linear matrix inequality constraints. Simulations are conducted for systems with magnitude and rate limits to evaluate the effectiveness of the proposed method.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091011-091011-12. doi:10.1115/1.4036231.
FREE TO VIEW

A run-to-run optimization controller uses a reduced set of measurement parameters, in comparison to more general feedback controllers, to converge to the best control point for a repetitive process. A new run-to-run optimization controller is presented for the scanning fiber device used for image acquisition and display. This controller utilizes very sparse measurements to estimate a system energy measure and updates the input parameterizations iteratively within a feedforward with exact-inversion framework. Analysis, simulation, and experimental investigations on the scanning fiber device demonstrate improved scan accuracy over previous methods and automatic controller adaptation to changing operating temperature. A specific application example and quantitative error analyses are provided of a scanning fiber endoscope that maintains high image quality continuously across a 20 °C temperature rise without interruption of the 56 Hz video.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091012-091012-14. doi:10.1115/1.4036071.

This paper first derives equations of motion of extensible and shearable slender beams with large motions under both deterministic and stochastic external loads. Boundary feedback controllers are then proposed to achieve almost surely globally practically asymptotic stability. The control design, well-posedness, and stability analysis are based on a Lyapunov-type theorem developed for a class of stochastic evolution systems (SESs) in Hilbert space.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091013-091013-10. doi:10.1115/1.4036072.

Vehicle steering comfort is an important issue for steering control of advanced driver assistance systems (ADAS), especially the shared steering control systems. However, it is difficult to be evaluated objectively, that is, usually evaluated subjectively by the driver. This paper aims to develop an objective evaluation method of vehicle steering comfort, which is mainly based on the steering efficiency of the driver estimated by electromyography (EMG). First, the driver steering efficiency, as a key factor reflecting driver's maneuver energetics and some neurological control behaviors, is calculated in two steering conditions based on the EMG. In this process, the subjective evaluation of the vehicle steering comfort is obtained simultaneously else by a test driver. Unlike the traditional steering efficiency calculated from steering gear, the driver steering efficiency does not only partly present the energy consumption of driver itself but also the driver–vehicle interaction. And then, the relation between the steering efficiency and subjective evaluation is analyzed based on both linear regression and spearman correlation analyses. This challenging work investigates the interaction between the quantitative energy consumption and driver's subjective feeling and builds bridge between them. At last, an objective evaluation method of vehicle steering comfort using the steering efficiency is proposed, which provides a selection with quantitative evaluation. The proposed method is helpful to improve the steering control by giving a quantitative index.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091014-091014-10. doi:10.1115/1.4036069.

This paper deals with a new systematic multimodel controller design for nonlinear systems. The design of local controllers based on performance requirements is incorporated with the concept of local models selection as an optimization problem. Gap metric and stability margin are used as measuring tool and operation space dividing criterion, respectively. The developed method provides support to design a simple structured multiple proportional-integral (PI) controller which guarantees both robust stability and time-domain performance specifications. The main advantages of the proposed method are avoiding model redundancy, not needing a priori knowledge about system, having simple structure, and easing the implementation. To evaluate the presented multimodel controller design procedure, three benchmark nonlinear systems are studied. Both simulations and experimental results prove the effectiveness of the proposed method in set point tracking and disturbance rejection.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091015-091015-6. doi:10.1115/1.4036235.

This paper considers the problem of robust output regulation of nonlinear systems in semi strict-feedback form in the presence of model uncertainties and nonvanishing disturbances. In the proposed procedure, two exosystems are considered to generate the disturbance and reference signals. In order to reduce both the conservatism of the control law and the chattering phenomena, a disturbance observer is designed for disturbance estimation instead of assuming the known upper bound for the disturbance. Moreover, a novel sliding surface is designed based on the tracking error to guarantee that the output of the system tracks the output of the exosystem. In this regard, some theorems are given and according to the Lyapunov approach, it is proved that the robust output regulation is guaranteed in the presence of model uncertainties and external disturbances. Finally, in order to show the applicability of the proposed controller, it is applied to the Van der Pol chaotic oscillator. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):091016-091016-10. doi:10.1115/1.4036083.

Drillstring vibration is detrimental to drilling operations. It is crucial to understand the underlying mechanisms to circumvent these vibrations and to help improve drilling performance. This paper presents a six degrees-of-freedom (DOF) finite element method (FEM) model to characterize the drillstring dynamics. In addition, a comprehensive bit-force model is developed and included as a boundary condition to the model, corresponding to the vibrations in axial, lateral, and torsional directions. This bit-force model considers the bottom hole assembly (BHA) eccentricity, mud damping, bit–rock interaction, and their coupling mechanisms. Simulation results have shown good agreement with field observations and experimental data in the literature. The utility of this modeling framework is demonstrated in the paper through case studies for normal operation, stick–slip vibration, and whirl vibration.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Dyn. Sys., Meas., Control. 2017;139(9):094501-094501-6. doi:10.1115/1.4036029.

Networked multirobot systems under the coordinated control can perform tasks more effectively than a group of individually operating robots. This paper studies the group regional consensus of networked multirobot systems (formulated by second-order Lagrangian dynamics) having input disturbances under directed acyclic topology. An adaptive control protocol is designed to achieve group regional consensus of the networked Lagrangian systems with parametric uncertainties for both leader and leaderless cases. Sufficient conditions are established to guarantee group regional consensus for any prior given desired consensus errors. Compared with the existing work, a distinctive feature of the proposed control algorithm is that the stability analysis indicates the global validity of the obtained consensus results. Numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(9):094502-094502-8. doi:10.1115/1.4036073.

Positive real constraints on the closed-loop of linear systems guarantee stable interaction with arbitrary passive environments. Two such methods of $H∞$ optimal controller synthesis subject to a positive real constraint are presented and demonstrated on numerical examples. The first approach is based on an established multi-objective optimal control framework using linear matrix inequalities and is shown to be overly restrictive and ultimately infeasible. The second method employs a sector transformation to substitute the positive real constraint with an equivalent $H∞$ constraint. In two examples, this method is shown to be more reliable and displays little change in the achieved $H∞$ norm compared to the unconstrained design, making it a promising tool for passivity-based controller design.

Commentary by Dr. Valentin Fuster